Unit 57 - Electronics Analogue
Contents 1
The Transistor
1
1.1
Transistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1.1
History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1.2
Importance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.1.3
Simplified operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.1.4
Comparison with vacuum tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
1.1.5
Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
1.1.6
Part numbering standards / specifications . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
1.1.7
Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.1.8
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.1.9
Directory of external websites with datasheets . . . . . . . . . . . . . . . . . . . . . . . . 12
1.1.10 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.1.11 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.1.12 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.2
Bipolar junction transistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.2.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.2.2
Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.2.3
Regions of operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.2.4
History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.2.5
Theory and modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.2.6
Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.2.7
Vulnerabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.2.8
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.2.9
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.2.10 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 1.3
Field-effect transistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 i
ii
CONTENTS 1.3.1
History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.3.2
Basic information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.3.3
More about terminals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.3.4
FET operation
1.3.5
Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.3.6
Types of field-effect transistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
1.3.7
Advantages of FET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.3.8
Disadvantages of FET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.3.9
Uses of FET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.3.10 See also FET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 1.3.11 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 1.3.12 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2 Semiconductor Materials 2.1
34
Silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.1.1
Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.1.2
Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.1.3
Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.1.4
History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.1.5
Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.1.6
Biological role . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.1.7
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.1.8
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.1.9
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.1.10 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.2
2.3
Germanium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.2.1
History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.2.2
Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.2.3
Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.2.4
Applications
2.2.5
Precautions for chemically reactive germanium compounds . . . . . . . . . . . . . . . . . 51
2.2.6
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.2.7
Footnotes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.2.8
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.2.9
External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Gallium arsenide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
CONTENTS
3
iii
2.3.1
Preparation and chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.3.2
Comparison with silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.3.3
Other applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.3.4
Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.3.5
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.3.6
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.3.7
External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Applications 3.1
63
Voltage-controlled oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.1.1
Types of VCO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.1.2
Control of frequency in VCOs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.1.3
Voltage-controlled crystal oscillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.1.4
VCO design and circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.1.5
Applications
3.1.6
Voltage-controlled crystal oscillator as a clock generator . . . . . . . . . . . . . . . . . . . 66
3.1.7
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.1.8
Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.1.9
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.1.10 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.2
3.3
Frequency-shift keying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.2.1
Implementations of FSK Modems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.2.2
Other forms of FSK
3.2.3
Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.2.4
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.2.5
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.2.6
External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.3.1
Figures of merit
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.3.2
Amplifier types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.3.3
Classification of amplifier stages and systems
3.3.4
Power amplifier classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.3.5
Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.3.6
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.3.7
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.3.8
External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
. . . . . . . . . . . . . . . . . . . . . . . . 73
iv
CONTENTS
4 Background Theory 4.1
4.2
89
Electron hole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.1.1
Solid-state physics
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.1.2
Holes in quantum chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.1.3
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.1.4
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
P–n junction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.2.1
Properties of a p–n junction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.2.2
Equilibrium (zero bias) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.2.3
Forward bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.2.4
Reverse bias
4.2.5
Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.2.6
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.2.7
Non-rectifying junctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.2.8
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.2.9
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.2.10 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4.2.11 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4.3
Bipolar transistor biasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4.3.1
Bias circuit requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.3.2
Types of bias circuit for Class A amplifiers
4.3.3
Class B and AB amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.3.4
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.3.5
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.3.6
Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.3.7
External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5 Common Integrated Circuits 5.1
. . . . . . . . . . . . . . . . . . . . . . . . . 97
104
555 timer IC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.1.1
Design
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.1.2
Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.1.3
Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.1.4
Example applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.1.5
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.1.6
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.1.7
Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
CONTENTS 5.1.8 5.2
v External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Operational amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 5.2.1
Circuit notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.2.2
Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.2.3
Op-amp characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.2.4
Internal circuitry of 741-type op-amp . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.2.5
Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5.2.6
Applications
5.2.7
Historical timeline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.2.8
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
5.2.9
Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5.2.10 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 5.2.11 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 5.2.12 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 5.3
Phase-locked loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 5.3.1
Practical analogies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
5.3.2
History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
5.3.3
Structure and function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
5.3.4
Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
5.3.5
Block diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
5.3.6
Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
5.3.7
Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
5.3.8
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
5.3.9
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
5.3.10 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 5.4
Voltage regulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 5.4.1
Measures of regulator quality
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
5.4.2
Electronic voltage regulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
5.4.3
Electromechanical regulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.4.4
Automatic voltage regulator
5.4.5
AC voltage stabilizers
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
5.4.6
DC voltage stabilizers
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
5.4.7
Active regulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
5.4.8
Example linear regulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
5.4.9
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
vi
CONTENTS 5.4.10 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 5.4.11 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 5.5
Comparator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 5.5.1
Differential Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
5.5.2
Op-amp voltage comparator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
5.5.3
Working
5.5.4
Key specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
5.5.5
Applications
5.5.6
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
5.5.7
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
5.5.8
External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
6 Sensors 6.1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
151
Thermistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 6.1.1
Basic operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
6.1.2
Steinhart–Hart equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
6.1.3
B or β parameter equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
6.1.4
Conduction model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
6.1.5
Self-heating effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
6.1.6
Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
6.1.7
History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
6.1.8
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
6.1.9
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.1.10 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 6.2
6.3
Photodiode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 6.2.1
Principle of operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.2.2
Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
6.2.3
Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
6.2.4
Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
6.2.5
Photodiode array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
6.2.6
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
6.2.7
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
6.2.8
External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
Photoresistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 6.3.1
Design considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
6.3.2
Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
CONTENTS
6.4
6.3.3
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
6.3.4
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
6.3.5
External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
Analogue switch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 6.4.1
7
vii
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
The Decibel 7.1
163
Decibel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 7.1.1
History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
7.1.2
Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
7.1.3
Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
7.1.4
Advantages and disadvantages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
7.1.5
Uses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
7.1.6
Suffixes and reference values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
7.1.7
Related units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
7.1.8
Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
7.1.9
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
7.1.10 Notes and references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 7.1.11 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 7.2
7.3
Noise (electronics) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 7.2.1
Noise types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
7.2.2
Coupled noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
7.2.3
Quantification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
7.2.4
Dither . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
7.2.5
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
7.2.6
Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
7.2.7
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
7.2.8
Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
7.2.9
External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
Switched capacitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 7.3.1
The switched capacitor resistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
7.3.2
The Parasitic Sensitive Integrator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
7.3.3
The Parasitic Insensitive Integrator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
7.3.4
The Multiplying Digital to Analog Converter
7.3.5
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
7.3.6
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
. . . . . . . . . . . . . . . . . . . . . . . . 180
viii
CONTENTS 7.4
7.5
H bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 7.4.1
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
7.4.2
Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
7.4.3
Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
7.4.4
Operation as an inverter
7.4.5
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
7.4.6
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
7.4.7
External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
Hall effect sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 7.5.1
Hall probe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
7.5.2
Working principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
7.5.3
Materials for Hall effect sensors
7.5.4
Signal processing and interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
7.5.5
Advantages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
7.5.6
Disadvantages
7.5.7
Applications
7.5.8
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
7.5.9
Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
8.2
8.3
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
8 Filters 8.1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
187
Low-pass filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 8.1.1
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
8.1.2
Ideal and real filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
8.1.3
Continuous-time low-pass filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
8.1.4
Electronic low-pass filters
8.1.5
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
8.1.6
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
8.1.7
External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
High-pass filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 8.2.1
First-order continuous-time implementation . . . . . . . . . . . . . . . . . . . . . . . . . 192
8.2.2
Discrete-time realization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
8.2.3
Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
8.2.4
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
8.2.5
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
8.2.6
External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
Band-pass filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
CONTENTS
9
ix
8.3.1
Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
8.3.2
Q-factor
8.3.3
Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
8.3.4
See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
8.3.5
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
8.3.6
External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
Text and image sources, contributors, and licenses
198
9.1
Text . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
9.2
Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
9.3
Content license . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
Chapter 1
The Transistor 1.1 Transistor
changes the current through another pair of terminals. Because the controlled (output) power can be higher than the controlling (input) power, a transistor can amplify a For other uses, see Transistor (disambiguation). signal. Today, some transistors are packaged individuA transistor is a semiconductor device used to amplify ally, but many more are found embedded in integrated circuits. The transistor is the fundamental building block of modern electronic devices, and is ubiquitous in modern electronic systems. Following its development in 1947 by American physicists John Bardeen, Walter Brattain, and William Shockley, the transistor revolutionized the field of electronics, and paved the way for smaller and cheaper radios, calculators, and computers, among other things. The transistor is on the list of IEEE milestones in electronics, and the inventors were jointly awarded the 1956 Nobel Prize in Physics for their achievement.
1.1.1 History Main article: History of the transistor The thermionic triode, a vacuum tube invented in 1907, propelled the electronics age forward, enabling amplified radio technology and long-distance telephony. The triode, however, was a fragile device that consumed a lot of power. Physicist Julius Edgar Lilienfeld filed a patent for a field-effect transistor (FET) in Canada in 1925, which was intended to be a solid-state replacement for the triode.[1][2] Lilienfeld also filed identical patents in the United States in 1926[3] and 1928.[4][5] However, Lilienfeld did not publish any research articles about his devices nor did his patents cite any specific examples of a working prototype. Because the production of high-quality semiconductor materials was still decades away, Lilienfeld’s solid-state amplifier ideas would not have found practical use in the 1920s and 1930s, even if such a device
Assorted discrete transistors. Packages in order from top to bottom: TO-3, TO-126, TO-92, SOT-23
and switch electronic signals and electrical power. It is composed of semiconductor material with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor’s terminals 1
2
CHAPTER 1. THE TRANSISTOR sresistance.[9][10][11] According to Lillian Hoddeson and Vicki Daitch, authors of a biography of John Bardeen, Shockley had proposed that Bell Labs’ first patent for a transistor should be based on the field-effect and that he be named as the inventor. Having unearthed Lilienfeld’s patents that went into obscurity years earlier, lawyers at Bell Labs advised against Shockley’s proposal because the idea of a field-effect transistor that used an electric field as a “grid” was not new. Instead, what Bardeen, Brattain, and Shockley invented in 1947 was the first point-contact transistor.[6] In acknowledgement of this accomplishment, Shockley, Bardeen, and Brattain were jointly awarded the 1956 Nobel Prize in Physics “for their researches on semiconductors and their discovery of the transistor effect.”[12]
In 1948, the point-contact transistor was independently invented by German physicists Herbert Mataré and Heinrich Welker while working at the Compagnie des Freins et Signaux, a Westinghouse subsidiary located had been built.[6] In 1934, German inventor Oskar Heil in Paris. Mataré had previous experience in developpatented a similar device.[7] ing crystal rectifiers from silicon and germanium in the German radar effort during World War II. Using this knowledge, he began researching the phenomenon of extquotedblinterference extquotedbl in 1947. By witnessing currents flowing through point-contacts, similar to what Bardeen and Brattain had accomplished earlier in December 1947, Mataré by June 1948, was able to produce consistent results by using samples of germanium produced by Welker. Realizing that Bell Labs’ scientists had already invented the transistor before them, the company rushed to get its “transistron” into production for amplified use in France’s telephone network.[13] A replica of the first working transistor.
John Bardeen, William Shockley and Walter Brattain at Bell Labs, 1948.
From November 17, 1947 to December 23, 1947, John Bardeen and Walter Brattain at AT&T's Bell Labs in the United States, performed experiments and observed that when two gold point contacts were applied to a crystal of germanium, a signal was produced with the output power greater than the input.[8] Solid State Physics Group leader William Shockley saw the potential in this, and over the next few months worked to greatly expand the knowledge of semiconductors. The term transistor was coined by John R. Pierce as a portmanteau of the term tran-
The first high-frequency transistor was the surface-barrier germanium transistor developed by Philco in 1953, capable of operating up to 60 MHz.[14] These were made by etching depressions into an N-type germanium base from both sides with jets of Indium(III) sulfate until it was a few ten-thousandths of an inch thick. Indium electroplated into the depressions formed the collector and emitter.[15][16] The first all-transistor car radio, which was produced in 1955 by Chrysler and Philco, used these transistors in its circuitry and also they were the first suitable for high-speed computers.[17][18][19][20] The first working silicon transistor was developed at Bell Labs on January 26, 1954 by Morris Tanenbaum.[21] The first commercial silicon transistor was produced by Texas Instruments in 1954.[22] This was the work of Gordon Teal, an expert in growing crystals of high purity, who
1.1. TRANSISTOR
3
A Darlington transistor opened up so the actual transistor chip (the small square) can be seen inside. A Darlington transistor is effectively two transistors on the same chip. One transistor is much larger than the other, but both are large in comparison to transistors in large-scale integration because this particular example is intended for power applications.
Philco surface-barrier transistor developed and produced in 1953
built in 2002 ... for [each] man, woman, and child on Earth.”[29]
The transistor’s low cost, flexibility, and reliability have made it a ubiquitous device. Transistorized mechatronic had previously worked at Bell Labs.[23] The first MOS circuits have replaced electromechanical devices in contransistor actually built was by Kahng and Atalla at Bell trolling appliances and machinery. It is often easier and Labs in 1960.[24] cheaper to use a standard microcontroller and write a computer program to carry out a control function than to design an equivalent mechanical control function.
1.1.2
Importance
The transistor is the key active component in practically all modern electronics. Many consider it to be one of the greatest inventions of the 20th century.[25] Its importance in today’s society rests on its ability to be mass-produced using a highly automated process (semiconductor device fabrication) that achieves astonishingly low per-transistor costs. The invention of the first transistor at Bell Labs was named an IEEE Milestone in 2009.[26] Although several companies each produce over a billion individually packaged (known as discrete) transistors every year,[27] the vast majority of transistors are now produced in integrated circuits (often shortened to IC, microchips or simply chips), along with diodes, resistors, capacitors and other electronic components, to produce complete electronic circuits. A logic gate consists of up to about twenty transistors whereas an advanced microprocessor, as of 2009, can use as many as 3 billion transistors (MOSFETs).[28] “About 60 million transistors were
1.1.3 Simplified operation The essential usefulness of a transistor comes from its ability to use a small signal applied between one pair of its terminals to control a much larger signal at another pair of terminals. This property is called gain. It can produce a stronger output signal, a voltage or current, that is proportional to a weaker input signal; that is, it can act as an amplifier. Alternatively, the transistor can be used to turn current on or off in a circuit as an electrically controlled switch, where the amount of current is determined by other circuit elements. There are two types of transistors, which have slight differences in how they are used in a circuit. A bipolar transistor has terminals labeled base, collector, and emitter. A small current at the base terminal (that is, flowing between the base and the emitter) can control or switch a much larger current between the collector and emitter
4
CHAPTER 1. THE TRANSISTOR
VCC
IBE
VOUT collector
VIN
base
1k
+6V
ICE
emitter
BJT used as an electronic switch, in grounded-emitter configuration.
A simple circuit diagram to show the labels of a n–p–n bipolar transistor.
terminals. For a field-effect transistor, the terminals are labeled gate, source, and drain, and a voltage at the gate can control a current between source and drain.
cause current is flowing from collector to emitter freely. When saturated, the switch is said to be on.[30] Providing sufficient base drive current is a key problem in the use of bipolar transistors as switches. The transistor provides current gain, allowing a relatively large current in the collector to be switched by a much smaller current into the base terminal. The ratio of these currents varies depending on the type of transistor, and even for a particular type, varies depending on the collector current. In the example light-switch circuit shown, the resistor is chosen to provide enough base current to ensure the transistor will be saturated.
The image to the right represents a typical bipolar transistor in a circuit. Charge will flow between emitter and collector terminals depending on the current in the base. Because internally the base and emitter connections behave like a semiconductor diode, a voltage drop develops between base and emitter while the base current exists. In any switching circuit, values of input voltage would be The amount of this voltage depends on the material the chosen such that the output is either completely off,[31] or completely on. The transistor is acting as a switch, and transistor is made from, and is referred to as VBE. this type of operation is common in digital circuits where only “on” and “off” values are relevant. Transistor as a switch
Transistor as an amplifier Transistors are commonly used as electronic switches, both for high-power applications such as switched-mode The common-emitter amplifier is designed so that a small power supplies and for low-power applications such as change in voltage (Vᵢ ) changes the small current through logic gates. the base of the transistor; the transistor’s current amplifiIn a grounded-emitter transistor circuit, such as the light- cation combined with the properties of the circuit mean switch circuit shown, as the base voltage rises, the emitter that small swings in Vᵢ produce large changes in Vₒᵤ . and collector currents rise exponentially. The collector voltage drops because of reduced resistance from collec- Various configurations of single transistor amplifier are tor to emitter. If the voltage difference between the col- possible, with some providing current gain, some voltage lector and emitter were zero (or near zero), the collector gain, and some both. current would be limited only by the load resistance (light From mobile phones to televisions, vast numbers of prodbulb) and the supply voltage. This is called saturation be- ucts include amplifiers for sound reproduction, radio
1.1. TRANSISTOR
5 to a simple electrical heating element, much like a light bulb filament.
V+
• Small size and minimal weight, allowing the development of miniaturized electronic devices.
R1 Vin
B
Cin
RC C
Vout Cout
E
R2
RE
• Low operating voltages compatible with batteries of only a few cells. • No warm-up period for cathode heaters required after power application. • Lower power dissipation and generally greater energy efficiency. • Higher reliability and greater physical ruggedness.
CE
Amplifier circuit, common-emitter configuration with a voltagedivider bias circuit.
• Extremely long life. Some transistorized devices have been in service for more than 50 years. • Complementary devices available, facilitating the design of complementary-symmetry circuits, something not possible with vacuum tubes. • Greatly reduced sensitivity to mechanical shock and vibration, thus reducing the problem of microphonics in sensitive applications, such as audio.
transmission, and signal processing. The first discretetransistor audio amplifiers barely supplied a few hundred milliwatts, but power and audio fidelity gradually Limitations increased as better transistors became available and am• Silicon transistors can age and fail.[32] plifier architecture evolved. Modern transistor audio amplifiers of up to a few hundred watts are common and relatively inexpensive.
1.1.4
Comparison with vacuum tubes
Prior to the development of transistors, vacuum (electron) tubes (or in the UK “thermionic valves” or just “valves”) were the main active components in electronic equipment. Advantages The key advantages that have allowed transistors to replace their vacuum tube predecessors in most applications are • No power consumption by a cathode heater; the characteristic orange glow of vacuum tubes is due
• High-power, high-frequency operation, such as that used in over-the-air television broadcasting, is better achieved in vacuum tubes due to improved electron mobility in a vacuum. • Solid-state devices are more vulnerable to electrostatic discharge in handling and operation • A vacuum tube momentarily overloaded will just get a little hotter; solid-state devices have less mass to absorb the heat due to overloads, in proportion to their rating • Sensitivity to radiation and cosmic rays (special radiation-hardened chips are used for spacecraft devices). • Vacuum tubes create a distortion, the so-called tube sound, that some people find to be more tolerable to the ear.[33]
6
1.1.5 Types BJT and JFET symbols JFET and IGFET symbols Transistors are categorized by
CHAPTER 1. THE TRANSISTOR Bipolar transistors are so named because they conduct by using both majority and minority carriers. The bipolar junction transistor, the first type of transistor to be mass-produced, is a combination of two junction diodes, and is formed of either a thin layer of p-type semiconductor sandwiched between two n-type semiconductors (an n–p–n transistor), or a thin layer of n-type semiconductor sandwiched between two p-type semiconductors (a p–n–p transistor). This construction produces two p–n junctions: a base–emitter junction and a base–collector junction, separated by a thin region of semiconductor known as the base region (two junction diodes wired together without sharing an intervening semiconducting region will not make a transistor).
• Semiconductor material (date first used): the metalloids germanium (1947) and silicon (1954)— in amorphous, polycrystalline and monocrystalline form; the compounds gallium arsenide (1966) and silicon carbide (1997), the alloy silicon-germanium (1989), the allotrope of carbon graphene (research ongoing since 2004), etc.—see Semiconductor maBJTs have three terminals, corresponding to the three terial layers of semiconductor—an emitter, a base, and a col• Structure: BJT, JFET, IGFET (MOSFET), lector. They are useful in amplifiers because the currents at the emitter and collector are controllable by a insulated-gate bipolar transistor, “other types” relatively small base current.”[35] In an n–p–n transistor • Electrical polarity (positive and negative): n–p–n, operating in the active region, the emitter–base junction is forward biased (electrons and holes recombine at the p–n–p (BJTs); n-channel, p-channel (FETs) junction), and electrons are injected into the base re• Maximum power rating: low, medium, high gion. Because the base is narrow, most of these electrons will diffuse into the reverse-biased (electrons and • Maximum operating frequency: low, medium, high, holes are formed at, and move away from the junction) radio (RF), microwave frequency (the maximum ef- base–collector junction and be swept into the collector; fective frequency of a transistor is denoted by the perhaps one-hundredth of the electrons will recombine in term fT , an abbreviation for transition frequency— the base, which is the dominant mechanism in the base the frequency of transition is the frequency at which current. By controlling the number of electrons that can the transistor yields unity gain) leave the base, the number of electrons entering the collector can be controlled.[35] Collector current is approx• Application: switch, general purpose, audio, high imately β (common-emitter current gain) times the base voltage, super-beta, matched pair current. It is typically greater than 100 for small-signal transistors but can be smaller in transistors designed for • Physical packaging: through-hole metal, throughhigh-power applications. hole plastic, surface mount, ball grid array, power Unlike the field-effect transistor (see below), the BJT is a modules—see Packaging low–input-impedance device. Also, as the base–emitter • Amplification factor h ₑ, βF (transistor beta)[34] or voltage (Vbe) is increased the base–emitter current and g (transconductance). hence the collector–emitter current (Ice) increase exponentially according to the Shockley diode model and the Thus, a particular transistor may be described as silicon, Ebers-Moll model. Because of this exponential relationsurface-mount, BJT, n–p–n, low-power, high-frequency ship, the BJT has a higher transconductance than the FET. switch. Bipolar junction transistor (BJT) Main article: Bipolar junction transistor
Bipolar transistors can be made to conduct by exposure to light, because absorption of photons in the base region generates a photocurrent that acts as a base current; the collector current is approximately β times the photocurrent. Devices designed for this purpose have
1.1. TRANSISTOR
7
a transparent window in the package and are called metal–semiconductor junction. These, and the HEMTs phototransistors. (high-electron-mobility transistors, or HFETs), in which a two-dimensional electron gas with very high carrier mobility is used for charge transport, are especially suitable Field-effect transistor (FET) for use at very high frequencies (microwave frequencies; several GHz). Main articles: Field-effect transistor, MOSFET and FETs are further divided into depletion-mode and JFET enhancement-mode types, depending on whether the channel is turned on or off with zero gate-to-source voltThe field-effect transistor, sometimes called a unipolar age. For enhancement mode, the channel is off at zero transistor, uses either electrons (in n-channel FET) or bias, and a gate potential can “enhance” the conduction. holes (in p-channel FET) for conduction. The four termi- For the depletion mode, the channel is on at zero bias, and nals of the FET are named source, gate, drain, and body a gate potential (of the opposite polarity) can “deplete” (substrate). On most FETs, the body is connected to the the channel, reducing conduction. For either mode, a source inside the package, and this will be assumed for more positive gate voltage corresponds to a higher current the following description. for n-channel devices and a lower current for p-channel In a FET, the drain-to-source current flows via a conduct- devices. Nearly all JFETs are depletion-mode because ing channel that connects the source region to the drain the diode junctions would forward bias and conduct if region. The conductivity is varied by the electric field that they were enhancement-mode devices; most IGFETs are is produced when a voltage is applied between the gate enhancement-mode types. and source terminals; hence the current flowing between the drain and source is controlled by the voltage applied between the gate and source. As the gate–source voltage (Vgs) is increased, the drain–source current (Ids) increases exponentially for Vgs below threshold, and then at a roughly quadratic rate ( Ids ∝ (Vgs −VT )2 ) (where VT is the threshold voltage at which drain current begins)[36] in the extquotedblspace-charge-limited extquotedbl region above threshold. A quadratic behavior is not observed in modern devices, for example, at the 65 nm technology node.[37]
Usage of bipolar and field-effect transistors
The bipolar junction transistor (BJT) was the most commonly used transistor in the 1960s and 70s. Even after MOSFETs became widely available, the BJT remained the transistor of choice for many analog circuits such as amplifiers because of their greater linearity and ease of manufacture. In integrated circuits, the desirable properties of MOSFETs allowed them to capture nearly all market share for digital circuits. Discrete MOSFETs can For low noise at narrow bandwidth the higher input resis- be applied in transistor applications, including analog circuits, voltage regulators, amplifiers, power transmitters tance of the FET is advantageous. and motor drivers. FETs are divided into two families: junction FET (JFET) and insulated gate FET (IGFET). The IGFET is more commonly known as a metal–oxide–semiconductor FET Other transistor types (MOSFET), reflecting its original construction from layers of metal (the gate), oxide (the insulation), and semi- For early bipolar transistors, see Bipolar junction tranconductor. Unlike IGFETs, the JFET gate forms a p–n sistor#Bipolar transistors. diode with the channel which lies between the source and drain. Functionally, this makes the n-channel JFET the solid-state equivalent of the vacuum tube triode which, • Bipolar junction transistor similarly, forms a diode between its grid and cathode. --- Heterojunction bipolar transistor, up to sevAlso, both devices operate in the depletion mode, they eral hundred GHz, common in modern ultraboth have a high input impedance, and they both conduct fast and RF circuits current under the control of an input voltage. --- Schottky transistor Metal–semiconductor FETs (MESFETs) are JFETs in which the reverse biased p–n junction is replaced by a
--- Avalanche transistor
8
CHAPTER 1. THE TRANSISTOR
Transistor symbol drawn on Portuguese pavement in the University of Aveiro.
--- Darlington transistors are two BJTs connected together to provide a high current gain equal to the product of the current gains of the two transistors. --- Insulated-gate bipolar transistors (IGBTs) use a medium-power IGFET, similarly connected to a power BJT, to give a high input impedance. Power diodes are often connected between certain terminals depending on specific use. IGBTs are particularly suitable for heavy-duty industrial applications. The Asea Brown Boveri (ABB) 5SNA2400E170100 illustrates just how far power semiconductor technology has advanced.[38] Intended for three-phase power supplies, this device houses three n–p–n IGBTs in a case measuring 38 by 140 by 190 mm and weighing 1.5 kg. Each IGBT is rated at 1,700 volts and can handle 2,400 amperes. --- Photo transistor --- Multiple-emitter transistor, used in transistor– transistor logic --- Multiple-base transistor, used to amplify verylow-level signals in noisy environments such as the pickup of a record player or radio front ends. Effectively, it is a very large number of transistors in parallel where, at the output, the signal is added constructively, but random noise is added only stochastically.[39] • Field-effect transistor
--- Carbon nanotube field-effect transistor (CNFET) --- JFET, where the gate is insulated by a reversebiased p–n junction --- MESFET, similar to JFET with a Schottky junction instead of a p–n junction ∗ High-electron-mobility transistor (HEMT, HFET, MODFET) --- MOSFET, where the gate is insulated by a shallow layer of insulator --- Inverted-T field-effect transistor (ITFET) --- FinFET, source/drain region shapes fins on the silicon surface. --- FREDFET, fast-reverse epitaxial diode fieldeffect transistor --- Thin-film transistor, in LCDs. --- Organic field-effect transistor (OFET), in which the semiconductor is an organic compound --- Ballistic transistor --- Floating-gate transistor, for non-volatile storage. --- FETs used to sense environment ∗ Ion-sensitive field effect transistor (IFSET), to measure ion concentrations in solution. ∗ EOSFET, electrolyte-oxidesemiconductor field-effect transistor (Neurochip) ∗ DNAFET, deoxyribonucleic acid fieldeffect transistor • Diffusion transistor, formed by diffusing dopants into semiconductor substrate; can be both BJT and FET • Unijunction transistors can be used as simple pulse generators. They comprise a main body of either Ptype or N-type semiconductor with ohmic contacts at each end (terminals Base1 and Base2). A junction with the opposite semiconductor type is formed at a point along the length of the body for the third terminal (Emitter). • Single-electron transistors (SET) consist of a gate island between two tunneling junctions. The tunneling current is controlled by a voltage applied to the gate through a capacitor.[40]
1.1. TRANSISTOR
9
• Nanofluidic transistor, controls the movement standards; in each the alphanumeric prefix provides clues of ions through sub-microscopic, water-filled to type of the device. channels.[41] • Multigate devices --- Tetrode transistor --- Pentode transistor --- Trigate transistors (Prototype by Intel) --- Dual-gate FETs have a single channel with two gates in cascode; a configuration optimized for high-frequency amplifiers, mixers, and oscillators. • Junctionless nanowire transistor (JNT), developed at Tyndall National Institute in Ireland, was the first transistor successfully fabricated without junctions. (Even MOSFETs have junctions, although its gate is electrically insulated from the region the gate controls.) Junctions are difficult and expensive to fabricate, and, because they are a significant source of current leakage, they waste significant power and generate significant waste heat. Eliminating them held the promise of cheaper and denser microchips. The JNT uses a simple nanowire of silicon surrounded by an electrically isolated “wedding ring” that acts to gate the flow of electrons through the wire. This method has been described as akin to squeezing a garden hose to gate the flow of water through the hose. The nanowire is heavily ndoped, making it an excellent conductor. Crucially the gate, comprising silicon, is heavily p-doped; and its presence depletes the underlying silicon nanowire thereby preventing carrier flow past the gate. • Vacuum-channel transistor: In 2012, NASA and the National Nanofab Center in South Korea were reported to have built a prototype vacuum-channel transistor in only 150 nanometers in size, can be manufactured cheaply using standard silicon semiconductor processing, can operate at high speeds even in hostile environments, and could consume just as much power as a standard transistor.[42]
Japanese Industrial Standard (JIS) The JIS-C-7012 specification for transistor part numbers starts with “2S”,[43] e.g. 2SD965, but sometimes the “2S” prefix is not marked on the package – a 2SD965 might only be marked “D965 extquotedbl; a 2SC1815 might be listed by a supplier as simply “C1815”. This series sometimes has suffixes (such as “R”, “O”, “BL”... standing for “Red”, “Orange”, “Blue” etc.) to denote variants, such as tighter hFE (gain) groupings.
European Electronic Component Manufacturers Association (EECA) The Pro Electron standard, the European Electronic Component Manufacturers Association part numbering scheme, begins with two letters: the first gives the semiconductor type (A for germanium, B for silicon, and C for materials like GaAs); the second letter denotes the intended use (A for diode, C for general-purpose transistor, etc.). A 3-digit sequence number (or one letter then 2 digits, for industrial types) follows. With early devices this indicated the case type. Suffixes may be used, with a letter (e.g. “C” often means high hFE, such as in: BC549C[44] ) or other codes may follow to show gain (e.g. BC327-25) or voltage rating (e.g. BUK854-800A[45] ). The more common prefixes are:
Joint Electron (JEDEC)
Devices
Engineering
Council
The JEDEC EIA370 transistor device numbers usually start with “2N”, indicating a three-terminal device (dualgate field-effect transistors are four-terminal devices, so begin with 3N), then a 2, 3 or 4-digit sequential number with no significance as to device properties (although 1.1.6 Part numbering standards / specifi- early devices with low numbers tend to be germanium). For example 2N3055 is a silicon n–p–n power transistor, cations 2N1301 is a p–n–p germanium switching transistor. A The types of some transistors can be parsed from the part letter suffix (such as “A”) is sometimes used to indicate number. There are three major semiconductor naming a newer variant, but rarely gain groupings.
10
CHAPTER 1. THE TRANSISTOR
Proprietary
Semiconductor material
Manufacturers of devices may have their own proprietary numbering system, for example CK722. Since devices are second-sourced, a manufacturer’s prefix (like “MPF” in MPF102, which originally would denote a Motorola FET) now is an unreliable indicator of who made the device. Some proprietary naming schemes adopt parts of other naming schemes, for example a PN2222A is a (possibly Fairchild Semiconductor) 2N2222A in a plastic case (but a PN108 is a plastic version of a BC108, not a 2N108, while the PN100 is unrelated to other xx100 devices).
The first BJTs were made from germanium (Ge). Silicon (Si) types currently predominate but certain advanced microwave and high-performance versions now employ the compound semiconductor material gallium arsenide (GaAs) and the semiconductor alloy silicon germanium (SiGe). Single element semiconductor material (Ge and Si) is described as elemental.
With so many independent naming schemes, and the abbreviation of part numbers when printed on the devices, ambiguity sometimes occurs. For example two different devices may be marked “J176” (one the J176 low-power Junction FET, the other the higher-powered MOSFET 2SJ176).
The density of mobile carriers in the channel of a MOSFET is a function of the electric field forming the channel and of various other phenomena such as the impurity level in the channel. Some impurities, called dopants, are introduced deliberately in making a MOSFET, to control the MOSFET electrical behavior.
As older “through-hole” transistors are given surfacemount packaged counterparts, they tend to be assigned many different part numbers because manufacturers have their own systems to cope with the variety in pinout arrangements and options for dual or matched n–p–n+p–n– p devices in one pack. So even when the original device (such as a 2N3904) may have been assigned by a standards authority, and well known by engineers over the years, the new versions are far from standardized in their naming.
The electron mobility and hole mobility columns show the average speed that electrons and holes diffuse through the semiconductor material with an electric field of 1 volt per meter applied across the material. In general, the higher the electron mobility the faster the transistor can operate. The table indicates that Ge is a better material than Si in this respect. However, Ge has four major shortcomings compared to silicon and gallium arsenide:
Rough parameters for the most common semiconductor materials used to make transistors are given in the table to the right; these parameters will vary with increase in temperature, electric field, impurity level, strain, and sundry Military part numbers sometimes are assigned their own other factors. codes, such as the British Military CV Naming System. The junction forward voltage is the voltage applied to the Manufacturers buying large numbers of similar parts may emitter–base junction of a BJT in order to make the base have them supplied with “house numbers”, identifying conduct a specified current. The current increases exa particular purchasing specification and not necessar- ponentially as the junction forward voltage is increased. ily a device with a standardized registered number. For The values given in the table are typical for a current of example, an HP part 1854,0053 is a (JEDEC) 2N2218 1 mA (the same values apply to semiconductor diodes). transistor[46][47] which is also assigned the CV number: The lower the junction forward voltage the better, as this means that less power is required to “drive” the transisCV7763[48] tor. The junction forward voltage for a given current decreases with increase in temperature. For a typical silicon junction the change is −2.1 mV/°C.[49] In some circuits special compensating elements (sensistors) must be used Naming problems to compensate for such changes.
• Its maximum temperature is limited; • it has relatively high leakage current;
1.1.7 Construction
• it cannot withstand high voltages; • it is less suitable for fabricating integrated circuits.
1.1. TRANSISTOR Because the electron mobility is higher than the hole mobility for all semiconductor materials, a given bipolar n– p–n transistor tends to be swifter than an equivalent p– n–p transistor. GaAs has the highest electron mobility of the three semiconductors. It is for this reason that GaAs is used in high-frequency applications. A relatively recent FET development, the high-electron-mobility transistor (HEMT), has a heterostructure (junction between different semiconductor materials) of aluminium gallium arsenide (AlGaAs)-gallium arsenide (GaAs) which has twice the electron mobility of a GaAs-metal barrier junction. Because of their high speed and low noise, HEMTs are used in satellite receivers working at frequencies around 12 GHz. HEMTs based on gallium nitride and aluminium gallium nitride (AlGaN/GaN HEMTs) provide a still higher electron mobility and are being developed for various applications.
11 through-hole (or leaded), and surface-mount, also known as surface-mount device (SMD). The ball grid array (BGA) is the latest surface-mount package (currently only for large integrated circuits). It has solder “balls” on the underside in place of leads. Because they are smaller and have shorter interconnections, SMDs have better high-frequency characteristics but lower power rating. Transistor packages are made of glass, metal, ceramic, or plastic. The package often dictates the power rating and frequency characteristics. Power transistors have larger packages that can be clamped to heat sinks for enhanced cooling. Additionally, most power transistors have the collector or drain physically connected to the metal enclosure. At the other extreme, some surface-mount microwave transistors are as small as grains of sand.
Often a given transistor type is available in several packages. Transistor packages are mainly standardized, but the assignment of a transistor’s functions to the terminals is not: other transistor types can assign other functions to the package’s terminals. Even for the same transisAl–Si junction refers to the high-speed (aluminum– tor type the terminal assignment can vary (normally indisilicon) metal–semiconductor barrier diode, commonly cated by a suffix letter to the part number, q.e. BC212L known as a Schottky diode. This is included in the ta- and BC212K). ble because some silicon power IGFETs have a parasitic reverse Schottky diode formed between the source and drain as part of the fabrication process. This diode can Flexible transistors Researchers have made several kinds of flexible transistors, including organic field-effect be a nuisance, but sometimes it is used in the circuit. transistors.[50][51][52] Flexible transistors are useful in some kinds of flexible displays and other flexible elecPackaging tronics. Max. junction temperature values represent a cross section taken from various manufacturers’ data sheets. This temperature should not be exceeded or the transistor may be damaged.
See also: Semiconductor package and Chip carrier Discrete transistors are individually packaged transis- 1.1.8
See also
• Band gap • Digital electronics • Moore’s law • Semiconductor device modeling • Transistor count • Transistor model Assorted discrete transistors
tors. Transistors come in many different semiconductor packages (see image). The two main categories are
• Transresistance • Very-large-scale integration
12
CHAPTER 1. THE TRANSISTOR
1.1.9 Directory of external websites with 1.1.10 datasheets • 2N3904/2N3906, BC182/BC212 and BC546/BC556: Ubiquitous, BJT, general-purpose, low-power, complementary pairs. They have plastic cases and cost roughly ten cents U.S. in small quantities, making them popular with hobbyists. • AF107: Germanium, 0.5 watt, 250 MHz p–n–p BJT. • BFP183: Low-power, 8 GHz microwave n–p–n BJT. • LM394: “supermatch pair”, with two n–p–n BJTs on a single substrate. • 2N2219A/2N2905A: BJT, general purpose, medium power, complementary pair. With metal cases they are rated at about one watt. • 2N3055/MJ2955: For years, the n–p–n 2N3055 has been the “standard” power transistor. Its complement, the p–n–p MJ2955 arrived later. These 1 MHz, 15 A, 60 V, 115 W BJTs are used in audiopower amplifiers, power supplies, and control. • 2SC3281/2SA1302: Made by Toshiba, these BJTs have low-distortion characteristics and are used in high-power audio amplifiers. They have been widely counterfeited .
References
[1] Vardalas, John, Twists and Turns in the Development of the Transistor IEEE-USA Today’s Engineer, May 2003. [2] Lilienfeld, Julius Edgar, “Method and apparatus for controlling electric current” U.S. Patent 1,745,175 1930-0128 (filed in Canada 1925-10-22, in US 1926-10-08). [3] “Method And Apparatus For Controlling Electric Currents”. United States Patent and Trademark Office. [4] “Amplifier For Electric Currents”. United States Patent and Trademark Office. [5] “Device For Controlling Electric Current”. United States Patent and Trademark Office. [6] “Twists and Turns in the Development of the Transistor”. Institute of Electrical and Electronics Engineers, Inc. [7] Heil, Oskar, “Improvements in or relating to electrical amplifiers and other control arrangements and devices”, Patent No. GB439457, European Patent Office, filed in Great Britain 1934-03-02, published 1935-12-06 (originally filed in Germany 1934-03-02). [8] “November 17 – December 23, 1947: Invention of the First Transistor”. American Physical Society. [9] Bell Laboratories (1983). S. Millman, ed. A History of Engineering and Science in the Bell System, Physical Science (1925-1980). AT&T Bell Laboratories. p. 102.
[10] David Bodanis (2005). Electric Universe. Crown Publishers, New York. ISBN 0-7394-5670-9.
• BU508: n–p–n, 1500 V power BJT. Designed for television horizontal deflection, its high voltage ca[11] “transistor”. American Heritage Dictionary (3rd ed.). pability also makes it suitable for use in ignition sysBoston: Houghton Mifflin. 1992. tems. [12] “The Nobel Prize in Physics 1956”.
• MJ11012/MJ11015: 30 A, 120 V, 200 W, high power Darlington complementary pair BJTs. Used [13] “1948 - The European Transistor Invention”. Computer History Museum. in audio amplifiers, control, and power switching. • 2N5457/2N5460: JFET (depletion mode), general [14] Proceeding of the IRE, Dec 1953, Author: W.E. Bradley - Philco Corp.,Research Division, Volume 41 issue 12, purpose, low power, complementary pair. pages 1702-1706
• BSP296/BSP171: IGFET (enhancement mode), medium power, near complementary pair. Used for [15] Wall Street Journal, Dec 04 1953, page 4, Article “Philco Claims Its Transistor Outperforms Others Now In Use” logic level conversion and driving power transistors in amplifiers. [16] Electronics magazine, January 1954, Article “Electroplated Transistors Announced”
• IRF3710/IRF5210: IGFET (enhancement mode), 40 A, 100 V, 200 W, near complementary pair. [17] Wall Street Journal, “Chrysler Promises Car Radio With For high-power amplifiers and power switches, esTransistors Instead of Tubes in '56”, April 28th 1955, page 1 pecially in automobiles.
1.1. TRANSISTOR
[18] Los Angeles Times, May 08, 1955, page A20, Article: “Chrysler Announces New Transistor Radio” [19] Philco TechRep Division Bulletin, May–June 1955, Volume 5 Number 3, page 28 [20] Article” Some Recollections of the Philco Transac S2000”, Author: Saul Rosen - Purdue University Computer Science Dept., June 1991, page 2 [21] IEEE Spectrum, The Lost History of the Transistor, Author: Michael Riordan, May 2004, pp 48-49 [22] J. Chelikowski, “Introduction: Silicon in all its Forms”, Silicon: evolution and future of a technology (Editors: P. Siffert, E. F. Krimmel), p.1, Springer, 2004 ISBN 3-54040546-1. [23] Grant McFarland, Microprocessor design: a practical guide from design planning to manufacturing, p.10, McGraw-Hill Professional, 2006 ISBN 0-07-145951-0. [24] W. Heywang, K. H. Zaininger, “Silicon: The Semiconductor Material”, Silicon: evolution and future of a technology (Editors: P. Siffert, E. F. Krimmel), p.36, Springer, 2004 ISBN 3-540-40546-1. [25] Robert W. Price (2004). Roadmap to Entrepreneurial Success. AMACOM Div American Mgmt Assn. p. 42. ISBN 978-0-8144-7190-6. [26] extquotedblMilestones:Invention of the First Transistor at Bell Telephone Laboratories, Inc., 1947”. IEEE Global History Network. IEEE. Retrieved 3 August 2011. [27] FETs/MOSFETs: Smaller apps push up surface-mount supply [28] extquotedblATI and Nvidia face off.” Oct 7, 2009. Retrieved on Feb 2, 2011. [29] Jim Turley. “The Two Percent Solution” 2002. [30] Kaplan, Daniel (2003). Hands-On Electronics. New York: Cambridge University Press. pp. 47–54, 60–61. ISBN 978-0-511-07668-8. [31] apart from a small value due to leakage currents [32] John Keane and Chris H. Kim, “Transistor Aging,” IEEE Spectrum (web feature), April 25, 2011. [33] van der Veen, M. (2005). “Universal system and output transformer for valve amplifiers”. 118th AES Convention, Barcelona, Spain. [34] “Transistor Example”. 071003 bcae1.com
13
[35] Streetman, Ben (1992). Solid State Electronic Devices. Englewood Cliffs, NJ: Prentice-Hall. pp. 301–305. ISBN 0-13-822023-9. [36] Horowitz, Paul; Winfield Hill (1989). The Art of Electronics (2nd ed.). Cambridge University Press. p. 115. ISBN 0-521-37095-7. [37] W. M. C. Sansen (2006). Analog design essentials. New York ; Berlin: Springer. p. §0152, p. 28. ISBN 0-38725746-2. [38] “IGBT Module 5SNA 2400E170100” (PDF). Retrieved 2012-06-30. [39] Zhong Yuan Chang, Willy M. C. Sansen, Low-Noise Wide-Band Amplifiers in Bipolar and CMOS Technologies, page 31, Springer, 1991 ISBN 0792390962. [40] “Single Electron Transistors”. Snow.stanford.edu. Retrieved 2012-06-30. [41] Sanders, Robert (2005-06-28). “Nanofluidic transistor, the basis of future chemical processors”. Berkeley.edu. Retrieved 2012-06-30. [42] The return of the vacuum tube? [43] “Clive TEC Transistors Japanese Industrial Standards”. Clivetec.0catch.com. Retrieved 2012-06-30. [44] “Datasheet for BC549, with A,B and C gain groupings” (PDF). Retrieved 2012-06-30. [45] “Datasheet for BUK854-800A (800volt IGBT) extquotedbl (PDF). Retrieved 2012-06-30. [46] “Richard Freeman’s HP Part numbers Crossreference”. Hpmuseum.org. Retrieved 2012-06-30. [47] Transistor–Diode Cross Reference – H.P. Part Numbers to JEDEC (pdf) [48] “CV Device Cross-reference by Andy Lake”. Qsl.net. Retrieved 2012-06-30. [49] A.S. Sedra and K.C. Smith (2004). Microelectronic circuits (Fifth ed.). New York: Oxford University Press. pp. 397 and Figure 5.17. ISBN 0-19-514251-9. [50] Jhonathan P. Rojas, Galo A. Torres Sevilla, and Muhammad M. Hussain. “Can We Build a Truly High Performance Computer Which is Flexible and Transparent? extquotedbl. [51] Kan Zhang, Jung-Hun Seo1, Weidong Zhou and Zhenqiang Ma. “Fast flexible electronics using transferrable silicon nanomembranes”. 2012. [52] Lisa Zyga. “Carbon nanotube transistors could lead to inexpensive, flexible electronics”. 2011.
14
CHAPTER 1. THE TRANSISTOR
1.1.11 Further reading • Amos S W & James M R (1999). Principles of Transistor Circuits. Butterworth-Heinemann. ISBN 0-7506-4427-3. • Bacon, W. Stevenson (1968). “The Transistor’s 20th Anniversary: How Germanium And A Bit of Wire Changed The World”. Bonnier Corp.: Popular Science, retrieved from Google Books 2009-0322 (Bonnier Corporation) 192 (6): 80–84. ISSN 0161-7370. • Horowitz, Paul & Hill, Winfield (1989). The Art of Electronics. Cambridge University Press. ISBN 0521-37095-7. • Riordan, Michael & Hoddeson, Lillian (1998). Crystal Fire. W.W Norton & Company Limited. ISBN 0-393-31851-6. The invention of the transistor & the birth of the information age • Warnes, Lionel (1998). Analogue and Digital Electronics. Macmillan Press Ltd. ISBN 0-333-658205. • “Herbert F. Mataré, An Inventor of the Transistor has his moment”. The New York Times. 24 February 2003.
• BBC: Building the digital age photo history of transistors • The Bell Systems Memorial on Transistors • IEEE Global History Network, The Transistor and Portable Electronics. All about the history of transistors and integrated circuits. • Transistorized. Historical and technical information from the Public Broadcasting Service • This Month in Physics History: November 17 to December 23, 1947: Invention of the First Transistor. From the American Physical Society • 50 Years of the Transistor. From Science Friday, December 12, 1997 • Charts showing many characteristics and giving direct access to most datasheets for 2N, 2SA, 2SB. 2SC, 2SD, 2SH-K, and other numbers. • Common transistor pinouts • Large table of transistor characteristics
1.2 Bipolar junction transistor
• Michael Riordan (2005). “How Europe Missed the Transistor”. IEEE Spectrum 42 (11): 52–57. “Junction transistor” redirects here. For other uses, see Junction transistor (disambiguation). doi:10.1109/MSPEC.2005.1526906. BJT redirects here. For the Japanese language profi• C. D. Renmore (1980). Silicon Chips and You. ciency test, see Business Japanese Proficiency Test. Schematic symbols for ISBN 0-8253-0022-3. PNP- and NPN-type • Wiley-IEEE Press. Complete Guide to Semiconduc- BJTs. tor Devices, 2nd Edition. A bipolar junction transistor (BJT or bipolar transistor) is a type of transistor that relies on the contact of two types of semiconductor for its operation. BJTs can be The CK722 Museum. Website devoted to the “classic” used as amplifiers, switches, or in oscillators. BJTs can be found either as individual discrete components, or in hobbyist germanium transistor large numbers as parts of integrated circuits. Jerry Russell’s Transistor Cross Reference Database. Bipolar transistors are so named because their operaThe DatasheetArchive. Searchable database of tran- tion involves both electrons and holes. These two kinds of charge carriers are characteristic of the two kinds sistor specifications and datasheets. of doped semiconductor material; electrons are majority The Transistor Educational content from Nobel- charge carriers in n-type semiconductors, whereas holes prize.org are majority charge carriers in p-type semiconductors. In
1.1.12 External links • • • •
1.2. BIPOLAR JUNCTION TRANSISTOR
15
contrast, unipolar transistors such as the field-effect tran- The electrons in the base are called minority carriers besistors have only one kind of charge carrier. cause the base is doped p-type, which makes holes the majority carrier in the base. Charge flow in a BJT is due to diffusion of charge carriers across a junction between two regions of different charge concentrations. The regions of a BJT are called emitter, collector, and base.[note 1] A discrete transistor has three leads for connection to these regions. Typically, the emitter region is heavily doped compared to the other two layers, whereas the majority charge carrier concentrations in base and collector layers are about the same. By design, most of the BJT collector current is due to the flow of charges injected from a high-concentration emitter into the base where there are minority carriers that diffuse toward the collector, and so BJTs are classified as minority-carrier devices.
1.2.1
Introduction n++ E
iE
iE
iEn iEp
n+
p
iC
electrons holes iB1
iB2
recombination
Voltage, current, and charge control
C iC
B vBE
To minimize the percentage of carriers that recombine before reaching the collector–base junction, the transistor’s base region must be thin enough that carriers can diffuse across it in much less time than the semiconductor’s minority carrier lifetime. In particular, the thickness of the base must be much less than the diffusion length of the electrons. The collector–base junction is reversebiased, and so little electron injection occurs from the collector to the base, but electrons that diffuse through the base towards the collector are swept into the collector by the electric field in the depletion region of the collector–base junction. The thin shared base and asymmetric collector–emitter doping is what differentiates a bipolar transistor from two separate and oppositely biased diodes connected in series.
iB
vCB
NPN BJT with forward-biased E–B junction and reverse-biased B–C junction
The collector–emitter current can be viewed as being controlled by the base–emitter current (current control), or by the base–emitter voltage (voltage control). These views are related by the current–voltage relation of the base–emitter junction, which is just the usual exponential current–voltage curve of a p-n junction (diode).[1] The physical explanation for collector current is the amount of minority carriers in the base region.[1][2][3] Due to low level injection (in which there are much fewer excess carriers than normal majority carriers) the ambipolar transport rates (in which the excess majority and minority carriers flow at the same rate) is in effect determined by the excess minority carriers.
BJTs come in two types, or polarities, known as PNP and NPN based on the doping types of the three main terminal regions. An NPN transistor comprises two semiconductor junctions that share a thin p-doped anode region, and a PNP transistor comprises two semiconducDetailed transistor models of transistor action, such as tor junctions that share a thin n-doped cathode region. In typical operation, the base–emitter junction is forward the Gummel–Poon model, account for the distribution biased, which means that the p-doped side of the junc- of this charge[4]explicitly to explain transistor behaviour tion is at a more positive potential than the n-doped side, more exactly. The charge-control view easily handles and the base–collector junction is reverse biased. In an phototransistors, where minority carriers in the base reNPN transistor, when positive bias is applied to the base– gion are created by the absorption of photons, and hanemitter junction, the equilibrium is disturbed between dles the dynamics of turn-off, or recovery time, which the thermally generated carriers and the repelling electric depends on charge in the base region recombining. Howfield of the n-doped emitter depletion region. This allows ever, because base charge is not a signal that is visible at thermally excited electrons to inject from the emitter into the terminals, the current- and voltage-control views are the base region. These electrons diffuse through the base generally used in circuit design and analysis. from the region of high concentration near the emitter to- In analog circuit design, the current-control view is somewards the region of low concentration near the collector. times used because it is approximately linear. That is, the
16 collector current is approximately βF times the base current. Some basic circuits can be designed by assuming that the emitter–base voltage is approximately constant, and that collector current is beta times the base current. However, to accurately and reliably design production BJT circuits, the voltage-control (for example, Ebers– Moll) model is required.[1] The voltage-control model requires an exponential function to be taken into account, but when it is linearized such that the transistor can be modelled as a transconductance, as in the Ebers–Moll model, design for circuits such as differential amplifiers again becomes a mostly linear problem, so the voltagecontrol view is often preferred. For translinear circuits, in which the exponential I–V curve is key to the operation, the transistors are usually modelled as voltage controlled with transconductance proportional to collector current. In general, transistor level circuit design is performed using SPICE or a comparable analog circuit simulator, so model complexity is usually not of much concern to the designer.
CHAPTER 1. THE TRANSISTOR than unity due to recombination of charge carriers as they cross the base region. Alpha and beta are more precisely related by the following identities (NPN transistor):
αF =
IC IE
IC IB αF βF βF = ⇐⇒ αF = 1 − αF βF + 1 βF =
1.2.2
Structure
E
B
C
n p
Turn-on, turn-off, and storage delay
n
The Bipolar transistor exhibits a few delay characteristics when turning on and off. Most transistors, and especially power transistors, exhibit long base-storage times Simplified cross section of a planar NPN bipolar junction tranthat limit maximum frequency of operation in switching sistor applications. One method for reducing this storage time is by using a Baker clamp. A BJT consists of three differently doped semiconductor regions, the emitter region, the base region and the collector region. These regions are, respectively, p type, n type Transistor parameters: alpha (α) and beta (β) and p type in a PNP transistor, and n type, p type and n type in an NPN transistor. Each semiconductor region The proportion of electrons able to cross the base and is connected to a terminal, appropriately labeled: emitter reach the collector is a measure of the BJT efficiency. (E), base (B) and collector (C). The heavy doping of the emitter region and light doping of the base region causes many more electrons to be The base is physically located between the emitter and the injected from the emitter into the base than holes to be collector and is made from lightly doped, high resistivinjected from the base into the emitter. The common- ity material. The collector surrounds the emitter region, emitter current gain is represented by βF or hFE; it is ap- making it almost impossible for the electrons injected proximately the ratio of the DC collector current to the into the base region to escape without being collected, DC base current in forward-active region. It is typically thus making the resulting value of α very close to unity, greater than 100 for small-signal transistors but can be and so, giving the transistor a large β. A cross section smaller in transistors designed for high-power applica- view of a BJT indicates that the collector–base junction tions. Another important parameter is the common-base has a much larger area than the emitter–base junction. current gain, αF. The common-base current gain is ap- The bipolar junction transistor, unlike other transistors, is proximately the gain of current from emitter to collec- usually not a symmetrical device. This means that intertor in the forward-active region. This ratio usually has changing the collector and the emitter makes the transisa value close to unity; between 0.98 and 0.998. It is less tor leave the forward active mode and start to operate in
1.2. BIPOLAR JUNCTION TRANSISTOR
17
reverse mode. Because the transistor’s internal structure for very high speed applications (see HBT, below). is usually optimized for forward-mode operation, interchanging the collector and the emitter makes the values of α and β in reverse operation much smaller than those in forward operation; often the α of the reverse mode NPN is lower than 0.5. The lack of symmetry is primarily due to the doping ratios of the emitter and the collector. The emitter is heavily doped, while the collector is lightly doped, allowing a large reverse bias voltage to be applied before the collector–base junction breaks down. The collector–base junction is reverse biased in normal operation. The reason the emitter is heavily doped is to increase the emitter injection efficiency: the ratio of carriers injected by the emitter to those injected by the base. For high current gain, most of the carriers injected into the emitter–base junction must come from the emitter.
B
C E
The symbol of an NPN BJT. The symbol is extquotedblnot pointing in.”
Die of a KSY34 high-frequency NPN transistor, base and emitter connected via bonded wires
The low-performance “lateral” bipolar transistors sometimes used in CMOS processes are sometimes designed symmetrically, that is, with no difference between forward and backward operation. Small changes in the voltage applied across the base– emitter terminals causes the current that flows between the emitter and the collector to change significantly. This effect can be used to amplify the input voltage or current. BJTs can be thought of as voltage-controlled current sources, but are more simply characterized as currentcontrolled current sources, or current amplifiers, due to the low impedance at the base.
NPN is one of the two types of bipolar transistors, consisting of a layer of P-doped semiconductor (the “base”) between two N-doped layers. A small current entering the base is amplified to produce a large collector and emitter current. That is, when there is a positive potential difference measured from the emitter of an NPN transistor to its base (i.e., when the base is high relative to the emitter) as well as positive potential difference measured from the base to the collector, the transistor becomes active. In this “on” state, current flows between the collector and emitter of the transistor. Most of the current is carried by electrons moving from emitter to collector as minority carriers in the P-type base region. To allow for greater current and faster operation, most bipolar transistors used today are NPN because electron mobility is higher than hole mobility.
Early transistors were made from germanium but most A mnemonic device for the NPN transistor symbol is exmodern BJTs are made from silicon. A significant minor- tquotedblnot pointing in extquotedbl, based on the arrows ity are also now made from gallium arsenide, especially in the symbol and the letters in the name.[5]
18
B
CHAPTER 1. THE TRANSISTOR
E
ΔφG
Δφn n
p Δφp
C
n
Bands in graded heterojunction NPN bipolar transistor. Barriers indicated for electrons to move from emitter to base, and for holes to be injected backward from base to emitter; Also, grading of bandgap in base assists electron transport in base region; Light colors indicate depleted regions
The symbol of a PNP BJT. The symbol extquotedblpoints in proudly.”
rier for holes to inject backward from the base into the emitter, denoted in the figure as Δφ , to be made large, while the barrier for electrons to inject into the base Δφ is made low. This barrier arrangement helps reduce miPNP nority carrier injection from the base when the emitterbase junction is under forward bias, and thus reduces base The other type of BJT is the PNP, consisting of a layer of current and increases emitter injection efficiency. N-doped semiconductor between two layers of P-doped material. A small current leaving the base is amplified The improved injection of carriers into the base allows in the collector output. That is, a PNP transistor is “on” the base to have a higher doping level, resulting in lower resistance to access the base electrode. In the more trawhen its base is pulled low relative to the emitter. ditional BJT, also referred to as homojunction BJT, the The arrows in the NPN and PNP transistor symbols are efficiency of carrier injection from the emitter to the base on the emitter legs and point in the direction of the is primarily determined by the doping ratio between the conventional current flow when the device is in forward emitter and base, which means the base must be lightly active mode. doped to obtain high injection efficiency, making its reA mnemonic device for the PNP transistor symbol is ex- sistance relatively high. In addition, higher doping in the tquotedblpointing in (proudly/permanently) extquotedbl, base can improve figures of merit like the Early voltage based on the arrows in the symbol and the letters in the by lessening base narrowing. name.[6] The grading of composition in the base, for example, by progressively increasing the amount of germanium in a SiGe transistor, causes a gradient in bandgap in the Heterojunction bipolar transistor neutral base, denoted in the figure by ΔφG, providing a The heterojunction bipolar transistor (HBT) is an im- “built-in” field that assists electron transport across the provement of the BJT that can handle signals of very high base. That drift component of transport aids the normal frequencies up to several hundred GHz. It is common in diffusive transport, increasing the frequency response of modern ultrafast circuits, mostly RF systems.[7][8] Het- the transistor by shortening the transit time across the erojunction transistors have different semiconductors for base. the elements of the transistor. Usually the emitter is com- Two commonly used HBTs are silicon–germanium and posed of a larger bandgap material than the base. The fig- aluminum gallium arsenide, though a wide variety of ure shows that this difference in bandgap allows the bar- semiconductors may be used for the HBT structure. HBT
1.2. BIPOLAR JUNCTION TRANSISTOR structures are usually grown by epitaxy techniques like MOCVD and MBE.
1.2.3
Regions of operation
19 charged carriers flowing from emitter to collector). This mode corresponds to a logical “on”, or a closed switch. • Cutoff: In cutoff, biasing conditions opposite of saturation (both junctions reverse biased) are present. There is very little current, which corresponds to a logical “off”, or an open switch. • Avalanche breakdown region The modes of operation can be described in terms of the applied voltages (this description applies to NPN transistors; polarities are reversed for PNP transistors): • Forward-active: base higher than emitter, collector higher than base (in this mode the collector current is proportional to base current by βF ).
The relationship between IC , UCE and IB .
Bipolar transistors have five distinct regions of operation, defined by BJT junction biases.
• Saturation: base higher than emitter, but collector is not higher than base. • Cut-Off: base lower than emitter, but collector is higher than base. It means the transistor is not letting conventional current go through from collector to emitter.
• Forward-active (or simply, active): The base– emitter junction is forward biased and the base– collector junction is reverse biased. Most bipo• Reverse-active: base lower than emitter, collector lar transistors are designed to afford the greatest lower than base: reverse conventional current goes common-emitter current gain, βF, in forward-active through transistor. mode. If this is the case, the collector–emitter current is approximately proportional to the base current, but many times larger, for small base current In terms of junction biasing: ('reverse biased base– variations. collector junction' means Vbc < 0 for NPN, opposite for • Reverse-active (or inverse-active or inverted): By PNP) reversing the biasing conditions of the forwardactive region, a bipolar transistor goes into reverseactive mode. In this mode, the emitter and collector regions switch roles. Because most BJTs are designed to maximize current gain in forward-active mode, the βF in inverted mode is several times smaller (2–3 times for the ordinary germanium transistor). This transistor mode is seldom used, usually being considered only for failsafe conditions and some types of bipolar logic. The reverse bias breakdown voltage to the base may be an order of magnitude lower in this region.
Although these regions are well defined for sufficiently large applied voltage, they overlap somewhat for small (less than a few hundred millivolts) biases. For example, in the typical grounded-emitter configuration of an NPN BJT used as a pulldown switch in digital logic, the “off” state never involves a reverse-biased junction because the base voltage never goes below ground; nevertheless the forward bias is close enough to zero that essentially no current flows, so this end of the forward active region can be regarded as the cutoff region.
Active-mode NPN transistors in circuits • Saturation: With both junctions forward-biased, a BJT is in saturation mode and facilitates high current The diagram shows a schematic representation of an conduction from the emitter to the collector (or the NPN transistor connected to two voltage sources. To other direction in the case of NPN, with negatively make the transistor conduct appreciable current (on the
20
CHAPTER 1. THE TRANSISTOR
IC
n VCE
IB
C
p
B
n
E
VBE
act value (for example see op-amp). The value of this gain for DC signals is referred to as hFE , and the value of this gain for small signals is referred to as hfe . That is, when a small change in the currents occurs, and sufficient time has passed for the new condition to reach a steady state hfe is the ratio of the change in collector current to the change in base current. The symbol β is used for both hFE and hfe .[9] The emitter current is related to VBE exponentially. At room temperature, an increase in VBE by approximately 60 mV increases the emitter current by a factor of 10. Because the base current is approximately proportional to the collector and emitter currents, they vary in the same way. Active-mode PNP transistors in circuits
IE Structure and use of NPN transistor. schematic.
IE
Arrow according to
VEB
order of 1 mA) from C to E, VBE must be above a minimum value sometimes referred to as the cut-in voltage. VCE The cut-in voltage is usually about 650 mV for silicon BJTs at room temperature but can be different depending on the type of transistor and its biasing. This applied voltIB age causes the lower P-N junction to 'turn on', allowing a flow of electrons from the emitter into the base. In active mode, the electric field existing between base and collector (caused by VCE) will cause the majority of these electrons to cross the upper P-N junction into the collector to form the collector current IC. The remainder of the electrons recombine with holes, the majority carriers in the base, making a current through the base connection to form the base current, IB. As shown in the diagram, the emitter current, IE, is the total transistor current, which is the sum of the other terminal currents, (i.e., IE = IB + Structure and use of PNP transistor. IC). In the diagram, the arrows representing current point in the direction of conventional current – the flow of electrons is in the opposite direction of the arrows because electrons carry negative electric charge. In active mode, the ratio of the collector current to the base current is called the DC current gain. This gain is usually 100 or more, but robust circuit designs do not depend on the ex-
p
E
n
B
p
C IC
The diagram shows a schematic representation of a PNP transistor connected to two voltage sources. To make the transistor conduct appreciable current (on the order of 1 mA) from E to C, VEB must be above a minimum value sometimes referred to as the cut-in voltage. The cut-in voltage is usually about 650 mV for silicon BJTs at room temperature but can be different depending on the type of
1.2. BIPOLAR JUNCTION TRANSISTOR transistor and its biasing. This applied voltage causes the upper P-N junction to 'turn-on' allowing a flow of holes from the emitter into the base. In active mode, the electric field existing between the emitter and the collector (caused by VCE ) causes the majority of these holes to cross the lower p-n junction into the collector to form the collector current IC . The remainder of the holes recombine with electrons, the majority carriers in the base, making a current through the base connection to form the base current, IB . As shown in the diagram, the emitter current, IE , is the total transistor current, which is the sum of the other terminal currents (i.e., IE = IB + IC).
21 Germanium transistors The germanium transistor was more common in the 1950s and 1960s, and while it exhibits a lower “cut off” voltage, typically around 0.2 V, making it more suitable for some applications, it also has a greater tendency to exhibit thermal runaway. Early manufacturing techniques Various methods of manufacturing bipolar transistors were developed.[10]
In the diagram, the arrows representing current point in the direction of conventional current – the flow of holes is in the same direction of the arrows because holes carry Bipolar transistors positive electric charge. In active mode, the ratio of the • Point-contact transistor – first transistor ever concollector current to the base current is called the DC curstructed (December 1947), a bipolar transistor, limrent gain. This gain is usually 100 or more, but robust ited commercial use due to high cost and noise. circuit designs do not depend on the exact value. The value of this gain for DC signals is referred to as hFE , --- Tetrode point-contact transistor – Pointand the value of this gain for AC signals is referred to contact transistor having two emitters. It beas hfe . However, when there is no particular frequency came obsolete in the middle 1950s. range of interest, the symbol β is used. • Junction transistors It should also be noted that the emitter current is related --- Grown-junction transistor – first bipolar juncto VEB exponentially. At room temperature, an increase tion transistor made.[11] Invented by William in VEB by approximately 60 mV increases the emitter curShockley at Bell Labs. Invented on June 23, rent by a factor of 10. Because the base current is approx1948.[12] Patent filed on June 26, 1948. imately proportional to the collector and emitter currents, they vary in the same way. --- Alloy-junction transistor – emitter and collector alloy beads fused to base. Developed at General Electric and RCA[13] in 1951. ∗ Micro-alloy transistor (MAT) – high speed type of alloy junction transistor. Developed at Philco.[14] 1.2.4 History ∗ Micro-alloy diffused transistor (MADT) – high speed type of alloy junction tranThe bipolar point-contact transistor was invented in Desistor, speedier than MAT, a diffusedcember 1947 at the Bell Telephone Laboratories by base transistor. Developed at Philco. John Bardeen and Walter Brattain under the direction of ∗ Post-alloy diffused transistor (PADT) – William Shockley. The junction version known as the high speed type of alloy junction transisbipolar junction transistor, invented by Shockley in 1948, tor, speedier than MAT, a diffused-base enjoyed three decades as the device of choice in the detransistor. Developed at Philips. sign of discrete and integrated circuits. Nowadays, the --- Tetrode transistor – high speed variant of use of the BJT has declined in favor of CMOS technology grown-junction transistor[15] or alloy junction in the design of digital integrated circuits. The incidental transistor[16] with two connections to base. low performance BJTs inherent in CMOS ICs, however, --- Surface-barrier transistor – high speed metal are often utilized as bandgap voltage reference, silicon bandgap temperature sensor and to handle electrostatic barrier junction transistor. Developed at Philco[17] in 1953.[18] discharge.
22
CHAPTER 1. THE TRANSISTOR --- Drift-field transistor – high speed bipolar junction transistor. Invented by Herbert Kroemer[19][20] at the Central Bureau of Telecommunications Technology of the German Postal Service, in 1953.
Emitter
diffusion
Base
drift
Collector
Ec
--- Spacistor – circa 1957.
Ef
--- Diffusion transistor – modern type bipolar junction transistor. Prototypes[21] developed at Bell Labs in 1954. ∗ Diffused-base transistor – first implementation of diffusion transistor. ∗ Mesa transistor – Developed at Texas Instruments in 1957. ∗ Planar transistor – the bipolar junction transistor that made mass-produced monolithic integrated circuits possible. Developed by Dr. Jean Hoerni[22] at Fairchild in 1959.
diffusion n-type
depletion region
p-type
depletion region
n-type
Ev
Band diagram for NPN transistor in active mode, showing injection of electrons from emitter to base, and their overshoot into the collector.
Both types of BJT function by letting a small current input to the base control an amplified output from the collector. The result is that the transistor makes a good switch that is controlled by its base input. The BJT also makes a good amplifier, since it can multiply a weak input signal --- Epitaxial transistor – a bipolar junction tran- to about 100 times its original strength. Networks of transistor made using vapor phase deposition. See sistors are used to make powerful amplifiers with many epitaxy. Allows very precise control of doping different applications. In the discussion below, focus is on the NPN bipolar transistor. In the NPN transistor in levels and gradients. what is called active mode, the base–emitter voltage VBE and collector–base voltage VCB are positive, forward biasing the emitter–base junction and reverse-biasing the 1.2.5 Theory and modeling collector–base junction. In the active mode of operation, electrons are injected from the forward biased n-type emitter region into the p-type base where they diffuse as Emitter Base Collector depletion depletion minority carriers to the reverse-biased n-type collector n-type region p-type region n-type and are swept away by the electric field in the reversebiased collector–base junction. For a figure describing forward and reverse bias, see semiconductor diodes. Ec Ef
Large-signal models Ev
In 1954 Jewell James Ebers and John L. Moll introduced their mathematical model of transistor currents:[23] Band diagram for NPN transistor at equilibrium.
Ebers–Moll model The DC emitter and collector curTransistors can be thought of as two diodes (P–N junc- rents in active mode are well modeled by an approximations) sharing a common region that minority carriers can tion to the Ebers–Moll model: move through. A PNP BJT will function like two diodes that share an N-type cathode region, and the NPN like ( VBE ) two diodes sharing a P-type anode region. Connecting IE = IES e VT − 1 two diodes with wires will not make a transistor, since minority carriers will not be able to get from one P–N junction to the other through the wire. IC = α F IE
1.2. BIPOLAR JUNCTION TRANSISTOR
αR ICD
αF IED
αR ICD IC
IE E
23
IED B
ICD
IB
C
αF IED
IED B
E
IED
IB
ICD
IB
ICD
C
Approximated Ebers–Moll Model for an NPN transistor in the forward active mode. The collector diode is reverse-biased so ICD is virtually zero. Most of the emitter diode current (αF is nearly 1) is drawn from the collector, providing the amplification of the base current.
• αF is the common base forward short circuit current gain (0.98 to 0.998)
IC
IE E
IC
IE
B
Ebers–Moll Model for an NPN transistor.[24] * IB, IC, IE: base, collector and emitter currents * ICD, IED: collector and emitter diode currents * αF, αR: forward and reverse common-base current gains
αR ICD
αF IED
C
Ebers–Moll Model for a PNP transistor.
IB = (1 − αF ) IE
• IES is the reverse saturation current of the base– emitter diode (on the order of 10−15 to 10−12 amperes) • VBE is the base–emitter voltage • Dn is the diffusion constant for electrons in the ptype base • W is the base width The α and forward β parameters are as described previously. A reverse β is sometimes included in the model.
The base internal current is mainly by diffusion (see The unapproximated Ebers–Moll equations used to describe the three currents in any operating region are given Fick’s law) and below. These equations are based on the transport model for a bipolar junction transistor.[25] qDn nbo VVEB e T Jn (base) = W ( VBE ) VBC ) IS ( VVBC iC = IS e VT − e VT − e T −1 where βR • VT is the thermal voltage kT /q (approximately 26 mV at 300 K ≈ room temperature). • IE is the emitter current • IC is the collector current
) ) IS ( VVBC IS ( VVBE e T −1 + e T −1 βF βR ( VBE ) ) VBC IS ( VVBE iE = IS e VT − e VT + e T −1 βF iB =
where
24
CHAPTER 1. THE TRANSISTOR
• iC is the collector current
Base-width modulation Main article: Early Effect
• iB is the base current
As the collector–base voltage ( VCB = VCE −VBE ) varies, the collector–base depletion region varies in size. An increase in the collector–base voltage, for example, causes • βF is the forward common emitter current gain (20 a greater reverse bias across the collector–base junction, increasing the collector–base depletion region width, and to 500) decreasing the width of the base. This variation in base • βR is the reverse common emitter current gain (0 to width often is called the extquotedblEarly effect extquot20) edbl after its discoverer James M. Early. • iE is the emitter current
• IS is the reverse saturation current (on the order of Narrowing of the base width has two consequences: 10−15 to 10−12 amperes) • There is a lesser chance for recombination within • VT is the thermal voltage (approximately 26 mV at the “smaller” base region. 300 K ≈ room temperature). • The charge gradient is increased across the base, • VBE is the base–emitter voltage and consequently, the current of minority carriers injected across the emitter junction increases. • VBC is the base–collector voltage Both factors increase the collector or “output” current of the transistor in response to an increase in the collector– base voltage.
VCE1 VBE
E
n
B p
Weff
E
n
p VBE
In the forward-active region, the Early effect modifies the collector current ( iC ) and the forward common emitter current gain ( βF ) as given by:
B
n ΔWeff
n
vBE
C
iC = IS e VT
( βF = βF 0
C
depletion regions
VCE2 Top: NPN base width for low collector-base reverse bias; Bottom: narrower NPN base width for large collector-base reverse bias. Hashed regions are depleted regions.
ro =
( ) VCE 1+ VA VCB 1+ VA
)
VA IC
where: • VCE is the collector–emitter voltage • VA is the Early voltage (15 V to 150 V) • βF 0 is forward common-emitter current gain when VCB = 0 V • ro is the output impedance • IC is the collector current
1.2. BIPOLAR JUNCTION TRANSISTOR
25
Punchthrough When the base–collector voltage reaches a certain (device specific) value, the base–collector depletion region boundary meets the base–emitter depletion region boundary. When in this state the transistor effectively has no base. The device thus loses all gain when in this state.
1 ii
io 2 hix
Vi
hrxVo
hfxii
hox Vo
Gummel–Poon charge-control model The Gummel– Poon model[26] is a detailed charge-controlled model of 3 BJT dynamics, which has been adopted and elaborated by others to explain transistor dynamics in greater detail than Generalized h-parameter model of an NPN BJT. the terminal-based models typically do . This model also Replace x with e, b or c for CE, CB and CC topologies respecincludes the dependence of transistor β -values upon the tively. direct current levels in the transistor, which are assumed current-independent in the Ebers–Moll model.[27] and output voltages. This two-port network is particularly suited to BJTs as it lends itself easily to the analysis Small-signal models of circuit behaviour, and may be used to develop further accurate models. As shown, the term “x” in the model rb'c represents a different BJT lead depending on the topology used. For common-emitter mode the various symrbb i C bols take on the specific values as: B i B' c
b
rb'e
• x = 'e' because it is a common-emitter topology
Cc Ce
gmvb'e
gce
E Hybrid-pi model
hybrid-pi model Main article: hybrid-pi model
• Terminal 1 = Base • Terminal 2 = Collector • Terminal 3 = Emitter • iᵢ = Base current (i ) • iₒ = Collector current (i ) • Vᵢ = Base-to-emitter voltage (VBE)
• Vₒ = Collector-to-emitter voltage (VCE) The hybrid-pi model is a popular circuit model used for analyzing the small signal behavior of bipolar junction and field effect transistors. Sometimes it is also called and the h-parameters are given by: Giacoletto model because it was introduced by L.J. Giacoletto in 1969. The model can be quite accurate for low• hᵢₓ = hᵢₑ – The input impedance of the transistor frequency circuits and can easily be adapted for higher (corresponding to the base resistance r ᵢ). frequency circuits with the addition of appropriate inter• hᵣₓ = hᵣₑ – Represents the dependence of the tranelectrode capacitances and other parasitic elements. sistor’s IB–VBE curve on the value of VCE. It is usually very small and is often neglected (assumed h-parameter model Another model commonly used to be zero). to analyze BJT circuits is the extquotedblh-parameter ex• h ₓ = h ₑ – The current-gain of the transistor. This tquotedbl model, closely related to the hybrid-pi model and the y-parameter two-port, but using input current and parameter is often specified as hFE or the DC output voltage as independent variables, rather than input current-gain (βDC) in datasheets.
26 • hₒₓ = 1/hₒₑ – The output impedance of transistor. The parameter hₒₑ usually corresponds to the output admittance of the bipolar transistor and has to be inverted to convert it to an impedance. As shown, the h-parameters have lower-case subscripts and hence signify AC conditions or analyses. For DC conditions they are specified in upper-case. For the CE topology, an approximate h-parameter model is commonly used which further simplifies the circuit analysis. For this the hₒₑ and hᵣₑ parameters are neglected (that is, they are set to infinity and zero, respectively). It should also be noted that the h-parameter model as shown is suited to low-frequency, small-signal analysis. For highfrequency analyses the inter-electrode capacitances that are important at high frequencies must be added.
CHAPTER 1. THE TRANSISTOR • Common emitter • Common base • Common collector Temperature sensors Main article: Silicon bandgap temperature sensor Because of the known temperature and current dependence of the forward-biased base–emitter junction voltage, the BJT can be used to measure temperature by subtracting two voltages at two different bias currents in a known ratio .
Etymology of hFE The 'h' refers to its being an hparameter, a set of parameters named for their origin in a hybrid equivalent circuit model. 'F' is from forward current amplification also called the current gain. 'E' refers to the transistor operating in a common emitter (CE) configuration. Capital letters used in the subscript indicate that hFE refers to a direct current circuit.
Logarithmic converters
1.2.6 Applications
1.2.7
The BJT remains a device that excels in some applications, such as discrete circuit design, due to the very wide selection of BJT types available, and because of its high transconductance and output resistance compared to MOSFETs. The BJT is also the choice for demanding analog circuits, especially for very-high-frequency applications, such as radio-frequency circuits for wireless systems. Bipolar transistors can be combined with MOSFETs in an integrated circuit by using a BiCMOS process of wafer fabrication to create circuits that take advantage of the application strengths of both types of transistor.
Exposure of the transistor to ionizing radiation causes radiation damage. Radiation causes a buildup of 'defects’ in the base region that act as recombination centers. The resulting reduction in minority carrier lifetime causes gradual loss of gain of the transistor.
Because base–emitter voltage varies as the log of the base–emitter and collector–emitter currents, a BJT can also be used to compute logarithms and anti-logarithms. A diode can also perform these nonlinear functions but the transistor provides more circuit flexibility.
Vulnerabilities
Power BJTs are subject to a failure mode called secondary breakdown, in which excessive current and normal imperfections in the silicon die cause portions of the silicon inside the device to become disproportionately hotter than the others. The doped silicon has a negative temperature coefficient, meaning that it conducts more current at higher temperatures. Thus, the hottest part of the die conducts the most current, causing its conductivity Amplifiers to increase, which then causes it to become progressively Main article: Electronic amplifier hotter again, until the device fails internally. The thermal runaway process associated with secondary breakdown, The transistor parameters α and β characterizes the once triggered, occurs almost instantly and may catascurrent gain of the BJT. It is this gain that allow BJTs trophically damage the transistor package. to be used as the building blocks of electronic amplifiers. If the emitter-base junction is reverse biased into avalanche or Zener mode and current flows for a short The three main BJT amplifier topologies are
1.2. BIPOLAR JUNCTION TRANSISTOR
27
period of time, the current gain of the BJT will be per- [10] Third case study – the solid state advent (PDF) manently degraded.
[11] Transistor Museum, Historic Transistor Photo Gallery, Bell Labs Type M1752
1.2.8
See also
• Bipolar transistor biasing • Gummel plot • Technology CAD (TCAD)
1.2.9
References
[1] See point-contact transistor for the historical origin of these names. [1] Paul Horowitz and Winfield Hill (1989). The Art of Electronics (2nd ed.). Cambridge University Press. ISBN 978-0-521-37095-0. [2] Juin Jei Liou and Jiann S. Yuan (1998). Semiconductor Device Physics and Simulation. Springer. ISBN 0-30645724-5.
[12] Morris, Peter Robin (1990). “4.2”. A History of the World Semiconductor Industry. IEE History of Technology Series 12. London: Peter Peregrinus Ltd. p. 29. ISBN 0-86341-227-0. [13] Transistor Museum, Historic Transistor Photo Gallery, RCA TA153 [14] High Speed Switching Transistor Handbook (2nd ed.). Motorola. 1963. p. 17. [15] Transistor Museum, Historic Transistor Photo Gallery, Western Electric 3N22 [16] The Tetrode Power Transistor PDF [17] Transistor Museum, Historic Transistor Photo Gallery, Philco A01 [18] Transistor Museum, Historic Transistor Photo Gallery, Surface Barrier Transistor
[3] General Electric (1962). Transistor Manual (6th ed.). p. 12. “If the principle of space charge neutrality is used in the analysis of the transistor, it is evident that the collector current is controlled by means of the positive charge (hole concentration) in the base region. ... When a transistor is used at higher frequencies, the fundamental limitation is the time it takes the carriers to diffuse across the base region...” (same in 4th and 5th editions)
[19] Herb’s Bipolar Transistors IEEE Transactions on Electron Devices, vol. 48, no. 11, November 2001 PDF
[4] Paolo Antognetti and Giuseppe Massobrio (1993). Semiconductor Device Modeling with Spice. McGraw–Hill Professional. ISBN 0-07-134955-3.
[22] Transistor Museum, Historic Transistor Photo Gallery, Fairchild 2N1613
[5] Alphonse J. Sistino (1996). Essentials of electronic circuitry. CRC Press. p. 64. ISBN 978-0-8247-9693-8.
[23] J.J. Ebers and J.L Moll (1954) “Large-signal behavior of junction transistors”, Proceedings of the Institute of Radio Engineers, 42 (12) : 1761–1772.
[6] Alphonse J. Sistino (1996). Essentials of electronic circuitry. CRC Press. p. 102. ISBN 978-0-8247-9693-8.
[20] Influence of Mobility and Lifetime Variations on DriftField Effects in Silicon-Junction Devices PDF [21] Transistor Museum, Historic Transistor Photo Gallery, Bell Labs Prototype Diffused Base Triode
[24] Adel S. Sedra and Kenneth C. Smith (1987). Microelectronic Circuits, second ed. p. 903. ISBN 0-03-007328-6.
[7] D.V. Morgan, Robin H. Williams (Editors) (1991). Physics and Technology of Heterojunction Devices. London: Institution of Electrical Engineers (Peter Peregrinus Ltd.). ISBN 0-86341-204-1.
[25] A.S. Sedra and K.C. Smith (2004). Microelectronic Circuits (5th ed.). New York: Oxford. Eqs. 4.103–4.110, p. 305. ISBN 0-19-514251-9.
[8] Peter Ashburn (2003). SiGe Heterojunction Bipolar Transistors. New York: Wiley. Chapter 10. ISBN 0-47084838-3.
[26] H. K. Gummel and R. C. Poon, “An integral charge control model of bipolar transistors,” Bell Syst. Tech. J., vol. 49, pp. 827–852, May–June 1970
[9] Paul Horowitz and Winfield Hill (1989). The Art of Electronics (2nd ed.). Cambridge University Press. pp. 62– 66. ISBN 978-0-521-37095-0.
[27] A.S. Sedra and K.C. Smith (2004). Microelectronic Circuits (5th ed.). New York: Oxford. p. 509. ISBN 0-19514251-9.
28
CHAPTER 1. THE TRANSISTOR
1.2.10 External links • Simulation of a BJT in the Common Emitter Circuit • Lessons In Electric Circuits – Bipolar Junction Transistors (Note: this site shows current as a flow of electrons, rather than the convention of showing it as a flow of holes) • EncycloBEAMia – Bipolar Junction Transistor • Characteristic curves • ENGI 242/ELEC 222: BJT Small Signal Models • Transistor Museum, Historic Transistor Timeline • ECE 327: Transistor Basics – Summarizes simple Ebers–Moll model of a bipolar transistor and gives several common BJT circuits. • ECE 327: Procedures for Output Filtering Lab – Section 4 (“Power Amplifier”) discusses design of a BJT-Sziklai-pair-based class-AB current driver in High-power N-channel field-effect transistor detail. • BJT Operation description for undergraduate and first year graduate students to describe the basic principles of operation of Bipolar Junction Transistor.
The field-effect transistor was first patented by Julius Edgar Lilienfeld in 1926 and by Oskar Heil in 1934, but practical semiconducting devices (the JFET) were developed only much later after the transistor effect was observed and explained by the team of William Shockley at Bell Labs in 1947, immediately after the 20-year patent period eventually expired. The MOSFET, which largely 1.3 Field-effect transistor superseded the JFET and had a more profound effect on electronic development, was invented by Dawon Kahng “FET” redirects here. For other uses, see FET (disamand Martin Atalla in 1960.[1] biguation). The field-effect transistor (FET) is a transistor that uses an electric field to control the shape and hence the 1.3.2 Basic information conductivity of a channel of one type of charge carrier in a semiconductor material. FETs are unipolar transistors See also: Charge carrier § Majority and minority carriers as they involve single-carrier-type operation. The concept of the FET predates the bipolar junction transistor (BJT), though it was not physically implemented until after BJTs FETs can be majority-charge-carrier devices, in which due to the limitations of semiconductor materials and the the current is carried predominantly by majority carriers, relative ease of manufacturing BJTs compared to FETs or minority-charge-carrier devices, in which the current is mainly due to a flow of minority carriers.[2] The device at the time. consists of an active channel through which charge carriers, electrons or holes, flow from the source to the drain. Source and drain terminal conductors are connected to 1.3.1 History the semiconductor through ohmic contacts. The conducMain article: History of the transistor tivity of the channel is a function of the potential applied across the gate and source terminals.
1.3. FIELD-EFFECT TRANSISTOR
29
The FET’s three terminals are:[3] • Source (S), through which the carriers enter the channel. Conventionally, current entering the channel at S is designated by IS. • Drain (D), through which the carriers leave the channel. Conventionally, current entering the channel at D is designated by ID. Drain-to-source voltage is VDS. • Gate (G), the terminal that modulates the channel conductivity. By applying voltage to G, one can control ID.
1.3.3
More about terminals
Oxide Source
or eliminating a channel between the source and drain. Electrons flow from the source terminal towards the drain terminal is influenced by an applied voltage. The body simply refers to the bulk of the semiconductor in which the gate, source and drain lie. Usually the body terminal is connected to the highest or lowest voltage within the circuit, depending on the type of the FET. The body terminal and the source terminal are sometimes connected together since the source is often connected to the highest or lowest voltage within the circuit, although there are several uses of FETs which do not have such a configuration, such as transmission gates and cascode circuits.
1.3.4 FET operation See also: Field effect (semiconductor) The FET controls the flow of electrons (or electron holes)
Gate
I DS
Drain
I DS
VDS
SAT
=
Linear region
VGS - VP Saturation region
VGS0 = 0 VGS1 < VGS0
x
n+
n+
p L Body Cross section of an n-type MOSFET
All FETs have source, drain, and gate terminals that correspond roughly to the emitter, collector, and base of BJTs. Most FETs have a fourth terminal called the body, base, bulk, or substrate. This fourth terminal serves to bias the transistor into operation; it is rare to make nontrivial use of the body terminal in circuit designs, but its presence is important when setting up the physical layout of an integrated circuit. The size of the gate, length L in the diagram, is the distance between source and drain. The width is the extension of the transistor, in the direction perpendicular to the cross section in the diagram. Typically the width is much larger than the length of the gate. A gate length of 1 µm limits the upper frequency to about 5 GHz, 0.2 µm to about 30 GHz. The names of the terminals refer to their functions. The gate terminal may be thought of as controlling the opening and closing of a physical gate. This gate permits electrons to flow through or blocks their passage by creating
VGS2 < VGS1
Saturation region Channel off
VGS
VP
Linear region
VGS3 < VGS2 Channel off
VGS4 < VVp
VDS
I–V characteristics and output plot of a JFET n-channel transistor.
from the source to drain by affecting the size and shape of a “conductive channel” created and influenced by voltage (or lack of voltage) applied across the gate and source terminals. (For simplicity, this discussion assumes that the body and source are connected.) This conductive channel is the “stream” through which electrons flow from source to drain. n-channel In an n-channel depletion-mode device, a negative gateto-source voltage causes a depletion region to expand in width and encroach on the channel from the sides, narrowing the channel. If the depletion region expands to completely close the channel, the resistance of the channel from source to drain becomes large, and the FET is effectively turned off like a switch. This is called pinch-off, and the voltage at which it occurs is called the pinch-off voltage. Conversely, a positive gate-to-source voltage in-
30
CHAPTER 1. THE TRANSISTOR
creases the channel size and allows electrons to flow eas- to be part of the ohmic or linear region, even where drain ily. current is not approximately linear with drain voltage. In an n-channel enhancement-mode device, a conductive channel does not exist naturally within the transistor, and a positive gate-to-source voltage is necessary to create one. The positive voltage attracts free-floating electrons within the body towards the gate, forming a conductive channel. But first, enough electrons must be attracted near the gate to counter the dopant ions added to the body of the FET; this forms a region with no mobile carriers called a depletion region, and the voltage at which this occurs is referred to as the threshold voltage of the FET. Further gate-to-source voltage increase will attract even more electrons towards the gate which are able to create a conductive channel from source to drain; this process is called inversion. p-channel In a p-channel depletion-mode device, a positive voltage from gate to body creates a depletion layer by forcing the positively charged holes away from the gate-insulator/semiconductor interface, leaving exposed a carrier-free region of immobile, negatively charged acceptor ions..
Even though the conductive channel formed by gate-tosource voltage no longer connects source to drain during saturation mode, carriers are not blocked from flowing. Considering again an n-channel enhancement-mode device, a depletion region exists in the p-type body, surrounding the conductive channel and drain and source regions. The electrons which comprise the channel are free to move out of the channel through the depletion region if attracted to the drain by drain-to-source voltage. The depletion region is free of carriers and has a resistance similar to silicon. Any increase of the drain-to-source voltage will increase the distance from drain to the pinchoff point, increasing the resistance of the depletion region in proportion to the drain-to-source voltage applied. This proportional change causes the drain-to-source current to remain relatively fixed, independent of changes to the drain-to-source voltage, quite unlike its ohmic behavior in the linear mode of operation. Thus, in saturation mode, the FET behaves as a constant-current source rather than as a resistor, and can effectively be used as a voltage amplifier. In this case, the gate-to-source voltage determines the level of constant current through the channel.
Operation
1.3.5
Composition
For either enhancement- or depletion-mode devices, at drain-to-source voltages much less than gate-to-source voltages, changing the gate voltage will alter the channel resistance, and drain current will be proportional to drain voltage (referenced to source voltage). In this mode the FET operates like a variable resistor and the FET is said to be operating in a linear mode or ohmic mode.[4][5]
The FET can be constructed from a number of semiconductors, with silicon being by far the most common. Most FETs are made with conventional bulk semiconductor processing techniques, using a single crystal semiconductor wafer as the active region, or channel.
If drain-to-source voltage is increased, this creates a significant asymmetrical change in the shape of the channel due to a gradient of voltage potential from source to drain. The shape of the inversion region becomes “pinched-off” near the drain end of the channel. If drainto-source voltage is increased further, the pinch-off point of the channel begins to move away from the drain towards the source. The FET is said to be in saturation mode;[6] although some authors refer to it as active mode, for a better analogy with bipolar transistor operating regions.[7][8] The saturation mode, or the region between ohmic and saturation, is used when amplification is needed. The in-between region is sometimes considered
Among the more unusual body materials are amorphous silicon, polycrystalline silicon or other amorphous semiconductors in thin-film transistors or organic field-effect transistors (OFETs) that are based on organic semiconductors; often, OFET gate insulators and electrodes are made of organic materials, as well. Such FETs are manufactured using a variety of materials such as silicon carbide (SiC), gallium arsenide (GaAs), gallium nitride (GaN), and indium gallium arsenide (InGaAs). In June 2011, IBM announced that it had successfully used graphene-based FETs in an integrated circuit.[9][10] These transistors are capable of about 2.23 GHz cutoff frequency, much higher than standard silicon FETs.[11]
1.3. FIELD-EFFECT TRANSISTOR
1.3.6
Types of field-effect transistors
31 • The DGMOSFET (dual-gate MOSFET) is a FET with two insulated gates. • The DEPFET is a FET formed in a fully depleted substrate and acts as a sensor, amplifier and memory node at the same time. It can be used as an image (photon) sensor. • The FREDFET (fast-reverse or fast-recovery epitaxial diode FET) is a specialized FET designed to provide a very fast recovery (turn-off) of the body diode. • The HIGFET (heterostructure insulated gate fieldeffect transistor) is now used mainly in research. • The MODFET (modulation-doped field-effect transistor) uses a quantum well structure formed by graded doping of the active region. • The TFET (tunnel field-effect transistor) is based on band-to-band tunneling.[12]
Depletion-type FETs under typical voltages: JFET, poly-silicon MOSFET, double-gate MOSFET, metal-gate MOSFET, MESFET. Depletion Electrons Holes Metal Insulator Top: source, bottom: drain, left: gate, right: bulk. Voltages that lead to channel formation are not shown.
The channel of a FET is doped to produce either an n-type semiconductor or a p-type semiconductor. The drain and source may be doped of opposite type to the channel, in the case of enhancement mode FETs, or doped of similar type to the channel as in depletion mode FETs. Field-effect transistors are also distinguished by the method of insulation between channel and gate. Types of FETs include: • The JFET (junction field-effect transistor) uses a reverse biased p–n junction to separate the gate from the body. • The MOSFET (metal–oxide–semiconductor fieldeffect transistor) utilizes an insulator (typically SiO2 ) between the gate and the body.
• The IGBT (insulated-gate bipolar transistor) is a device for power control. It has a structure akin to a MOSFET coupled with a bipolar-like main conduction channel. These are commonly used for the 200– 3000 V drain-to-source voltage range of operation. Power MOSFETs are still the device of choice for drain-to-source voltages of 1 to 200 V. • The HEMT (high-electron-mobility transistor), also called a HFET (heterostructure FET), can be made using bandgap engineering in a ternary semiconductor such as AlGaAs. The fully depleted wide-band-gap material forms the isolation between gate and body. • The ISFET (ion-sensitive field-effect transistor) can be used to measure ion concentrations in a solution; when the ion concentration (such as H+ , see pH electrode) changes, the current through the transistor will change accordingly. • The BioFET (Biologically sensitive field-effect transistor) is a class of sensors/biosensors based on ISFET technology which are utilized to detect charged molecules; when a charged molecule is present, changes in the electrostatic field at the BioFET surface result in a measurable change in current through the transistor. These include EnFETs, ImmunoFETs, GenFETs, DNAFETs, CPFETs, BeetleFETs, and FETs based on ionchannels/protein binding. [13]
32
CHAPTER 1. THE TRANSISTOR
• The MESFET (metal–semiconductor field-effect 1.3.8 Disadvantages of FET transistor) substitutes the p–n junction of the JFET with a Schottky barrier; and is used in GaAs and It has a relatively low gain-bandwidth product comother III-V semiconductor materials. pared to a BJT. The MOSFET has a drawback of being very susceptible to overload voltages, thus requiring spe• The NOMFET is a nanoparticle organic memory cial handling during installation.[15] The fragile insulatfield-effect transistor. ing layer of the MOSFET between the gate and channel makes it vulnerable to electrostatic damage during han• The GNRFET (graphene nanoribbon field-effect dling. This is not usually a problem after the device has transistor) uses a graphene nanoribbon for its chan- been installed in a properly designed circuit. nel. FETs often have a very low 'on' resistance and have a high • The VeSFET (vertical-slit field-effect transistor) is 'off' resistance. However the intermediate resistances are a square-shaped junctionless FET with a narrow slit significant, and so FETs can dissipate large amounts of connecting the source and drain at opposite corners. power while switching. Thus efficiency can put a preTwo gates occupy the other corners, and control the mium on switching quickly, but this can cause transients that can excite stray inductances and generate significant current through the slit. voltages that can couple to the gate and cause uninten• The CNTFET (carbon nanotube field-effect transis- tional switching. FET circuits can therefore require very careful layout and can involve trades between switching tor). speed and power dissipation. • The OFET (organic field-effect transistor) uses an organic semiconductor in its channel. • The DNAFET (DNA field-effect transistor) is a 1.3.9 Uses of FET specialized FET that acts as a biosensor, by using a gate made of single-strand DNA molecules to de- The most commonly used FET is the MOSFET. The CMOS (complementary metal oxide semiconductor) tect matching DNA strands. process technology is the basis for modern digital • The QFET (quantum field effect transistor) takes integrated circuits. This process technology uses an advantage of quantum tunneling to greatly increase arrangement where the (usually “enhancement-mode”) the speed of transistor operation by eliminating the p-channel MOSFET and n-channel MOSFET are contraditional transistor’s area of electron conduction. nected in series such that when one is ON, the other is OFF.
1.3.7 Advantages of FET The main advantage of the fet is its high input resistance, on the order of 100 MΩ or more. Thus, it is a voltagecontrolled device, and shows a high degree of isolation between input and output. It is a unipolar device, depending only on majority current flow.. Because base current noise will increase with shaping time,[14] a FET typically produces less noise than a bipolar junction transistor (BJT), and is thus found in noise sensitive electronics such as tuners and low-noise amplifiers for VHF and satellite receivers. It is relatively immune to radiation. It exhibits no offset voltage at zero drain current and hence makes an excellent signal chopper. It typically has better thermal stability than a BJT.[3]
In FETs, electrons can flow in either direction through the channel when operated in the linear mode. The naming convention of drain terminal and source terminal is somewhat arbitrary, as the devices are typically (but not always) built symmetrically from source to drain. This makes FETs suitable for switching analog signals between paths (multiplexing). With this concept, one can construct a solid-state mixing board, for example. A common use of the FET is as an amplifier. For example, due to its large input resistance and low output resistance, it is effective as a buffer in common-drain (source follower) configuration. IGBTs see application in switching internal combustion engine ignition coils, where fast switching and voltage blocking capabilities are important.
1.3. FIELD-EFFECT TRANSISTOR
1.3.10
See also FET
• Chemical field-effect transistor • Quantum field effect transistor • ISFET • MOSFET • FET amplifier
1.3.11
References
[1] http://www.computerhistory.org/semiconductor/ timeline/1960-MOS.html [2] Jacob Millman (1985). Electronic devices and circuits. Singapore: McGraw-Hill International. p. 397. ISBN 0-07-085505-6. [3] Millman (1985). Electronic devices and circuits. Singapore: McGraw-Hill. pp. 384–385. ISBN 0-07-0855056. [4] C Galup-Montoro & Schneider MC (2007). MOSFET modeling for circuit analysis and design. London/Singapore: World Scientific. p. 83. ISBN 981-256810-7.
33
[11] http://physicsworld.com/cws/article/news/2012/dec/10/ flexible-graphene-transistor-sets-new-records [12] Ionescu, A. M.; Riel, H. (2011). “Tunnel field-effect transistors as energy-efficient electronic switches”. Nature 479 (7373): 329–337. doi:10.1038/nature10679. PMID 22094693. [13] Poghossianb, Arshak (2002). “Recent advances in biologically sensitive field-effect transistors (BioFETs) extquotedbl. Analyst 127: 1137–1151. doi:10.1039/B204444G. [14] http://www-physics.lbl.gov/~{}spieler/physics_198_ notes/PDF/VIII-5-noise.pdf [15] Allen Mottershead (2004). Electronic devices and circuits. New Delhi: Prentice-Hall of India. ISBN 81-203-01242.
1.3.12 External links • Field Effect Transistor Applications • PBS The Field Effect Transistor • Junction Field Effect Transistor • CMOS gate circuitry • Winning the Battle Against Latchup in CMOS Analog Switches
[5] Norbert R Malik (1995). Electronic circuits: analysis, simulation, and design. Englewood Cliffs, NJ: Prentice Hall. pp. 315–316. ISBN 0-02-374910-5.
• Nanotube FETs at IBM Research
[6] RR Spencer & Ghausi MS (2001). Microelectronic circuits. Upper Saddle River NJ: Pearson Education/Prentice-Hall. p. 102. ISBN 0-201-36183-3.
• The Field Effect Transistor as a Voltage Controlled Resistor
[7] A. S. Sedra and K.C. Smith (2004). Microelectronic circuits (Fifth Edition ed.). New York: Oxford. p. 552. ISBN 0-19-514251-9. [8] PR Gray, PJ Hurst, SH Lewis & RG Meyer (2001). Analysis and design of analog integrated circuits (Fourth Edition ed.). New York: Wiley. pp. §1.5.2 p. 45. ISBN 0-471-32168-0. [9] http://www.physorg.com/news/ 2011-06-ibm-graphene-based-circuit.html [10] Lin, Y.-M., Valdes-Garcia, A., Han, S.-J., Farmer, D. B., Sun, Y, Wu, Y, Dimitrakopoulos, C., Grill, A, Avouris, P, and Jenkins, K. A. (2011). “Wafer-Scale Graphene Integrated Circuit”. Science 332: 1294–1297. doi:10.1126/science.1204428. PMID 21659599.
• Field Effect Transistors in Theory and Practice
Chapter 2
Semiconductor Materials 2.1 Silicon
combined with silica sand and gravel, to make concrete. Silicates are also in whiteware ceramics such as porcelain, and in traditional quartz-based soda-lime glass and many This article is about the chemical element. For other other specialty glasses. More modern silicon compounds uses, see Silicon (disambiguation). such as silicon carbide form abrasives and high-strength “Element 14” redirects here. For other uses, see Element ceramics. Silicon is the basis of the widely-used synthetic 14 (disambiguation). polymers called silicones. Not to be confused with the silicon-containing synthetic Elemental silicon also has a large impact on the modern polymer silicone. world economy. Although most free silicon is used in the steel refining, aluminium-casting, and fine chemical inSilicon is a chemical element with symbol Si and atomic dustries (often to make fumed silica), the relatively small number 14. It is a tetravalent metalloid, less reactive than portion of very highly purified silicon that is used in semiits chemical analog carbon, the nonmetal directly above it conductor electronics (< 10%) is perhaps even more critin the periodic table, but more reactive than germanium, ical. Because of wide use of silicon in integrated circuits, the metalloid directly below it in the table. Controversy the basis of most computers, a great deal of modern techabout silicon’s character dates to its discovery; it was first nology depends on it. prepared and characterized in pure form in 1823. In Silicon is an essential element in biology, although only 1808, it was given the name silicium (from Latin: silex, tiny traces of it appear to be required by animals.[8] Howhard stone or flint), with an -ium word-ending to suggest ever, various sea sponges as well as microorganisms like a metal, a name which the element retains in several nondiatoms and radiolaria secrete skeletal structures made English languages. However, its final English name, first of silica. Silica is often deposited in plant tissues, such suggested in 1817, reflects the more physically similar elas in the bark and wood of Chrysobalanaceae and the ements carbon and boron. silica cells and silicified trichomes of Cannabis sativa, Silicon is the eighth most common element in the uni- horsetails and many grasses.[9] verse by mass, but very rarely occurs as the pure free element in nature. It is most widely distributed in dusts, sands, planetoids, and planets as various forms of silicon 2.1.1 Characteristics dioxide (silica) or silicates. Over 90% of the Earth’s crust is composed of silicate minerals, making silicon the Physical second most abundant element in the Earth’s crust (about 28% by mass) after oxygen.[7] Further information: Monocrystalline silicon Most silicon is used commercially without being separated, and indeed often with little processing of compounds from nature. These include direct industrial building-use of clays, silica sand and stone. Silicate goes into Portland cement for mortar and stucco, and when
Silicon is a solid at room temperature, with relatively high melting and boiling points of 1414 and 3265 °C, respectively. It has a greater density in a liquid state than a solid state. It does not contract when it freezes like most sub-
34
2.1. SILICON
Silicon crystallizes in a diamond cubic crystal structure
35
Silicon powder
and form five or six bonds in a sometimes more labile stances, but expands, similar to how ice is less dense than silicate form. Tetra-valent silicon is relatively inert, but water. With a relatively high thermal conductivity of 149 still reacts with halogens and dilute alkalis, but most acids W·m−1 ·K−1 , silicon conducts heat well and as a result is (except for some hyper-reactive combinations of nitric not often used to insulate hot objects. acid and hydrofluoric acid) have no known effect on it. In its crystalline form, pure silicon has a gray color However, having four bonding electrons gives it, like carand a metallic luster. Like germanium, silicon is rather bon, many opportunities to combine with other elements strong, very brittle, and prone to chipping. Silicon, like or compounds in the right circumstances. carbon and germanium, crystallizes in a diamond cubic crystal structure, with a lattice spacing of 0.5430710 nm (5.430710 Å).[10] Isotopes The outer electron orbital of silicon, like that of carbon, has four valence electrons. The 1s, 2s, 2p and 3s subshells Main article: isotopes of silicon are completely filled while the 3p subshell contains two electrons out of a possible six. Naturally occurring silicon is composed of three staSilicon is a semiconductor. It has a negative temperature ble isotopes, silicon-28, silicon-29, and silicon-30, with coefficient of resistance, since the number of free charge silicon-28 being the most abundant (92% natural abun[12] carriers increases with temperature. The electrical re- dance). Out of these, only silicon-29 is of use in NMR [13] Twenty radioisotopes have sistance of single crystal silicon significantly changes and EPR spectroscopy. under the application of mechanical stress due to the been characterized, with the most stable being silicon-32 with a half-life of 170 years, and silicon-31 with a halfpiezoresistive effect.[11] life of 157.3 minutes.[12] All of the remaining radioactive isotopes have half-lives that are less than seven seconds, and the majority of these have half-lives that are less than Chemical one tenth of a second.[12] Silicon does not have any known [12] Silicon is a metalloid, readily either donating or shar- nuclear isomers. ing its four outer electrons, allowing for many forms of The isotopes of silicon range in mass number from 22 chemical bonding. Like carbon, it typically forms four to 44.[12] The most common decay mode of six isotopes bonds. Unlike carbon, it can accept additional electrons with mass numbers lower than the most abundant stable
36 isotope, silicon-28, is β+, primarily forming aluminium isotopes (13 protons) as decay products.[12] The most common decay mode(s) for 16 isotopes with mass numbers higher than silicon-28 is β−, primarily forming phosphorus isotopes (15 protons) as decay products.[12]
Occurrence
CHAPTER 2. SEMICONDUCTOR MATERIALS supernova dust which formed the protoplanetary disk in the formation and evolution of the Solar System, they formed many complex silicates which accreted into larger rocky planetesimals that formed the terrestrial planets. Here, the reduced silicate mineral matrix entrapped the metals reactive enough to be oxidized (aluminium, calcium, sodium, potassium and magnesium). After loss of volatile gases, as well as carbon and sulfur via reaction with hydrogen, this silicate mixture of elements formed most of the Earth’s crust. These silicates were of relatively low density with respect to iron, nickel, and other metals non-reactive to oxygen and thus a residuum of uncombined iron and nickel sank to the planet’s core, leaving a thick mantle consisting mostly of magnesium and iron silicates. These are thought to be mostly silicate perovskites, followed in abundance by the magnesium/iron oxide ferropericlase.[15] Examples of silicate minerals in the crust include those in the pyroxene, amphibole, mica, and feldspar groups. These minerals occur in clay and various types of rock such as granite and sandstone.
Quartz crystal cluster from Tibet. The naturally occurring mineral is a network solid with the formula SiO2 .
See also: Silicate minerals Measured by mass, silicon makes up 27.7% of the Earth’s crust and is the second most abundant element in the crust, with only oxygen having a greater abundance.[14] Silicon is usually found in the form of complex silicate minerals, and less often as silicon dioxide (silica, a major component of common sand). Pure silicon crystals are very rarely found in nature. The silicate minerals—various minerals containing silicon, oxygen and reactive metals—account for 90% of the mass of the Earth’s crust. This is due to the fact that at the high temperatures characteristic of the formation of the inner solar system, silicon and oxygen have a great affinity for each other, forming networks of silicon and oxygen in chemical compounds of very low volatility. Since oxygen and silicon were the most common non-gaseous and non-metallic elements in the debris from
Silica occurs in minerals consisting of very pure silicon dioxide in different crystalline forms, quartz, agate amethyst, rock crystal, chalcedony, flint, jasper, and opal. The crystals have the empirical formula of silicon dioxide, but do not consist of separate silicon dioxide molecules in the manner of solid carbon dioxide. Rather, silica is structurally a network-solid consisting of silicon and oxygen in three-dimensional crystals, like diamond. Less pure silica forms the natural glass obsidian. Biogenic silica occurs in the structure of diatoms, radiolaria and siliceous sponges. Silicon is also a principal component of many meteorites, and is a component of tektites, a silicate mineral of possibly lunar origin, or (if Earth-derived) which has been subjected to unusual temperatures and pressures, possibly from meteorite strike.
2.1.2
Production
Alloys Ferrosilicon, an iron-silicon alloy that contains varying ratios of elemental silicon and iron, accounts for about 80% of the world’s production of elemental silicon, with China, the leading supplier of elemental silicon, providing 4.6 million tonnes (or 2/3 of the world output) of silicon, most of which is in the form of ferrosilicon. It
2.1. SILICON
37 of the following ways: SiO2 + C → SiO + CO or SiO + 2 C → SiC + CO. However, provided the concentration of SiO2 is kept high, the silicon carbide can be eliminated by the chemical reaction 2 SiC + SiO2 → 3 Si + 2 CO. As noted above, metallurgical grade silicon “metal” has its primary use in the aluminium casting industry to make aluminium-silicon alloy parts. The remainder (about 45%) is used by the chemical industry, where it is primarily employed to make fumed silica, with the rest used in production of other fine chemicals such as silanes and some types of silicones.[18]
Ferrosilicon alloy
As of September 2008, metallurgical grade silicon costs about US$1.45 per pound ($3.20/kg),[19] up from $0.77 per pound ($1.70/kg) in 2005.[20]
is followed by Russia (610,000 t), Norway (330,000 t), Brazil (240,000 t) and the United States (170,000 t).[16] Electronic grade Ferrosilicon is primarily used by the steel industry (see The use of silicon in semiconductor devices demands a below). much greater purity than afforded by metallurgical grade Aluminium-silicon alloys (called silumin alloys) are heavsilicon. Very pure silicon (>99.9%) can be extracted diily used in the aluminium alloy casting industry, where rectly from solid silica or other silicon compounds by silicon is the single most important additive to aluminium molten salt electrolysis.[21][22] This method, known as to improve its casting properties. Since cast aluminium early as 1854[23] (see also FFC Cambridge process), has is widely used in the automobile industry, this use of silthe potential to directly produce solar-grade silicon withicon is thus the single largest industrial use (about 55% out any carbon dioxide emission at much lower energy of the total) of “metallurgical grade” pure silicon (as this consumption. purified silicon is added to pure aluminium, whereas ferrosilicon is never purified before being added to steel).[17] Solar grade silicon cannot be used for microelectronics. To properly control the quantum mechanical properties, the purity of the silicon must be very high. Bulk siliMetallurgical grade con wafers used at the beginning of the integrated circuit making process must first be refined to a purity of Elemental silicon not alloyed with significant quantities 99.9999999% often referred to as “9N” for “9 nines”, a of other elements, and usually > 95%, is often referred to process which requires repeated applications of refining loosely as silicon metal. It makes up about 20% of the technology. world total elemental silicon production, with less than 1 to 2% of total elemental silicon (5–10% of metallurgi- The majority of silicon crystals grown for device produccal grade silicon) ever purified to higher grades for use in tion are produced by the Czochralski process, (CZ-Si) It electronics. Metallurgical grade silicon is commercially was the cheapest method available. However, single crysprepared by the reaction of high-purity silica with wood, tals grown by the Czochralski process contain impurities charcoal, and coal in an electric arc furnace using carbon because the crucible containing the melt often dissolves. electrodes. At temperatures over 1,900 °C (3,450 °F), Historically, a number of methods have been used to prothe carbon in the aforementioned materials and the sili- duce ultra-high-purity silicon. con undergo the chemical reaction SiO2 + 2 C → Si + 2 Early silicon purification techniques were based on the CO. Liquid silicon collects in the bottom of the furnace, fact that if silicon is melted and re-solidified, the last parts which is then drained and cooled. The silicon produced in of the mass to solidify contain most of the impurities. this manner is called metallurgical grade silicon and is at The earliest method of silicon purification, first described least 98% pure. Using this method, silicon carbide (SiC) in 1919 and used on a limited basis to make radar compomay also form from an excess of carbon in one or both nents during World War II, involved crushing metallurgi-
38
CHAPTER 2. SEMICONDUCTOR MATERIALS
cal grade silicon and then partially dissolving the silicon powder in an acid. When crushed, the silicon cracked so that the weaker impurity-rich regions were on the outside of the resulting grains of silicon. As a result, the impurity-rich silicon was the first to be dissolved when treated with acid, leaving behind a more pure product.
lizes tribromosilane in place of trichlorosilane and fluid bed technology. It requires lower deposition temperatures, lower capital costs to build facilities and operate, no hazardous polymers nor explosive material, and produces no amorphous silicon dust waste, all of which are drawbacks of the Siemens process.[29] However, there are In zone melting, also called zone refining, the first silicon yet to be any major factories built using this process. purification method to be widely used industrially, rods of metallurgical grade silicon are heated to melt at one 2.1.3 Compounds end. Then, the heater is slowly moved down the length of the rod, keeping a small length of the rod molten as the • Silicon forms binary compounds called silicides silicon cools and re-solidifies behind it. Since most imwith many metallic elements whose properties range purities tend to remain in the molten region rather than from reactive compounds, e.g. magnesium silicide, re-solidify, when the process is complete, most of the imMg2 Si through high melting refractory compounds purities in the rod will have been moved into the end that such as molybdenum disilicide, MoSi2 .[30] was the last to be melted. This end is then cut off and discarded, and the process repeated if a still higher purity is • Silicon carbide, SiC (carborundum) is a hard, high desired.[24] melting solid and a well known abrasive. It may also At one time, DuPont produced ultra-pure silicon by reacting silicon tetrachloride with high-purity zinc vapors at 950 °C, producing silicon by SiCl4 + 2 Zn → Si + 2 ZnCl2 . However, this technique was plagued with practical problems (such as the zinc chloride byproduct solidifying and clogging lines) and was eventually abandoned in favor of the Siemens process. In the Siemens process, high-purity silicon rods are exposed to trichlorosilane at 1150 °C. The trichlorosilane gas decomposes and deposits additional silicon onto the rods, enlarging them because 2 HSiCl3 → Si + 2 HCl + SiCl4 . Silicon produced from this and similar processes is called polycrystalline silicon. Polycrystalline silicon typically has impurity levels of less than one part per billion.[25][26][27] In 2006 REC announced construction of a plant based on fluidized bed (FB) technology using silane: 3 SiCl4 + Si + 2 H2 → 4 HSiCl3 , 4 HSiCl3 → 3 SiCl4 + SiH4 , SiH4 → Si + 2 H2 .[28] The advantage of fluid bed technology is that processes can be run continuously, yielding higher yields than Siemens Process, which is a batch process. Today, silicon is purified by converting it to a silicon compound that can be more easily purified by distillation than in its original state, and then converting that silicon compound back into pure silicon. Trichlorosilane is the silicon compound most commonly used as the intermediate, although silicon tetrachloride and silane are also used. When these gases are blown over silicon at high temperature, they decompose to high-purity silicon. In addition, there is the Schumacher process, which uti-
be sintered into a type of high-strength ceramic used in armor. • Silane, SiH4 , is a pyrophoric gas with a similar tetrahedral structure to methane, CH4 . When pure, it does not react with pure water or dilute acids; however, even small amounts of alkali impurities from the laboratory glass can result in a rapid hydrolysis.[31] There is a range of catenated silicon hydrides that form a homologous series of compounds, Si nH 2n+2 where n = 2–8 (analogous to the alkanes). These are all readily hydrolyzed and are thermally unstable, particularly the heavier members.[32][33] • Disilenes contain a silicon-silicon double bond (analogous to the alkenes) and are generally highly reactive requiring large substituent groups to stabilize them.[34] A disilyne with a silicon-silicon triple bond was first isolated in 2004; although as the compound is non-linear, the bonding is dissimilar to that in alkynes.[35] • Tetrahalides, SiX4 , are formed with all the halogens.[36] Silicon tetrachloride, for example, reacts with water, unlike its carbon analogue, carbon tetrachloride.[37] Silicon dihalides are formed by the high temperature reaction of tetrahalides and silicon; with a structure analogous to a carbene they are reactive compounds. Silicon difluoride condenses to form a polymeric compound, (SiF
2.1. SILICON 2) n.[33] • Silicon dioxide (silica) is a high melting solid with a number of crystal forms; the most familiar of which is the mineral quartz. In crystalline quartz each silicon atom is surrounded by four oxygen atoms that bridge to other silicon atoms to form a three dimensional lattice (see below for the vitreous or glass form of pure silica). [37] Silica is soluble in water at high temperatures forming a range of compounds called monosilicic acid, Si(OH)4 .[38] • Under the right conditions monosilicic acid readily polymerizes to form more complex silicic acids, ranging from the simplest condensate, disilicic acid (H6 Si2 O7 ) to linear, ribbon, layer and lattice structures which form the basis of the many silicate minerals and are called polysilicic acids {Siₓ(OH)₄– ₂ₓ} .[38] • Silica can be fused directly into glass form, as socalled fused quartz, which contains no crystalline structure. With with oxides of other elements, the high temperature reaction of silicon dioxide can give a wide range of mixed glasses and glass-like network solids with various properties.[39] Examples include soda-lime glass, borosilicate glass and lead crystal glass. • Silicon sulfide, SiS2 , is a polymeric solid (unlike its carbon analogue the liquid CS2 ).[40] • Silicon forms a nitride, Si3 N4 which is a ceramic.[41] Silatranes, a group of tricyclic compounds containing five-coordinate silicon, may have physiological properties.[42] • Many transition metal complexes containing a metal-silicon bond are now known, which include complexes containing SiH nX 3−n ligands, SiX3 ligands, and Si(OR)3 ligands.[42]
39 some are optically active when central chirality exists. Long chain polymers containing a silicon backbone are known, such as polydimethysilylene (SiMe 2) n.[44] Polycarbosilane, [(SiMe 2) 2CH 2] n with a backbone containing a repeating -Si-Si-C unit, is a precursor in the production of silicon carbide fibers.[44]
2.1.4 History Attention was first drawn to silica as the possible oxide of a fundamental chemical element by Antoine Lavoisier, in 1787.[45] After an attempt to isolate silicon in 1808, Sir Humphry Davy proposed the name “silicium” for silicon, from the Latin silex, silicis for flint, flints, and adding the extquotedbl-ium” ending because he believed it was a metal.[46] In 1811, Gay-Lussac and Thénard are thought to have prepared impure amorphous silicon, through the heating of recently isolated potassium metal with silicon tetrafluoride, but they did not purify and characterize the product, nor identify it as a new element.[47] Silicon was given its present name in 1817 by Scottish chemist Thomas Thomson. He retained part of Davy’s name but added extquotedbl-on” because he believed that silicon was a nonmetal similar to boron and carbon.[48] In 1823, Berzelius prepared amorphous silicon using approximately the same method as Gay-Lussac (potassium metal and potassium fluorosilicate), but purifying the product to a brown powder by repeatedly washing it.[49] As a result he is usually given credit for the element’s discovery.[50][51]
Silicon in its more common crystalline form was not prepared until 31 years later, by Deville.[52][53] By electrolyzing impure sodium-aluminium chloride containing approximately 10% silicon, he was able to obtain a slightly impure allotrope of silicon in 1854.[54] Later, • Silicones are large group of polymeric compounds more cost-effective methods have been developed to isowith an (Si-O-Si) backbone. An example is the late silicon in several allotrope forms, the most recent besilicone oil PDMS (polydimethylsiloxane). These ing silicene. polymers can be crosslinked to produce resins and Because silicon is an important element in semiconducelastomers.[43] tors and high-technology devices, many places in the • Many organosilicon compounds are known which world bear its name. For example, Silicon Valley in contain a silicon-carbon single bond. Many of these California, bears the element’s name since it is the base are based on a central tetrahedral silicon atom, and for a number of computer technology-related industries.
40 Other geographic locations with connections to the industry have since been named after silicon as well. Examples include Silicon Forest in Oregon, Silicon Hills in Austin, Texas, Silicon Saxony in Germany, Silicon Valley in India, Silicon Border in Mexicali, Mexico, Silicon Fen in Cambridge, England, Silicon Roundabout in London, Silicon Glen in Scotland, and Silicon Gorge in Bristol, England.
2.1.5 Applications Compounds Building materials. Most silicon is used industrially without being separated into the element, and indeed often with comparatively little processing from natural occurrence. Over 90% of the Earth’s crust is composed of silicate minerals, which are compounds of silicon and oxygen, often with metallic ions when charged silicate anions require cations to balance charge. Many of these have direct commercial uses, such as clays, silica sand and most kinds of building stone. Thus, the vast majority of uses for silicon are as structural compounds, either as the silicate minerals or silica (crude silicon dioxide). Silicates are used in making Portland cement (made mostly of calcium silicates) which is used in building mortar and modern stucco, but more importantly, combined with silica sand, and gravel (usually containing silicate minerals like granite), to make the concrete that is the basis of most of the very largest industrial building projects of the modern world. [55]
CHAPTER 2. SEMICONDUCTOR MATERIALS of the inner planets of the solar system make planetary silicon compounds found there mostly silicates and silica. Free silicon, or compounds of silicon in which the element is covalently attached to hydrogen, boron, or elements other than oxygen, are mostly artificially produced. They are described below. Silicon compounds of more modern origin function as high-technology abrasives and new high-strength ceramics based upon silicon carbide. Silicon is a component of some superalloys. Alternating silicon-oxygen chains with hydrogen attached to the remaining silicon bonds form the ubiquitous silicon-based polymeric materials known as silicones. These compounds containing silicon-oxygen and occasionally silicon-carbon bonds have the capability to act as bonding intermediates between glass and organic compounds, and to form polymers with useful properties such as impermeability to water, flexibility and resistance to chemical attack. Silicones are often used in waterproofing treatments, molding compounds, mold-release agents, mechanical seals, high temperature greases and waxes, and caulking compounds. Silicone is also sometimes used in breast implants, contact lenses, explosives and pyrotechnics.[56] Silly Putty was originally made by adding boric acid to silicone oil.[57] Alloys Elemental silicon is added to molten cast iron as ferrosilicon or silicocalcium alloys to improve performance in casting thin sections and to prevent the formation of cementite where exposed to outside air. The presence of elemental silicon in molten iron acts as a sink for oxygen, so that the steel carbon content, which must be kept within narrow limits for each type of steel, can be more closely controlled. Ferrosilicon production and use is a monitor of the steel industry, and although this form of elemental silicon is grossly impure, it accounts for 80% of the world’s use of free silicon. Silicon is an important constituent of electrical steel, modifying its resistivity and ferromagnetic properties.
Ceramics and glass. Silica is used to make fire brick, a type of ceramic. Silicate minerals are also in whiteware ceramics, an important class of products usually containing various types of fired clay minerals (natural aluminium phyllosilicates). An example is porcelain which is based on the silicate mineral kaolinite. Ceramics include art objects, and domestic, industrial and building products. Traditional glass (silica-based soda-lime glass) also functions in many of the same ways, and is also used for windows and containers. In addition, specialty silica based glass fibers are used for optical fiber, as well as The properties of silicon can be used to modify alloys fiberglass used for structural support and insulation. with metals other than iron. “Metallurgical grade” siliArtificial silicon compounds. Very occasional elemen- con is silicon of 95–99% purity. About 55% of the world tal silicon is found in nature, and also naturally-occurring consumption of metallurgical purity silicon goes for procompounds of silicon and carbon (silicon carbide) or ni- duction of aluminium-silicon alloys (silumin alloys) for trogen (silicon nitride) are found in stardust samples or aluminium part casts, mainly for use in the automotive meteorites in presolar grains, but the oxidizing conditions industry. Silicon’s importance in aluminium casting is
2.1. SILICON
41
that a significantly high amount (12%) of silicon in aluminium forms a eutectic mixture which solidifies with very little thermal contraction. This greatly reduces tearing and cracks formed from stress as casting alloys cool to solidity. Silicon also significantly improves the hardness and thus wear-resistance of aluminium.[17][18]
der the proper conditions. Silicon has become the most popular material to build both high power semiconductors and integrated circuits. The reason is that silicon is the semiconductor that can withstand the highest temperatures and electrical powers without becoming dysfunctional due to avalanche breakdown (a process in which an electron avalanche is created by a chain reaction process whereby heat produces free electrons and holes, which in turn produce more current which produces more heat). In Electronics addition, the insulating oxide of silicon is not soluble in water, which gives it an advantage over germanium (an Main article: Semiconductor device fabrication Since most elemental silicon produced remains as fer- element with similar properties which can also be used rosilicon alloy, only a relatively small amount (20%) of in semiconductor devices) in certain type of fabrication [58] the elemental silicon produced is refined to metallurgical techniques. grade purity (a total of 1.3–1.5 million metric tons/year). Monocrystalline silicon is expensive to produce, and is The fraction of silicon metal which is further refined to usually only justified in production of integrated circuits, semiconductor purity is estimated at only 15% of the where tiny crystal imperfections can interfere with tiny world production of metallurgical grade silicon.[18] How- circuit paths. For other uses, other types of pure silicon ever, the economic importance of this small very high- which do not exist as single crystals may be employed. purity fraction (especially the ~ 5% which is processed to These include hydrogenated amorphous silicon and upmonocrystalline silicon for use in integrated circuits) is graded metallurgical-grade silicon (UMG-Si) which are disproportionately large. used in the production of low-cost, large-area electronPure monocrystalline silicon is used to produce silicon ics in applications such as liquid crystal displays, and of wafers used in the semiconductor industry, in electron- large-area, low-cost, thin-film solar cells. Such semiics and in some high-cost and high-efficiency photovoltaic conductor grades of silicon which are either slightly less applications. In terms of charge conduction, pure sili- pure than those used in integrated circuits, or which are con is an intrinsic semiconductor which means that unlike produced in polycrystalline rather than monocrystalline metals it conducts electron holes and electrons that may form, make up roughly similar amount of silicon as are be released from atoms within the crystal by heat, and produced for the monocrystalline silicon semiconducthus increase silicon’s electrical conductivity with higher tor industry, or 75,000 to 150,000 metric tons per year. temperatures. Pure silicon has too low a conductivity However, production of such materials is growing more (i.e., too high a resistivity) to be used as a circuit element quickly than silicon for the integrated circuit market. By in electronics. In practice, pure silicon is doped with 2013 polycrystalline silicon production, used mostly in small concentrations of certain other elements, a pro- solar cells, is projected to reach 200,000 metric tons per cess that greatly increases its conductivity and adjusts its year, while monocrystalline semiconductor silicon proelectrical response by controlling the number and charge duction (used in computer microchips) remains below [18] (positive or negative) of activated carriers. Such control 50,000 tons/year. is necessary for transistors, solar cells, semiconductor detectors and other semiconductor devices, which are used in the computer industry and other technical applications. 2.1.6 Biological role For example, in silicon photonics, silicon can be used as a continuous wave Raman laser medium to produce co- Although silicon is readily available in the form of herent light, though it is ineffective as an everyday light silicates, very few organisms have a use for it. Diatoms, source. radiolaria and siliceous sponges use biogenic silica as In common integrated circuits, a wafer of monocrystalline silicon serves as a mechanical support for the circuits, which are created by doping, and insulated from each other by thin layers of silicon oxide, an insulator that is easily produced by exposing the element to oxygen un-
a structural material to construct skeletons. In more advanced plants, the silica phytoliths (opal phytoliths) are rigid microscopic bodies occurring in the cell; some plants, for example rice, need silicon for their growth.[59][60][61] The possible biological potential of sili-
42
CHAPTER 2. SEMICONDUCTOR MATERIALS
con as bioavailable orthosilicic acid and the potential beneficial effects on human health has been reviewed.[62]
[2] Physical Properties of Silicon. New Semiconductor Materials. Characteristics and Properties. Ioffe Institute
Silicon is needed for synthesis of elastin and collagen; the aorta contains the highest quantity of elastin and silicon.[63] Silicon is currently under consideration for elevation to the status of a “plant beneficial substance by the Association of American Plant Food Control Officials (AAPFCO).”[64][65] Silicon has been shown in university and field studies to improve plant cell wall strength and structural integrity,[66] improve drought and frost resistance, decrease lodging potential and boost the plant’s natural pest and disease fighting systems.[67] Silicon has also been shown to improve plant vigor and physiology by improving root mass and density, and increasing above ground plant biomass and crop yields.[66]
[3] Magnetic susceptibility of the elements and inorganic compounds, in Lide, D. R., ed. (2005). CRC Handbook of Chemistry and Physics (86th ed.). Boca Raton (FL): CRC Press. ISBN 0-8493-0486-5.
Hypothetical silicon-based lifeforms are the subject of silicon biochemistry, by analogy with carbon-based lifeforms. Silicon, being below carbon in the periodic table, is thought to have similar enough properties that would make silicon-based life possible, but much different from life as we know it.
2.1.7 See also • Amorphous silicon • Black silicon • Covalent superconductors • List of silicon producers • Monocrystalline silicon • Polycrystalline silicon • Printed silicon electronics • Silicon tombac • Silicon Valley • Silicon Wadi • Transistor
2.1.8 References [1] Ram, R. S. et al. (1998). “Fourier Transform Emission Spectroscopy of the A2D–X2P Transition of SiH and SiD”. J. Mol. Spectr. 190: 341–352. PMID 9668026.
[4] Hopcroft, Matthew A.; Nix, William D.; Kenny, Thomas W. (2010). “What is the Young’s Modulus of Silicon? extquotedbl. Journal of Microelectromechanical Systems 19 (2): 229. doi:10.1109/JMEMS.2009.2039697. [5] Weeks, Mary Elvira (1932). “The discovery of the elements: XII. Other elements isolated with the aid of potassium and sodium: beryllium, boron, silicon, and aluminum”. Journal of Chemical Education 9 (8): 1386–1412. Bibcode:1932JChEd...9.1386W. doi:10.1021/ed009p1386. [6] Voronkov, M. G. (2007). “Silicon era”. sian Journal of Applied Chemistry 80 (12): doi:10.1134/S1070427207120397.
Rus2190.
[7] Nave, R. Abundances of the Elements in the Earth’s Crust, Georgia State University [8] Nielsen, Forrest H. (1984). “Ultratrace Elements in Nutrition”. Annual Review of Nutrition 4: 21– 41. doi:10.1146/annurev.nu.04.070184.000321. PMID 6087860. [9] Cutter, Elizabeth G. (1978). Plant Anatomy. Part 1 Cells and Tissues (2 ed.). London: Edward Arnold. ISBN 0 7131 2639 6. [10] O'Mara, William C. (1990). Handbook of Semiconductor Silicon Technology. William Andrew Inc. pp. 349–352. ISBN 0-8155-1237-6. [11] Hull, Robert (1999). Properties of crystalline silicon. p. 421. ISBN 978-0-85296-933-5. [12] NNDC contributors (2008). Alejandro A. Sonzogni (Database Manager), ed. “Chart of Nuclides”. Upton (NY): National Nuclear Data Center, Brookhaven National Laboratory. Retrieved 2008-09-13. [13] Jerschow, Alexej. “Interactive NMR Frequency Map”. New York University. Retrieved 2011-10-20. [14] Geological Survey (U.S.) (1975). Geological Survey professional paper. [15] Anderson, Don L. (2007) New Theory of the Earth. Cambridge University Press. ISBN 978-0-521-84959-3, ISBN 0-521-84959-4
2.1. SILICON
[16] “Silicon Commodities Report 2011”. USGS. Retrieved 2011-10-20. [17] Apelian, D. (2009) Aluminum Cast Alloys: Enabling Tools for Improved Performance. North American Die Casting Association, Wheeling, Illinois. [18] Corathers, Lisa A. 2009 Minerals Yearbook. USGS [19] “Metallurgical silicon could become a rare commodity – just how quickly that happens depends to a certain extent on the current financial crisis”. Photon International. Retrieved 2009-03-04. [20] “Silicon”. usgs.gov. Retrieved 2008-02-20. [21] Rao, Gopalakrishna M. (1980). “Electrowinning of Silicon from K2 SiF6 -Molten Fluoride Systems”. Journal of the Electrochemical Society 127 (9): 1940. doi:10.1149/1.2130041. [22] De Mattei, Robert C. (1981). “Electrodeposition of Silicon at Temperatures above Its Melting Point”. Journal of the Electrochemical Society 128 (8): 1712. doi:10.1149/1.2127716. [23] Deville, H. St. C. (1854). “Recherches sur les métaux, et en particulier sur l'aluminium et sur une nouvelle forme du silicium”. Ann. Chim. Phys. 43: 31. [24] Siffert, Paul; Krimmel, E. F (2004). Silicon: Evolution and future of a technology. p. 33. ISBN 978-3-54040546-7. [25] Yasuda, Kouji; Saegusa, Kunio; Okabe, Toru H. (2010). “Production of Solar-grade Silicon by Halidothermic Reduction of Silicon Tetrachloride”. Metallurgical and Materials Transactions B 42: 37. Bibcode:2011MMTB...42...37Y. doi:10.1007/s11663010-9440-y. [26] Yasuda, Kouji; Okabe, Toru H. (2010). “Solargrade silicon production by metallothermic reduction”. JOM 62 (12): 94. Bibcode:2010JOM....62l..94Y. doi:10.1007/s11837-010-0190-8. [27] Van Der Linden, P. C.; De Jonge, J. (2010). “The preparation of pure silicon”. Recueil des Travaux Chimiques des Pays-Bas 78 (12): 962. doi:10.1002/recl.19590781204. [28] “Analyst silicon field trip”. hugin.info. March 28, 2007. Retrieved 2008-02-20. [29] High Purity Polysilicon – Schumacher Process. Peak Sun Silicon. Retrieved on 2011-08-07. [30] Greenwood 1997, pp. 335–337. [31] Greenwood 1997, p. 339.
43
[32] Greenwood 1997, p. 337. [33] Holleman, Arnold F.; Wiberg, Nils (2007). Lehrbuch der anorganischen Chemie (102 ed.). Berlin: de Gruyter. ISBN 3-11-017770-6. [34] Stone, F. G.; West, Robert (1996) Multiply Bonded Main Group Metals and Metalloids, Academic Press, ISBN 012-031139-9, p. 255 [35] Sekiguchi, A; Kinjo, R; Ichinohe, M (2004). “A stable compound containing a silicon-silicon triple bond”. Science 305 (5691): 1755–7. Bibcode:2004Sci...305.1755S. doi:10.1126/science.1102209. PMID 15375262. [36] Greenwood 1997, pp. 340–341. [37] Greenwood 1997, p. 342. [38] Greenwood 1997, p. 346. [39] Greenwood 1997, p. 344. [40] Greenwood 1997, pp. 359–360. [41] Greenwood 1997, p. 360. [42] Lickiss, Paul D. (1994). Inorganic Compounds of Silicon, in Encyclopedia of Inorganic Chemistry. John Wiley & Sons. pp. 3770–3805. ISBN 0-471-93620-0. [43] Greenwood 1997, pp. 364–365. [44] Mark, James. E (2005). Inorganic polymers. Oxford University Press. pp. 200–245. ISBN 0-19-513119-3. [45] In his table of the elements, Lavoisier listed five “salifiable earths” (i.e., ores that could be made to react with acids to produce salts (salis = salt, in Latin)): chaux (calcium oxide), magnésie (magnesia, magnesium oxide), baryte (barium sulfate), alumine (alumina, aluminium oxide), and silice (silica, silicon dioxide). About these “elements”, Lavoisier speculates: “We are probably only acquainted as yet with a part of the metallic substances existing in nature, as all those which have a stronger affinity to oxygen than carbon possesses, are incapable, hitherto, of being reduced to a metallic state, and consequently, being only presented to our observation under the form of oxyds, are confounded with earths. It is extremely probable that barytes, which we have just now arranged with earths, is in this situation; for in many experiments it exhibits properties nearly approaching to those of metallic bodies. It is even possible that all the substances we call earths may be only metallic oxyds, irreducible by any hitherto known process.” – from page 218 of: Lavoisier with Robert Kerr, trans., Elements of Chemistry, … , 4th ed. (Edinburgh, Scotland: William Creech, 1799). (The original passage appears in: Lavoisier, Traité Élémentaire de Chimie, … (Paris, France: Cuchet, 1789), vol. 1, page 174.)
44
CHAPTER 2. SEMICONDUCTOR MATERIALS
[46] Davy, Humphry (1808) “Electro chemical researches, on the decomposition of the earths; with observations on the metals obtained from the alkaline earths, and on the amalgam procured from ammonia,” Philosophical Transactions of the Royal Society [of London], 98 : 333–370. On page 353 Davy coins the name “silicium” : “Had I been so fortunate as to have obtained more certain evidences on this subject, and to have procured the metallic substances I was in search of, I should have proposed for them the names of silicium [silicon], alumium [aluminium], zirconium, and glucium [beryllium].”
• Reprinted in English in: Berzelius (1825) “On the mode of obtaining silicium, and on the characters and properties of that substance,” Philosophical Magazine, 65 (324) : 254–267.
[47] Gay-Lussac and Thenard, Recherches physico-chimiques … (Paris, France: Deterville, 1811), vol. 1, pages 313– 314 ; vol. 2, page 55–65. [48] Thomas Thomson, A System of Chemistry in Four Volumes, 5th ed. (London, England: Baldwin, Cradock, and Joy, 1817), vol. 1. From page 252: “The base of silica has been usually considered as a metal, and called silicium. But as there is not the smallest evidence for its metallic nature, and as it bears a close resemblance to boron and carbon, it is better to class it along with these bodies, and to give it the name of silicon.” [49] See: • Berzelius announced his discovery of silicon (“silicium”) in: Berzelius, J. (presented: 1823 ; published: 1824) “Undersökning af flusspatssyran och dess märkvärdigaste föreningar” (Investigation of hydrofluoric acid and of its most noteworthy compounds), Kongliga Vetenskaps-Academiens Handlingar [Proceedings of the Royal Science Academy], 12 : 46–98. The isolation of silicon and its characterization are detailed in the section titled “Flussspatssyrad kisseljords sönderdelning med kalium,” pages 46–68. • The above article was reprinted in German in: J. J. Berzelius (1824) extquotedblII. Untersuchungen über Flussspathsäure und deren merkwürdigsten Verbindungen extquotedbl (II. Investigations of hydrofluoric acid and its most noteworthy compounds), Annalen der Physik, 77 : 169–230. The isolation of silicon is detailed in the section titled: “Zersetzung der flussspaths. Kieselerde durch Kalium” (Decomposition of silicate fluoride by potassium), pages 204–210. • The above article was reprinted in French in: Berzelius (1824) “Décomposition du fluate de silice par le potassium” (Decomposition of silica fluoride by potassium), Annales de Chimie et de Physique, 27 : 337–359.
[50] Weeks, Mary Elvira (1932). “The discovery of the elements: XII. Other elements isolated with the aid of potassium and sodium: beryllium, boron, silicon, and aluminum”. Journal of Chemical Education 9 (8): 1386–1412. Bibcode:1932JChEd...9.1386W. doi:10.1021/ed009p1386. [51] Voronkov, M. G. (2007). “Silicon era”. sian Journal of Applied Chemistry 80 (12): doi:10.1134/S1070427207120397.
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[52] In 1854, Deville was trying to prepare aluminium metal from aluminium chloride that was heavily contaminated with silicon chloride. Deville used two methods to prepare aluminium: heating aluminium chloride with sodium metal in an inert atmosphere (of hydrogen); and melting aluminum chloride with sodium chloride and then electrolyzing the mixture. In both cases, pure silicon was produced: the silicon dissolved in the molten aluminium, but crystallized upon cooling. Dissolving the crude aluminum in hydrochloric acid revealed flakes of crystallized silicon. See: Henri Sainte-Claire Deville (1854) “Note sur deux procédés de préparation de l'aluminium et sur une nouvelle forme du silicium” (Note on two procedures for the preparation of aluminium and on a new form of silicon), Comptes rendus, 39 : 321–326. Subsequently Deville obtained crystalline silicon by heating the chloride or fluoride of silicon with sodium metal, isolating the amorphous silicon, then melting the amorphous form with salt and heating the mixture until most of the salt evaporated. See: H. Sainte-Claire Deville (1855) “Du silicium et du titane” (On silicon and titanium), Comptes rendus, 40 : 1034–1036. [53] Information on silicon – history, thermodynamic, chemical, physical and electronic properties: Etacude.com. Elements.etacude.com. Retrieved on 2011-08-07. [54] Silicon: History. Nautilus.fis.uc.pt. Retrieved on 201108-07. [55] Greenwood 1997, p. 356. [56] Koch, E.C.; Clement, D. (2007). “Special Materials in Pyrotechnics: VI. Silicon – An Old Fuel with New Perspectives”. Propellants, Explosives, Pyrotechnics 32 (3): 205. doi:10.1002/prep.200700021. [57] Walsh, Tim (2005). “Silly Putty”. Timeless toys: classic toys and the playmakers who created them. Andrews McMeel Publishing. ISBN 978-0-7407-5571-2.
2.2. GERMANIUM
[58] Semiconductors Without the Quantum Physics. Electropaedia [59] Rahman, Atta-ur-. “Silicon”. Studies in Natural Products Chemistry 35. p. 856. ISBN 978-0-444-53181-0. [60] Exley, C (1998). “Silicon in life:A bioinorganic solution to bioorganic essentiality”. Journal of Inorganic Biochemistry 69 (3): 139. doi:10.1016/S0162-0134(97)10010-1. [61] Epstein, Emanuel (1999). “SILICON”. Annual Review of Plant Physiology and Plant Molecular Biology 50: 641–664. doi:10.1146/annurev.arplant.50.1.641. PMID 15012222.
45 • Mineral.Galleries.com – Silicon • WebElements.com – Silicon • CDC – NIOSH Pocket Guide to Chemical Hazards
2.2 Germanium Not to be confused with Geranium.
Germanium is a chemical element with symbol Ge and atomic number 32. It is a lustrous, hard, grayish-white [62] Martin, Keith R. (2013). “Chapter 14. Silicon: The metalloid in the carbon group, chemically similar to its Health Benefi ts of a Metalloid”. In Astrid Sigel, Helmut group neighbors tin and silicon. Purified germanium is a Sigel and Roland K. O. Sigel. Interrelations between Essemiconductor, with an appearance most similar to elesential Metal Ions and Human Diseases. Metal Ions in Life mental silicon. Like silicon, germanium naturally reacts Sciences 13. Springer. pp. 451–473. doi:10.1007/978and forms complexes with oxygen in nature. Unlike sil94-007-7500-8_14. icon, it is too reactive to be found naturally on Earth in [63] LOEPER J., LOEPER J., FRAGNY M. The physiologi- the free (native) state. cal role of the silicon and its antiatheromatous action Biochemistry of silicon and related problems. Nobel Fondation Symposium 40. Edited by Gerd BENDZ and Ingvar LINDQVIST. Plenum Press. New York and London. 1978. ISBN 0-306-33710-X [64]
[65]
[66] [67]
Because very few minerals contain it in high concentration, germanium was discovered comparatively late in the history of chemistry. Germanium ranks near fiftieth in relative abundance of the elements in the Earth’s crust. In 1869, Dmitri Mendeleev predicted its existence “AAPFCO Board of Directors 2006 Mid-Year Meeting”. and some of its properties based on its position on his Association of American Plant Food Control Officials. periodic table and called the element ekasilicon. Nearly Retrieved 2011-07-18. two decades later, in 1886, Clemens Winkler found the Miranda, Stephen R.; Bruce Barker. “Silicon: Summary new element along with silver and sulfur, in a rare mineral of Extraction Methods”. Harsco Minerals. August 4, called argyrodite. Although the new element somewhat 2009. Retrieved 2011-07-18. resembled arsenic and antimony in appearance, its combining ratios in the new element’s compounds agreed with “Silicon nutrition in plants”. Plant Health Care,Inc.: 1. 12 Mendeleev’s predictions for a relative of silicon. Winkler December 2000. Retrieved 2011-07-01. named the element after his country, Germany. Today, Prakash, Dr. N.B. (2007). “Evaluation of the calcium sil- germanium is mined primarily from sphalerite (the priicate as a source of silicon in aerobic and wet rice”. Uni- mary ore of zinc), though germanium is also recovered versity of Agricultural Science Bangalore: 1. commercially from silver, lead, and copper ores.
Germanium “metal” (isolated germanium) is used as a semiconductor in transistors and various other electronic 2.1.9 Bibliography devices. Historically the first decade of semiconduc• Greenwood, Norman N; Earnshaw, Alan (1997). tor electronics was based entirely on germanium. ToChemistry of the Elements (2 ed.). Oxford: day, however, its production for use in semiconductor electronics is a small fraction (2%) of that of ultra-high Butterworth-Heinemann. ISBN 0-08-037941-9. purity silicon, which has largely replaced it. Presently, germanium’s major end uses are in fibre-optic systems, infrared optics and in solar cell applications. Germa2.1.10 External links nium compounds are also used for polymerization cat• Silicon at The Periodic Table of Videos (University alysts and have most recently found use in the producof Nottingham) tion of nanowires. This element forms a large number
46
CHAPTER 2. SEMICONDUCTOR MATERIALS
of organometallic compounds, such as tetraethylgermane, con” confirmed that it belonged in this place on the periwhich are useful in organometallic chemistry. odic table.[6][13] With further material from 500 kg of ore from the mines in Saxony, Winkler confirmed the chemiGermanium is not thought to be an essential element cal properties of the new element in 1887.[5][6][14] He also for any living organism. Some complexed organic gerdetermined an atomic weight of 72.32 by analyzing pure manium compounds are being investigated as possible germanium tetrachloride (GeCl pharmaceuticals, though none have yet proven success4), while Lecoq de Boisbaudran deduced 72.3 by a ful. Similar to silicon and aluminum, natural germacomparison of the lines in the spark spectrum of the nium compounds tend to be insoluble in water, and [15] element. thus have little oral toxicity. However, synthetic soluble germanium salts are nephrotoxic, and synthetic chemi- Winkler was able to prepare several new compounds cally reactive germanium compounds with halogens and of germanium, including its fluorides, chlorides, hydrogen are irritants and toxins. sulfides, germanium dioxide, and tetraethylgermane (Ge(C2 H5 )4 ), the first organogermane.[5] The physical data from these compounds — which corresponded well with Mendeleev’s predictions — made the discovery an 2.2.1 History important confirmation of Mendeleev’s idea of element periodicity. Here is a comparison between the prediction See also: History of the transistor and Winkler’s data:[5] In his report on The Periodic Law of the Chemical Elements, in 1869, the Russian chemist Dmitri Ivanovich Mendeleev predicted the existence of several unknown chemical elements, including one that would fill a gap in the carbon family in his Periodic Table of the Elements, located between silicon and tin.[3] Because of its position in his Periodic Table, Mendeleev called it ekasilicon (Es), and he estimated its atomic weight as about 72.0. In mid-1885, at a mine near Freiberg, Saxony, a new mineral was discovered and named argyrodite, because of its high silver content.[n 1] The chemist Clemens Winkler analyzed this new mineral, which proved to be a combination of silver, sulfur, and a new element. Winkler was able to isolate this new element and found it somewhat similar to antimony, in 1886.[5][6] Before Winkler published his results on the new element, he decided that he would name his element neptunium, since the recent discovery of planet Neptune in 1846 had been preceded by mathematical predictions of its existence.[n 2] However, the name “neptunium” had already been given to another proposed chemical element (though not the element that today bears the name neptunium, which was discovered in 1940),[n 3] so instead, Winkler named the new element germanium (from the Latin word, Germania, for Germany) in honor of his homeland.[6] Argyrodite proved empirically to be Ag8 GeS6 . Because this new element showed some similarities with the elements arsenic and antimony, its proper place in the periodic table was under consideration, but its similarities with Dmitri Mendeleev’s predicted element “ekasili-
Until the late 1930s, germanium was thought to be a poorly conducting metal.[16] Germanium did not become economically significant until after 1945, when its properties as a semiconductor were recognized as being useful in electronics. During World War II, small amounts of germanium had begun to be used in some special electronic devices, mostly diodes.[17][18] Its first major use was the point-contact Schottky diodes for radar pulse detection during the War.[16] The first silicon-germanium alloys were obtained in 1955.[19] Before 1945, only a few hundred kilograms of germanium were produced in smelters each year, but by the end of the 1950s, the annual worldwide production had reached 40 metric tons.[20] The development of the germanium transistor in 1948[21] opened the door to countless applications of solid state electronics.[22] From 1950 through the early 1970s, this area provided an increasing market for germanium, but then high-purity silicon began replacing germanium in transistors, diodes, and rectifiers.[23] For example, the company that became Fairchild Semiconductor was founded in 1957 with the express purpose of producing silicon transistors. Silicon has superior electrical properties, but it requires much greater purity, which could not be commercially achieved in the early years of semiconductor electronics.[24] Meanwhile, the demand for germanium for use in fiber optics communication networks, infrared night vision systems, and polymerization catalysts increased dramatically.[20] These end uses represented 85% of
2.2. GERMANIUM worldwide germanium consumption in 2000.[23] The US government even designated germanium as a strategic and critical material, calling for a 146 ton (132 t) supply in the national defense stockpile in 1987.[20] Germanium differs from silicon in that the supply for germanium is limited by the availability of exploitable sources, while the supply of silicon is only limited by production capacity since silicon comes from ordinary sand or quartz. As a result, while silicon could be bought in 1998 for less than $10 per kg,[20] the price of 1 kg of germanium was then almost $800.[20]
2.2.2
Characteristics
Under standard conditions germanium is a brittle, silverywhite, semi-metallic element.[25] This form constitutes an allotrope technically known as α-germanium, which has a metallic luster and a diamond cubic crystal structure, the same as diamond.[23] At pressures above 120 kbar, a different allotrope known as β-germanium forms, which has the same structure as β-tin.[26] Along with silicon, gallium, bismuth, antimony, and water, it is one of the few substances that expands as it solidifies (i.e. freezes) from its molten state.[26] Germanium is a semiconductor. Zone refining techniques have led to the production of crystalline germanium for semiconductors that has an impurity of only one part in 1010 ,[27] making it one of the purest materials ever obtained.[28] The first metallic material discovered (in 2005) to become a superconductor in the presence of an extremely strong electromagnetic field was an alloy of germanium with uranium and rhodium.[29] Pure germanium is known to spontaneously extrude very long screw dislocations. They are one of the primary reasons for the failure of older diodes and transistors made from germanium; depending on what they eventually touch, they may lead to an electrical short. Chemistry Elemental germanium oxidizes slowly to GeO2 at 250 °C.[30] Germanium is insoluble in dilute acids and alkalis but dissolves slowly in concentrated sulfuric acid and reacts violently with molten alkalis to produce germanates ([GeO 3]2− ). Germanium occurs mostly in the oxidation state +4 al-
47 though many compounds are known with the oxidation state of +2.[31] Other oxidation states are rare, such as +3 found in compounds such as Ge2 Cl6 , and +3 and +1 observed on the surface of oxides,[32] or negative oxidation states in germanes, such as −4 in GeH 4. Germanium cluster anions (Zintl ions) such as Ge4 2− , Ge9 4− , Ge9 2− , [(Ge9 )2 ]6− have been prepared by the extraction from alloys containing alkali metals and germanium in liquid ammonia in the presence of ethylenediamine or a cryptand.[31][33] The oxidation states of the element in these ions are not integers— similar to the ozonides O3 − . Two oxides of germanium are known: germanium dioxide (GeO 2, germania) and germanium monoxide, (GeO).[26] The dioxide, GeO2 can be obtained by roasting germanium disulfide (GeS 2), and is a white powder that is only slightly soluble in water but reacts with alkalis to form germanates.[26] The monoxide, germanous oxide, can be obtained by the high temperature reaction of GeO2 with Ge metal.[26] The dioxide (and the related oxides and germanates) exhibits the unusual property of having a high refractive index for visible light, but transparency to infrared light.[34][35] Bismuth germanate, Bi4 Ge3 O12 , (BGO) is used as a scintillator.[36] Binary compounds with other chalcogens are also known, such as the disulfide (GeS 2), diselenide (GeSe 2), and the monosulfide (GeS), selenide (GeSe), and telluride (GeTe).[31] GeS2 forms as a white precipitate when hydrogen sulfide is passed through strongly acid solutions containing Ge(IV).[31] The disulfide is appreciably soluble in water and in solutions of caustic alkalis or alkaline sulfides. Nevertheless, it is not soluble in acidic water, which allowed Winkler to discover the element.[37] By heating the disulfide in a current of hydrogen, the monosulfide (GeS) is formed, which sublimes in thin plates of a dark color and metallic luster, and is soluble in solutions of the caustic alkalis.[26] Upon melting with alkaline carbonates and sulfur, germanium compounds form salts known as thiogermanates.[38] Four tetrahalides are known. Under normal conditions GeI4 is a solid, GeF4 a gas and the others volatile liquids. For example, germanium tetrachloride, GeCl4 , is obtained as a colorless fuming liquid boiling at 83.1 °C by heating the metal with chlorine.[26] All the tetrahalides are readily hydrolyzed to hydrated germanium
48 dioxide.[26] GeCl4 is used in the production of organogermanium compounds.[31] All four dihalides are known and in contrast to the tetrahalides are polymeric solids.[31] Additionally Ge2 Cl6 and some higher compounds of formula GenCl₂n₊₂ are known.[26] The unusual compound Ge6 Cl16 has been prepared that contains the Ge5 Cl12 unit with a neopentane structure.[39]
CHAPTER 2. SEMICONDUCTOR MATERIALS Isotopes Main article: Isotopes of germanium Germanium has five naturally occurring isotopes, 70Ge, 72Ge, 73Ge, 74Ge, 76Ge. Of these, 76Ge is very slightly radioactive, decaying by double beta decay with a halflife of 1.78×1021 years. 74Ge is the most common isotope, having a natural abundance of approximately 36%. 76Ge is the least common with a natural abundance of approximately 7%.[44] When bombarded with alpha particles, the isotope 72Ge will generate stable 77Se, releasing high energy electrons in the process.[45] Because of this, it is used in combination with radon for nuclear batteries.[45]
Germane (GeH4 ) is a compound similar in structure to methane. Polygermanes—compounds that are similar to alkanes—with formula GenH₂n₊₂ containing up to five germanium atoms are known.[31] The germanes are less volatile and less reactive than their corresponding silicon analogues.[31] GeH4 reacts with alkali metals in liquid ammonia to form white crystalline MGeH3 which contain the GeH3 − anion.[31] The germanium hydrohalides with one, two and three halogen atoms are colorless reAt least 27 radioisotopes have also been synthesized rangactive liquids.[31] ing in atomic mass from 58 to 89. The most stable of The first organogermanium compound was synthesized these is 68Ge, decaying by electron capture with a halfby Winkler in 1887; the reaction of germanium tetrachlo- life of 270.95 d. The least stable is 60Ge with a half-life ride with diethylzinc yielded tetraethylgermane (Ge(C of 30 ms. While most of germanium’s radioisotopes de2H cay by beta decay, 61Ge and 64Ge decay by β+ delayed 5) proton emission.[44] 84Ge through 87Ge isotopes also ex4).[5] Organogermanes of the type R4 Ge (where R is an hibit minor β− delayed neutron emission decay paths.[44] alkyl) such as tetramethylgermane (Ge(CH 3) 4) and tetraethylgermane are accessed through the cheapest available germanium precursor germanium tetrachloride and alkyl nucleophiles. Organic germanium hydrides Occurrence such as isobutylgermane ((CH 3) Germanium is created through stellar nucleosynthesis, 2CHCH mostly by the s-process in asymptotic giant branch stars. 2GeH The s-process is a slow neutron capture of lighter el3) were found to be less hazardous and may be ements inside pulsating red giant stars.[46] Germanium used as a liquid substitute for toxic germane gas has been detected in the atmosphere of Jupiter[47] and in semiconductor applications. Many germanium in some of the most distant stars.[48] Its abundance in the reactive intermediates are known: germyl free radicals, Earth’s crust is approximately 1.6 ppm.[49] There are only germylenes (similar to carbenes), and germynes (similar a few minerals like argyrodite, briartite, germanite, and to carbynes).[40][41] The organogermanium compound 2- renierite that contain appreciable amounts of germanium, carboxyethylgermasesquioxane was first reported in the but no mineable deposits exist for any of them.[23][50] 1970s, and for a while was used as a dietary supplement Some zinc-copper-lead ore bodies contain enough gerand thought to possibly have anti-tumor qualities.[42] manium that it can be extracted from the final ore [49] Using a ligand called Eind (1,1,3,3,5,5,7,7-octaethyl-s- concentrate. An unusual enrichment process causes a hydrindacen-4-yl) germanium is able to form a double high content of germanium in some coal seams, which was discovered by Victor Moritz Goldschmidt during a bond with oxygen (germanone).[43] broad survey for germanium deposits.[51][52] The highest concentration ever found was in the Hartley coal ash with up to 1.6% of germanium.[51][52] The coal deposits near Xilinhaote, Inner Mongolia, contain an estimated 1600 tonnes of germanium.[49]
2.2. GERMANIUM
2.2.3
Production
49 oxide is reduced by the reaction with hydrogen to obtain germanium suitable for the infrared optics or semiconductor industry:
About 118 tonnes of germanium was produced in 2011 worldwide, mostly in China (80 t), Russia (5 t) and United States (3 t).[23] Germanium is recovered as a byGeO2 + 2 H2 → Ge + 2 H2 O product from sphalerite zinc ores where it is concentrated in amounts of up to 0.3%,[53] especially from sedimentindustrial hosted, massive Zn–Pb–Cu(–Ba) deposits and carbonate- The germanium for steel production and other [56] processes is normally reduced using carbon: hosted Zn–Pb deposits. Figures for worldwide Ge reserves are not available, but in the US it is estimated at GeO2 + C → Ge + CO2 450 tonnes.[23] In 2007 35% of the demand was met by recycled germanium.[49] While it is produced mainly from sphalerite, it is also found in silver, lead, and copper ores. Another source of germanium is fly ash of coal power plants which use coal from certain coal deposits with a large concentration of germanium. Russia and China used this as a source for germanium.[54] Russia’s deposits are located in the far east of the country on Sakhalin Island. The coal mines northeast of Vladivostok have also been used as a germanium source. The deposits in China are mainly located in the lignite mines near Lincang, Yunnan; coal mines near Xilinhaote, Inner Mongolia are also used.[49]
2.2.4 Applications The major end uses for germanium in 2007, worldwide, were estimated to be: 35% for fiber-optic systems, 30% infrared optics, 15% for polymerization catalysts, and 15% for electronics and solar electric applications.[23] The remaining 5% went into other uses such as phosphors, metallurgy, and chemotherapy.[23] Optics
The ore concentrates are mostly sulfidic; they are converted to the oxides by heating under air, in a process The most notable physical characteristics of germania (GeO2 ) are its high index of refraction and its low optical known as roasting: dispersion. These make it especially useful for wideangle camera lenses, microscopy, and for the core part GeS2 + 3 O2 → GeO2 + 2 SO2 of optical fibers.[57][58] It also replaced titania as the silica dopant for silica fiber, eliminating the need for subPart of the germanium ends up in the dust produced dur- sequent heat treatment, which made the fibers brittle.[59] ing this process, while the rest is converted to germanates At the end of 2002 the fiber optics industry accounted for which are leached together with the zinc from the cin- 60% of the annual germanium use in the United States, der by sulfuric acid. After neutralization only the zinc but this use accounts for less than 10% of world wide stays in solution and the precipitate contains the germa- consumption.[58] GeSbTe is a phase change material used nium and other metals. After reducing the amount of for its optic properties, such as in rewritable DVDs.[60] zinc in the precipitate by the Waelz process, the residing Waelz oxide is leached a second time. The dioxide is ob- Because germanium is transparent in the infrared it is tained as precipitate and converted with chlorine gas or a very important infrared optical material, that can be hydrochloric acid to germanium tetrachloride, which has readily cut and polished into lenses and windows. It is especially used as the front optic in thermal imaga low boiling point and can be distilled off:[54] ing cameras working in the 8 to 14 micron wavelength range for passive thermal imaging and for hot-spot deGeO2 + 4 HCl → GeCl4 + 2 H2 O tection in military, night vision system in cars, and fire GeO2 + 2 Cl2 → GeCl4 + O2 fighting applications.[56] It is therefore used in infrared spectroscopes and other optical equipment which require Germanium tetrachloride is either hydrolyzed to the ox- extremely sensitive infrared detectors.[58] The material ide (GeO2 ) or purified by fractional distillation and then has a very high refractive index (4.0) and so needs to hydrolyzed.[54] The highly pure GeO2 is now suitable for be anti-reflection coated. Particularly, a very hard spethe production of germanium glass. The pure germanium cial antireflection coating of diamond-like carbon (DLC),
50
CHAPTER 2. SEMICONDUCTOR MATERIALS
refractive index 2.0, is a good match and produces a cious metal alloys. In sterling silver alloys, for instance, it diamond-hard surface that can withstand much environ- has been found to reduce firescale, increase tarnish resismental rough treatment.[61][62] tance, and increase the alloy’s response to precipitation hardening. A tarnish-proof sterling silver alloy, trademarked Argentium, contains 1.2% germanium.[23] Electronics High purity germanium single crystal detectors can preSilicon-germanium alloys are rapidly becoming an im- cisely identify radiation sources—for example in airport [69] Germanium is useful for monochromators portant semiconductor material, for use in high-speed security. integrated circuits. Circuits utilizing the properties of for beamlines used in single crystal neutron scattering Si-SiGe junctions can be much faster than those using and synchrotron X-ray diffraction. The reflectivity has silicon alone.[63] Silicon-germanium is beginning to re- advantages over silicon in neutron and high energy X[70] Crystals of high purity germanium place gallium arsenide (GaAs) in wireless communica- ray applications. [23] tions devices. The SiGe chips, with high-speed prop- are used in detectors for gamma spectroscopy and the [71] The slightly radioactive Gererties, can be made with low-cost, well-established pro- search for dark matter. [23] manium 76, which decays only through double-beta deduction techniques of the silicon chip industry. cay, is used to study that process (for example, in the onThe recent rise in energy cost has improved the eco- going MAJORANA demonstrator experiment). nomics of solar panels, a potential major new use of germanium.[23] Germanium is the substrate of the wafers for high-efficiency multijunction photovoltaic cells for Inorganic germanium and health hazard space applications. Because germanium and gallium arsenide have very sim- Inorganic germanium and organic germanium are differilar lattice constants, germanium substrates can be used ent chemical compounds of germanium and their properto make gallium arsenide solar cells.[64] The Mars Ex- ties are different. Inorganic germanium will accumulate ploration Rovers and several satellites use triple junction inside the body and will impose health hazards after consumed. Organic germanium is reported to be potentially gallium arsenide on germanium cells.[65] beneficial for health.[72] Germanium-on-insulator substrates are seen as a potential replacement for silicon on miniaturized chips.[23] Germanium is not thought to be essential to the health Other uses in electronics include phosphors in fluorescent of plants or animals. Germanium in the environment lamps,[27] and germanium-base solid-state light-emitting has little or no health impact. This is primarily bediodes (LEDs).[23] Germanium transistors are still used in cause it usually occurs only as a trace element in ores some effects pedals by musicians who wish to reproduce and carbonaceous materials, and is used in very small in its varithe distinctive tonal character of the “fuzz extquotedbl- quantities that are not likely to be ingested, [23] ous industrial and electronic applications. For similar tone from the early rock and roll era, most notably the reasons, germanium in end-uses has little impact on the [66] Dallas Arbiter Fuzz Face. environment as a biohazard. Some reactive intermediate compounds of germanium are poisonous (see precautions, below).[73] Other uses As early as 1922, doctors in the United States used the inorganic form of germanium to treat patients with anemia.[73] It was used in other forms of treatments, such as a purported immune system booster, but its efficiency has been dubious. Its role in cancer treatments has been debated, with the American Cancer Society contending that no anticancer effects have been demonstrated.[74][75] U.S. Food and Drug Administration research has concluded that inorganic germanium, when used as a nutritional supplement, “presents potential huIn recent years germanium has seen increasing use in pre- man health hazard extquotedbl.[42]
Germanium dioxide is also used in catalysts for polymerization in the production of polyethylene terephthalate (PET).[67] The high brilliance of the produced polyester is especially used for PET bottles marketed in Japan.[67] However, in the United States, no germanium is used for polymerization catalysts.[23] Due to the similarity between silica (SiO2 ) and germanium dioxide (GeO2 ), the silica stationary phase in some gas chromatography columns can be replaced by GeO2 .[68]
2.2. GERMANIUM
51
Certain germanium compounds are available in low dose [3] R. Hermann published claims in 1877 of his discovery of a new element beneath tantalum in the periodic table, which in the U.S. as nonprescription dietary “supplements” in he named neptunium, after the Greek god of the oceans oral capsules or tablets. Other germanium compounds and seas.[9][10] However this metal was later recognized to have been administered by alternative medical practibe an alloy of the elements niobium and tantalum.[11] The tioners as non-FDA-allowed injectable solutions. Soluname extquotedblneptunium extquotedbl was much later ble inorganic forms of germanium used at first, notably given to the synthetic element one step past uranium in the the citrate-lactate salt, led to a number of cases of renal Periodic Table, which was discovered by nuclear physics dysfunction, hepatic steatosis and peripheral neuropathy researchers in 1940.[12] in individuals using them on a chronic basis. Plasma and urine germanium concentrations in these individuals, several of whom died, were several orders of mag- 2.2.8 References nitude greater than endogenous levels. A more recent organic form, beta-carboxyethylgermanium sesquioxide [1] Magnetic susceptibility of the elements and inorganic compounds, in Handbook of Chemistry and Physics 81st (propagermanium), has not exhibited the same spectrum edition, CRC press. of toxic effects.[76] Certain compounds of germanium have low toxicity to mammals, but have toxic effects against certain bacteria.[25]
2.2.5
Precautions for chemically reactive germanium compounds
Some of germanium’s artificially-produced compounds are quite reactive and present an immediate hazard to human health on exposure. For example, germanium chloride and germane (GeH4 ) are a liquid and gas, respectively, that can be very irritating to the eyes, skin, lungs, and throat.[72]
2.2.6
See also
• Transistor • Vitrain
2.2.7
Footnotes
[1] From Greek, argyrodite means silver-containing.[4] [2] Just as the existence of the new element had been predicted, the existence of the planet Neptune had been predicted in about 1843 by the two mathematicians John Couch Adams and Urbain Le Verrier, using the calculation methods of celestial mechanics. They did this in attempts to explain the fact that the planet Uranus, upon very close observation, appeared to be being pulled slightly out of position in the sky.[7] James Challis started searching for it in July 1846, and he sighted this planet on September 23, 1846.[8]
[2] “Properties of Germanium”. Ioffe Institute. [3] Kaji, Masanori (2002). “D. I. Mendeleev’s concept of chemical elements and The Principles of Chemistry extquotedbl (PDF). Bulletin for the History of Chemistry 27 (1): 4–16. Retrieved 2008-08-20. [4] (PDF) Argyrodite—Ag 8GeS 6 (Report). Mineral Data Publishing. http://www. handbookofmineralogy.org/pdfs/argyrodite.pdf. Retrieved 2008-09-01. [5] Winkler, Clemens (1887). “Mittheilungen über des Germanium. Zweite Abhandlung”. J. Prak. Chemie (in German) 36 (1): 177–209. doi:10.1002/prac.18870360119. Retrieved 2008-08-20. [6] Winkler, Clemens (1887). “Germanium, Ge, a New Nonmetal Element”. Berichte der deutschen chemischen Gesellschaft (in German) 19 (1): 210–211. doi:10.1002/cber.18860190156. English translation at the Wayback Machine (archived December 7, 2008) [7] Adams, J. C. (November 13, 1846). “Explanation of the observed irregularities in the motion of Uranus, on the hypothesis of disturbance by a more distant planet”. Monthly Notices of the Royal Astronomical Society (Blackwell Publishing) 7: 149. Bibcode:1846MNRAS...7..149A. [8] Challis, Rev. J. (November 13, 1846). “Account of observations at the Cambridge observatory for detecting the planet exterior to Uranus”. Monthly Notices of the Royal Astronomical Society (Blackwell Publishing) 7: 145–149. Bibcode:1846MNRAS...7..145C. [9] Sears, Robert (July 1877). “Scientific Miscellany”. The Galaxy (Columbus, O[hio]: Siebert & Lilley) 24 (1): 131. ISBN 0-665-50166-8. OCLC 16890343 243523661 77121148.
52
[10] “Editor’s Scientific Record”. Harper’s new monthly magazine 55 (325): 152–153. June 1877. [11] van der Krogt, Peter. “Elementymology & Elements Multidict: Niobium”. Retrieved 2008-08-20. [12] Westgren, A. (1964). “The Nobel Prize in Chemistry 1951: presentation speech”. Nobel Lectures, Chemistry 1942–1962. Elsevier. [13] “Germanium, a New Non-Metallic Element”. The Manufacturer and Builder: 181. 1887. Retrieved 2008-08-20. [14] Brunck, O. (1886). “Obituary: Clemens Winkler”. Berichte der deutschen chemischen Gesellschaft (in German) 39 (4): 4491–4548. doi:10.1002/cber.190603904164. [15] de Boisbaudran, M. Lecoq (1886). “Sur le poids atomique du germanium”. Comptes rendus (in French) 103: 452. Retrieved 2008-08-20. [16] Haller, E. E. “Germanium: From Its Discovery to SiGe Devices” (PDF). Department of Materials Science and Engineering, University of California, Berkeley, and Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley,. Retrieved 2008-08-22. [17] W. K. (1953-05-10). “Germanium for Electronic Devices”. NY Times. Retrieved 2008-08-22.
CHAPTER 2. SEMICONDUCTOR MATERIALS
[25] Emsley, John (2001). Nature’s Building Blocks. Oxford: Oxford University Press. pp. 506–510. ISBN 0-19850341-5. [26] Holleman, A. F.; Wiberg, E.; Wiberg, N. (2007). Lehrbuch der Anorganischen Chemie, 102nd ed. de Gruyter. ISBN 978-3-11-017770-1. OCLC 145623740 180963521 219549154. [27] “Germanium”. Los Alamos National Laboratory. Retrieved 2008-08-28. [28] Chardin, B. (2001). “Dark Matter: Direct Detection”. In Binetruy, B. The Primordial Universe: 28 June – 23 July 1999. Springer. p. 308. ISBN 3-540-41046-5. [29] Lévy, F.; Sheikin, I.; Grenier, B.; Huxley, Ad. (August 2005). “Magnetic field-induced superconductivity in the ferromagnet URhGe”. Science 309 (5739): 1343–1346. Bibcode:2005Sci...309.1343L. doi:10.1126/science.1115498. PMID 16123293. [30] Tabet, N; Salim, Mushtaq A. (1998). “KRXPS study of the oxidation of Ge(001) surface”. Applied Surface Science 134 (1–4): 275. Bibcode:1998ApSS..134..275T. doi:10.1016/S0169-4332(98)00251-7. [31] Greenwood, Norman N.; Earnshaw, Alan (1997). Chemistry of the Elements (2nd ed.). Butterworth-Heinemann. ISBN 0080379419.
[19] “SiGe History”. University of Cambridge. Retrieved 2008-08-22.
[32] Tabet, N; Salim, M.A; Al-Oteibi, A.L (1999). “XPS study of the growth kinetics of thin films obtained by thermal oxidation of germanium substrates”. Journal of Electron Spectroscopy and Related Phenomena. 101–103: 233. doi:10.1016/S0368-2048(98)00451-4.
[20] Halford, Bethany (2003). “Germanium”. Chemical & Engineering News (American Chemical Society). Retrieved 2008-08-22.
[33] Xu, Li; Sevov, Slavi C. (1999). “Oxidative Coupling of Deltahedral [Ge9 ]4− Zintl Ions”. J. Am. Chem. Soc. 121 (39): 9245–9246. doi:10.1021/ja992269s.
[21] Bardeen, J.; Brattain, W. H. (1948). “The Transistor, A Semi-Conductor Triode”. Physical Reviews 74 (2): 230–231. Bibcode:1948PhRv...74..230B. doi:10.1103/PhysRev.74.230.
[34] Bayya, Shyam S.; Sanghera, Jasbinder S.; Aggarwal, Ishwar D.; Wojcik, Joshua A. (2002). “Infrared Transparent Germanate Glass-Ceramics”. Journal of the American Ceramic Society 85 (12): 3114–3116. doi:10.1111/j.1151-2916.2002.tb00594.x.
[18] “1941 – Semiconductor diode rectifiers serve in WW II”. Computer History Museum. Retrieved 2008-08-22.
[22] “Electronics History 4 – Transistors”. National Academy of Engineering. Retrieved 2008-08-22. [23] U.S. Geological Survey (2008). “Germanium—Statistics and Information”. U.S. Geological Survey, Mineral Commodity Summaries. Retrieved 2008-08-28. “Select 2008” [24] Teal, Gordon K. (July 1976). “Single Crystals of Germanium and Silicon-Basic to the Transistor and Integrated Circuit”. IEEE Transactions on Electron Devices. ED-23 (7): 621–639. doi:10.1109/T-ED.1976.18464.
[35] Drugoveiko, O. P.; Evstrop'ev, K. K.; Kondrat'eva, B. S.; Petrov, Yu. A.; Shevyakov, A. M. (1975). “Infrared reflectance and transmission spectra of germanium dioxide and its hydrolysis products”. Journal of Applied Spectroscopy 22 (2): 191. Bibcode:1975JApSp..22..191D. doi:10.1007/BF00614256. [36] Lightstone, A. W.; McIntyre, R. J.; Lecomte, R.; Schmitt, D. (1986). “A Bismuth Germanate-Avalanche Photodiode Module Designed for Use in High Resolution Positron
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Emission Tomography”. IEEE Transactions on Nuclear Science 33 (1): 456–459. Bibcode:1986ITNS...33..456L. doi:10.1109/TNS.1986.4337142.
H2 O/ and the Jovian D/H isotopic ratio”. Astrophysical Journal 263: 443–467. Bibcode:1982ApJ...263..443K. doi:10.1086/160516.
[37] Johnson, Otto H. (1952). “Germanium and its Inorganic Compounds”. Chem. Rev. 3 (3): 431. doi:10.1021/cr60160a002.
[48] Cowan, John (2003-05-01). “Astronomy: Elements of surprise”. Nature 423 (29): 29. Bibcode:2003Natur.423...29C. doi:10.1038/423029a. PMID 12721614.
[38] Fröba, Michael; Oberender, Nadine (1997). “First synthesis of mesostructured thiogermanates”. Chemical Communications (18): 1729. doi:10.1039/a703634e. [39] Beattie, I.R.; Jones, P.J.; Reid, G.; Webster, M.; (1998). “The Crystal Structure and Raman Spectrum of Ge5 Cl12 ·GeCl4 and the Vibrational Spectrum of Ge2 Cl6 extquotedbl. Inorg. Chem. 37 (23): 6032–6034. doi:10.1021/ic9807341. PMID 11670739. [40] Satge, Jacques (1984). “Reactive intermediates in organogermanium chemistry”. Pure & Appl. Chem. 56 (1): 137–150. doi:10.1351/pac198456010137. [41] Quane, Denis; Bottei, Rudolph S. (1963). “Organogermanium Chemistry”. Chemical Reviews 63 (4): 403–442. doi:10.1021/cr60224a004. [42] Tao, S. H.; Bolger, P. M. (June 1997). “Hazard Assessment of Germanium Supplements”. Regulatory Toxicology and Pharmacology 25 (3): 211–219. doi:10.1006/rtph.1997.1098. PMID 9237323. [43] Broadwith, Phillip (25 March 2012). “Germaniumoxygen double bond takes centre stage”. Chemistry World. Retrieved 2014-05-15. [44] Audi, G.; Bersillon, O.; Blachot, J.; Wapstra, A.H. (2003). “Nubase2003 Evaluation of Nuclear and Decay Properties”. Nuclear Physics A (Atomic Mass Data Center) 729 (1): 3–128. Bibcode:2003NuPhA.729....3A. doi:10.1016/j.nuclphysa.2003.11.001. [45] Perreault, Bruce A. “Alpha Fusion Electrical Energy Valve”, US Patent 7800286, issued September 21, 2010. PDF copy at the Wayback Machine (archived October 12, 2007). [46] Sterling, N. C.; Dinerstein, Harriet L.; Bowers, Charles W. (2002). “Discovery of Enhanced Germanium Abundances in Planetary Nebulae with the Far Ultraviolet Spectroscopic Explorer”. The Astrophysical Journal Letters 578 (1): L55–L58. arXiv:astro-ph/0208516. Bibcode:2002ApJ...578L..55S. doi:10.1086/344473. [47] Kunde, V.; Hanel, R.; Maguire, W.; Gautier, D.; Baluteau, J. P.; Marten, A.; Chedin, A.; Husson, N.; Scott, N. (1982). “The tropospheric gas composition of Jupiter’s north equatorial belt /NH3 , PH3 , CH3 D, GeH4 ,
[49] Höll, R.; Kling, M.; Schroll, E. (2007). “Metallogenesis of germanium—A review”. Ore Geology Reviews 30 (3– 4): 145–180. doi:10.1016/j.oregeorev.2005.07.034. [50] Lifton, Jack (2007-04-26). “Byproducts II: Another Germanium Rush? extquotedbl. Resource Investor.com. Retrieved 2008-09-09. [51] Goldschmidt, V. M. (1930). “Ueber das Vorkommen des Germaniums in Steinkohlen und Steinkohlenprodukten”. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse: 141–167. [52] Goldschmidt, V. M.; Peters, Cl. (1933). “Zur Geochemie des Germaniums”. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse: 141–167. [53] Bernstein, L (1985). “Germanium geochemistry and mineralogy”. Geochimica et Cosmochimica Acta 49 (11): 2409. Bibcode:1985GeCoA..49.2409B. doi:10.1016/0016-7037(85)90241-8. [54] Naumov, A. V. (2007). “World market of germanium and its prospects”. Russian Journal of Non-Ferrous Metals 48 (4): 265–272. doi:10.3103/S1067821207040049. [55] R.N. Soar (1977). “USGS Minerals Information”. U.S. Geological Survey Mineral Commodity Summaries (U.S. Geological Survey). January 2003, January 2004, January 2005, January 2006, January 2007,January 2010. ISBN 0-85934-039-2. OCLC 16437701. [56] Moskalyk, R. R. (2004). “Review of germanium processing worldwide”. Minerals Engineering 17 (3): 393–402. doi:10.1016/j.mineng.2003.11.014. [57] Rieke, G.H. (2007). “Infrared Detector Arrays for Astronomy”. Annual Review of Astronomy and Astrophysics 45 (1): 77. Bibcode:2007ARA&A..45...77R. doi:10.1146/annurev.astro.44.051905.092436. [58] Brown, Jr., Robert D. (2000). “Germanium” (PDF). U.S. Geological Survey. Retrieved 2008-09-22. [59] “Chapter III: Optical Fiber For Communications”. Stanford Research Institute. Retrieved 2008-08-22.
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[60] “Understanding Recordable & Rewritable DVD First Edition” (PDF). Optical Storage Technology Association (OSTA). Archived from the original on 2009-04-19. Retrieved 2008-09-22.
(1996). “Optimization of Germanium for Neutron Diffractometers”. International Journal of Modern Physics E 5 (1): 131. Bibcode:1996IJMPE...5..131A. doi:10.1142/S0218301396000062.
[61] Lettington, Alan H. (1998). “Applications of diamondlike carbon thin films”. Carbon 36 (5–6): 555–560. doi:10.1016/S0008-6223(98)00062-1.
[71] Diehl, R.; Prantzos, N; Vonballmoos, P (2006). “Astrophysical constraints from gamma-ray spectroscopy”. Nuclear Physics A 777: 70. arXiv:astroph/0502324. Bibcode:2006NuPhA.777...70D. doi:10.1016/j.nuclphysa.2005.02.155.
[62] Gardos, Michael N.; Bonnie L. Soriano; Steven H. Propst (1990). “Study on correlating rain erosion resistance with sliding abrasion resistance of DLC on germanium”. In Feldman, Albert; Holly, Sandor. Proc. SPIE. SPIE Proceedings 1325 (Mechanical Properties): 99. doi:10.1117/12.22449. [63] Washio, K. (2003). “SiGe HBT and BiCMOS technologies for optical transmission and wireless communication systems”. IEEE Transactions on Electron Devices 50 (3): 656. Bibcode:2003ITED...50..656W. doi:10.1109/TED.2003.810484. [64] Bailey, Sheila G.; Raffaelle, Ryne; Emery, Keith (2002). “Space and terrestrial photovoltaics: synergy and diversity”. Progress in Photovoltaics Research and Applications 10 (6): 399. doi:10.1002/pip.446. [65] Crisp, D.; Pathare, A.; Ewell, R. C. (2004). “The performance of gallium arsenide/germanium solar cells at the Martian surface”. Acta Astronautica 54 (2): 83–101. Bibcode:2004AcAau..54...83C. doi:10.1016/S00945765(02)00287-4. [66] Szweda, Roy (2005). “Germanium phoenix”. III-Vs Review 18 (7): 55. doi:10.1016/S0961-1290(05)71310-7. [67] Thiele, Ulrich K. (2001). “The Current Status of Catalysis and Catalyst Development for the Industrial Process of Poly(ethylene terephthalate) Polycondensation”. International Journal of Polymeric Materials 50 (3): 387–394. doi:10.1080/00914030108035115. [68] Fang, Li; Kulkarni, Sameer; Alhooshani, Khalid; Malik, Abdul (2007). “Germania-Based, Sol-Gel Hybrid Organic-Inorganic Coatings for Capillary Microextraction and Gas Chromatography”. Anal. Chem. 79 (24): 9441–9451. doi:10.1021/ac071056f. PMID 17994707.
[72] Gerber, G.B.; Léonard, A. (1997). “Mutagenicity, carcinogenicity and teratogenicity of germanium compounds”. Regulatory Toxicology and Pharmacology 387 (3): 141–146. doi:10.1016/S1383-5742(97)00034-3. [73] Brown Jr., Robert D. (PDF). Commodity Survey:Germanium (Report). US Geological Surveys. http://minerals.usgs.gov/minerals/pubs/commodity/ germanium/220798.pdf. Retrieved 2008-09-09. [74] “Germanium”. American Cancer Society. Retrieved 2008-08-31. [75] Slavik, Milan; Blanc, Oscar; Davis, Joan (1983). “Spirogermanium: A new investigational drug of novel structure and lack of bone marrow toxicity”. Investigational New Drugs 1 (3): 225–234. doi:10.1007/BF00208894. PMID 6678870. [76] Baselt, R. (2008). Disposition of Toxic Drugs and Chemicals in Man (8 ed.). Foster City, CA: Biomedical Publications. pp. 693–694.
2.2.9
External links
• Germanium at The Periodic Table of Videos (University of Nottingham)
2.3 Gallium arsenide
Gallium arsenide (GaAs) is a compound of the elements gallium and arsenic. It is a III-V direct bandgap [69] Keyser, Ronald; Twomey, Timothy; Upp, Daniel. semiconductor with a zinc blende crystal structure. Gal“Performance of Light-Weight, Battery-Operated, High lium arsenide is used in the manufacture of devices such Purity Germanium Detectors for Field Use” (PDF). as microwave frequency integrated circuits, monolithic Oak Ridge Technical Enterprise Corporation (ORTEC). microwave integrated circuits, infrared light-emitting Archived from the original on October 26, 2007. Re- diodes, laser diodes, solar cells and optical windows.[2] trieved 2008-09-06. [70] Ahmed, F. U.; Yunus, S.M.; Kamal, I.; Begum, S.; Khan, Aysha A.; Ahsan, M.H.; Ahmad, A.A.Z.
GaAs is often used as a substrate material for the epitaxial growth of other III-V semiconductors including: Indium gallium arsenide, aluminum gallium arsenide and others.
2.3. GALLIUM ARSENIDE
2.3.1
55
Preparation and chemistry
Oxidation of GaAs occurs in air and degrades performance of the semiconductor. The surface can be passiIn the compound, gallium has a +3 oxidation state. Gal- vated by depositing a cubic gallium(II) sulfide layer using lium arsenide single crystals can be prepared by three in- a tert-butyl gallium sulfide compound such as (t BuGaS) dustrial processes:[2] 7.[5] • The vertical gradient freeze (VGF) process. Most GaAs wafers are produced using this process.[3] Semi-insulating crystals • Crystal growth using a horizontal zone furnace in the If a GaAs boule is grown with excess arsenic present, it Bridgman-Stockbarger technique, in which gallium gets certain defects, in particular arsenic antisite defects and arsenic vapors react, and free molecules deposit (an arsenic atom at a gallium atom site within the crystal on a seed crystal at the cooler end of the furnace. lattice). The electronic properties of these defects (inter• Liquid encapsulated Czochralski (LEC) growth is acting with others) cause the Fermi level to be pinned to used for producing high-purity single crystals that near the center of the bandgap, so that this GaAs crystal can exhibit semi-insulating characteristics (see be- has very low concentration of electrons and holes. This low carrier concentration is similar to an intrinsic (perlow). fectly undoped) crystal, but much easier to achieve in practice. These crystals are called “semi-insulating”, reAlternative methods for producing films of GaAs flecting their high resistivity of 107 –109 Ω·cm (which is include:[2][4] quite high for a semiconductor, but still much lower than a true insulator like glass).[6] • VPE reaction of gaseous gallium metal and arsenic trichloride: Etching 2 Ga + 2 AsCl 3 → 2 GaAs + 3 Cl 2 • MOCVD reaction of trimethylgallium and arsine: Ga(CH 3) 3 + AsH 3 → GaAs + 3 CH 4 • Molecular beam epitaxy (MBE) of gallium and arsenic:
Wet etching of GaAs industrially uses an oxidizing agent such as hydrogen peroxide or bromine water,[7] and the same strategy has been described in a patent relating to processing scrap components containing GaAs where the Ga3+ is complexed with a hydroxamic acid (“HA”), for example:[8] GaAs + H 2O 2 + “HA” → “GaA” complex + H 3AsO 4+4H 2O This reaction produces arsenic acid.
4 Ga + As 4 → 4 GaAs or
2.3.2 Comparison with silicon GaAs advantages
2 Ga + As 2 → 2 GaAs
Some electronic properties of gallium arsenide are superior to those of silicon. It has a higher saturated electron
56
CHAPTER 2. SEMICONDUCTOR MATERIALS
velocity and higher electron mobility, allowing gallium arsenide transistors to function at frequencies in excess of 250 GHz. Unlike silicon junctions, GaAs devices are relatively insensitive to heat owing to their wider bandgap. Also, GaAs devices tend to have less noise than silicon devices, especially at high frequencies. This is a result of higher carrier mobilities and lower resistive device parasitics. These properties recommend GaAs circuitry in mobile phones, satellite communications, microwave point-to-point links and higher frequency radar systems. It is used in the manufacture of Gunn diodes for generation of microwaves.
(MOVPE). Because GaAs and AlAs have almost the same lattice constant, the layers have very little induced strain, which allows them to be grown almost arbitrarily thick. This allows for extremely high performance high electron mobility, HEMT transistors and other quantum well devices.
One of the first GaAs microprocessors was developed in the early 1980s by the RCA corporation and was considered for the Star Wars program of the United States Department of Defense. Those processors were several times faster and several orders of magnitude more radiation hard than silicon counterparts, but they were rather expensive.[9] Other GaAs processors were implemented by the supercomputer vendors Cray Computer Corporation, Convex, and Alliant in an attempt to stay ahead of the ever-improving CMOS microprocessor. Cray eventually built one GaAs-based machine in the early 1990s, the Cray-3, but the effort was not adequately capitalized, and the company filed for bankruptcy in 1995.
ers are adherent to the underlying Si. SiO2 is not only a good insulator (with a band gap of 8.9 eV), but the SiSiO2 interface can be easily engineered to have excellent electrical properties, most importantly low density of interface states. GaAs does not have a native oxide and does not easily support a stable adherent insulating layer. Aluminum oxide (Al2 O3 ) has been extensively studied as a possible gate oxide for GaAs (and InGaAs). However, at this point the electrical properties of the interfaces aren't comparable to those of the Si-SiO2 interface.
Silicon advantages
Silicon has three major advantages over GaAs for integrated circuit manufacture. First, silicon is abundant and Another advantage of GaAs is that it has a direct band cheap to process. Si is highly abundant in the Earth’s gap, which means that it can be used to absorb and emit crust, in the form of silicate minerals. The economy of light efficiently. Silicon has an indirect bandgap and so scale available to the silicon industry has also reduced the is relatively poor at emitting light. Nonetheless, advances adoption of GaAs. silicon LEDs and lasers may be possible. In addition, a Si crystal has an extremely stable structure As a wide direct band gap material with resulting resis- mechanically and it can be grown to very large diameter tance to radiation damage, GaAs is an excellent material boules and can be processed with very high yields. It is for space electronics and optical windows in high power also a decent thermal conductor, thus enabling very dense applications. packing of transistors that need to get rid of their heat of Because of its wide bandgap, pure GaAs is highly resis- operation, all very desirable for design and manufacturing tive. Combined with the high dielectric constant, this of very large ICs. Such good mechanical characteristics property makes GaAs a very good electrical substrate and also makes it a suitable material for the rapidly developing unlike Si provides natural isolation between devices and field of nanoelectronics. circuits. This has made it an ideal material for microwave The second major advantage of Si is the existence of a and millimeter wave integrated circuits, MMICs, where native oxide (silicon dioxide, SiO ), which is used as an 2 active and essential passive components can readily be insulator in electronic devices. Silicon dioxide can easproduced on a single slice of GaAs. ily be incorporated onto silicon circuits, and such lay-
Complex layered structures of gallium arsenide in combination with aluminium arsenide (AlAs) or the alloy AlₓGa₁-ₓAs can be grown using molecular beam epitaxy (MBE) or using metalorganic vapor phase epitaxy
The third, advantage of silicon is that it possesses a higher hole mobility compared to GaAs (500 versus 400 cm2 V−1 s−1 ).[10] This high mobility allows the fabrication of higher-speed P-channel field effect transistors, which are required for CMOS logic. Because they lack a fast CMOS structure, GaAs circuits must use logic styles which have much higher power consumption; this has made GaAs circuits less able to compete with silicon logic circuits.
2.3. GALLIUM ARSENIDE For manufacturing solar cells, silicon has relatively low absorptivity for the sunlight meaning about 100 micrometers of Si is needed to absorb most sunlight. Such a layer is relatively robust and easy to handle. In contrast, the absorptivity of GaAs is so high that only a few micrometers of thickness are needed to absorb all of the light. Consequently GaAs thin films must be supported on a substrate material.[11] Silicon is a pure element, avoiding the problems of stoichiometric imbalance and thermal unmixing of GaAs. Silicon has a nearly perfect lattice, impurity density is very low and allows very small structures to be built (currently down to 16 nm[12] ). GaAs in contrast has a very high impurity density, which makes it difficult to build integrated circuits with small structures, so the 500 nm process is a common process for GaAs.
2.3.3
57 sensitive to infrared radiation (QWIP). GaAs diodes can be used for the detection of X-rays.[19] Light-emission devices GaAs has been used to produce (near-infrared) laser diodes since 1962.[20]
2.3.4 Safety The environment, health and safety aspects of gallium arsenide sources (such as trimethylgallium and arsine) and industrial hygiene monitoring studies of metalorganic precursors have been reported.[21] California lists gallium arsenide as a carcinogen.[22] However, there is no evidence for a primary carcinogenic effect of GaAs.[23]
Other applications 2.3.5 See also
Solar cells and detectors Another important application of GaAs is for high efficiency solar cells. Gallium arsenide (GaAs) is also known as single-crystalline thin film and are high-cost high-efficiency solar cells. In 1970, the first GaAs heterostructure solar cells were created by the team led by Zhores Alferov in the USSR.[13][14][15] In the early 1980s, the efficiency of the best GaAs solar cells surpassed that of silicon solar cells, and in the 1990s GaAs solar cells took over from silicon as the cell type most commonly used for Photovoltaic arrays for satellite applications. Later, dual- and triplejunction solar cells based on GaAs with germanium and indium gallium phosphide layers were developed as the basis of a triple-junction solar cell, which held a record efficiency of over 32% and can operate also with light as concentrated as 2,000 suns. This kind of solar cell powers the rovers Spirit and Opportunity, which are exploring Mars' surface. Also many solar cars utilize GaAs in solar arrays. GaAs-based devices hold the world record for the highest-efficiency single-junction solar cell at 28.8%.[16] This high efficiency is attributed to the extreme high quality GaAs epitaxial growth, surface passivation by the AlGaAs,[17] and the promotion of photon recycling by the thin film design.[18] Complex designs of AlₓGa₁₋ₓAs-GaAs devices can be
• Aluminium arsenide • Aluminium gallium arsenide • Arsine • Cadmium telluride • Gallium antimonide • Gallium arsenide phosphide • Gallium manganese arsenide • Gallium phosphide • Gallium nitride • Heterostructure emitter bipolar transistor • MESFET • Indium arsenide • Indium gallium arsenide • Indium phosphide • Light-emitting diode • Metal semiconductor field effect transistor • MOVPE
58 • Multijunction • Photomixing • Trimethylgallium
2.3.6 References [1] Refractive index of GaAs. Ioffe database [2] Moss, S. J. and Ledwith, A. (1987). The Chemistry of the Semiconductor Industry. Springer. ISBN 0-216-92005-1. [3] Scheel, Hans J., and Tsuguo Fukuda. (2003). Crystal Growth Technology. Wiley. ISBN 0471490598. [4] Smart, Lesley and Moore, Elaine A. (2005). Solid State Chemistry: An Introduction. CRC Press. ISBN 0-74877516-1. [5] “Chemical vapor deposition from single organometallic precursors” A. R. Barron, M. B. Power, A. N. MacInnes, A. F.Hepp, P. P. Jenkins U.S. Patent 5,300,320 (1994) [6] Dopants and Defects in Semiconductors, by Matthew D. McCluskey, Eugene E. Haller, pp. 41 and 66, ISBN 9781439831526 [7] Brozel, M. R. and Stillman, G. E. (1996). Properties of Gallium Arsenide. IEEE Inspec. ISBN 0-85296-885-X. [8] “Oxidative dissolution of gallium arsenide and separation of gallium from arsenic” J. P. Coleman and B. F. Monzyk U.S. Patent 4,759,917 (1988) [9] Šilc, Von Jurij; Robič, Borut and Ungerer, Theo (1999). Processor architecture: from dataflow to superscalar and beyond. Springer. p. 34. ISBN 3-540-64798-8. [10] Appendix G, Sze, S. M. (1985). Semiconductor Devices Physics and Technology, John Wiley & Sons ISBN 0-47187424-8 [11] Single-Crystalline Thin Film. US Department of Energy [12] Handy, Jim (17 July 2013) Micron NAND Reaches 16nm. thememoryguy.com [13] Alferov, Zh. I., V. M. Andreev, M. B. Kagan, I. I. Protasov and V. G. Trofim, 1970, ‘‘Solar-energy converters based on p-n AlₓGa₁-ₓAs-GaAs heterojunctions,’’ Fiz. Tekh. Poluprovodn. 4, 2378 (Sov. Phys. Semicond. 4, 2047 (1971)) [14] Nanotechnology in energy applications. im.isu.edu.tw. 16 November 2005 (in Chinese) p. 24 [15] Nobel Lecture by Zhores Alferov at nobelprize.org, p. 6
CHAPTER 2. SEMICONDUCTOR MATERIALS
[16] Yablonovitch, Eli; Miller, Owen D.; Kurtz, S. R. (2012). “The opto-electronic physics that broke the efficiency limit in solar cells”. 2012 38th IEEE Photovoltaic Specialists Conference. p. 001556. doi:10.1109/PVSC.2012.6317891. ISBN 978-1-46730066-7. [17] Schnitzer, I. et al. (1993). “Ultrahigh spontaneous emission quantum efficiency, 99.7% internally and 72% externally, from AlGaAs/GaAs/AlGaAs double heterostructures”. Applied Physics Letters 62 (2): 131. doi:10.1063/1.109348. [18] Wang, X. et al. (2013). “Design of GaAs Solar Cells Operating Close to the Shockley–Queisser Limit”. IEEE Journal of Photovoltaics 3 (2): 737. doi:10.1109/JPHOTOV.2013.2241594. [19] Glasgow University report on CERN detector. Ppewww.physics.gla.ac.uk. Retrieved on 2013-1016. [20] Hall, Robert N.; Fenner, G. E.; Kingsley, J. D.; Soltys, T. J. and Carlson, R. O. (1962). “Coherent Light Emission From GaAs Junctions”. Physical Review Letters 9 (9): 366–369. Bibcode:1962PhRvL...9..366H. doi:10.1103/PhysRevLett.9.366. [21] Shenai-Khatkhate, D V; Goyette, R; DiCarlo, R L and Dripps, G (2004). “Environment, health and safety issues for sources used in MOVPE growth of compound semiconductors”. Journal of Crystal Growth 272 (1–4): 816–821. Bibcode:2004JCrGr.272..816S. doi:10.1016/j.jcrysgro.2004.09.007. [22] “Chemicals Listed Effective August 1, 2008 as Known to the State of California to Cause Cancer or Reproductive Toxicity: gallium arsenide, hexafluoroacetone, nitrous oxide and vinyl cyclohexene dioxide”. OEHHA. 2008-08-01. [23] Bomhard, E. M.; Gelbke, H.; Schenk, H.; Williams, G. M.; Cohen, S. M. (2013). “Evaluation of the carcinogenicity of gallium arsenide”. Critical Reviews in Toxicology 43 (5): 436–466. doi:10.31.109/104084444.2013.792329/.
2.3.7
External links
• Case Studies in Environmental Medicine: Arsenic Toxicity • Physical properties of gallium arsenide (Ioffe Institute) • Facts and figures on processing gallium arsenide
2.3. GALLIUM ARSENIDE
59
A polycrystalline silicon rod made by the Siemens process
PDMS – a silicone compound
Monocrystalline silicon ingot grown by the Czochralski process
60
CHAPTER 2. SEMICONDUCTOR MATERIALS
Germane is similar to methane.
Silicon wafer with mirror finish Nucleophilic addition with an organogermanium compound.
Silica skeletons of radiolaria in false color. Renierite
2.3. GALLIUM ARSENIDE
61
A PET bottle
A typical single-mode optical fiber. Germanium oxide is a dopant of the core silica (Item 1). 1. Core 8 µm 2. Cladding 125 µm 3. Buffer 250 µm 4. Jacket 400 µm
A pristine 2-inch single crystal gallium arsenide wafer with a (100) surface orientation. Purple features are a reflection of a nitrile glove.
62
CHAPTER 2. SEMICONDUCTOR MATERIALS
Energy (eV)
3
GaAs T = 300 K
Conduction band
2 0.38 eV
0.29 eV 1
E g= 1.42 eV 0
-1 Valence band
L[111]
Γ
Wave vector k
X[100]
Band structure of GaAs. The direct gap of GaAs results in efficient emission of infrared light at 1.424 eV (~870 nm).
High-efficiency, triple-junction gallium arsenide solar cells covering the MidSTAR-1 satellite
Chapter 3
Applications 3.1 Voltage-controlled oscillator
input controls the resonant frequency. A varactor diode’s capacitance is controlled by the voltage across the diode. Consequently, a varactor can be used to change the capacitance (and hence the frequency) of an LC tank. A varactor can also change (“pull”) the resonant frequency of a crystal resonator.
A voltage-controlled oscillator or VCO is an electronic oscillator whose oscillation frequency is controlled by a voltage input. The applied input voltage determines the instantaneous oscillation frequency. Consequently, modulating signals applied to control input may cause Relaxation oscillators can generate a sawtooth or trifrequency modulation (FM) or phase modulation (PM). angular waveform. They are commonly used in monoA VCO may also be part of a phase-locked loop. lithic integrated circuits (ICs). They can provide a wide range of operational frequencies with a minimal number of external components. Relaxation oscillator VCOs can have three topologies: 1) grounded-capacitor VCOs, 2) emitter-coupled VCOs, and 3) delay-based ring VCOs. The first two of these types operate similarly. The time spent in each state depends on the rate of charge or discharge of a capacitor. The delay-based ring VCO operates somewhat differently however. For this type, the gain stages are connected in a ring. The output frequency is then a function of the delay in each stage. A microwave (12-18 GHz) Voltage Controlled Oscillator
3.1.1
Harmonic oscillator VCOs have these advantages over relaxation oscillators.
Types of VCO
• Frequency stability with respect to temperature, noise, and power supply is much better for harmonic oscillator VCOs.
VCOs can be generally categorized into two groups based on the type of waveform produced: 1) harmonic oscillators, and 2) relaxation oscillators. Linear or harmonic oscillators generate a sinusoidal waveform. Harmonic oscillators in electronics usually consist of a resonator with an amplifier that replaces the resonator losses (to prevent the amplitude from decaying) and isolates the resonator from the output (so the load does not affect the resonator). Some examples of harmonic oscillators are LC-tank oscillators and crystal oscillators. In a voltage-controlled oscillator, a voltage
• They have good accuracy for frequency control since the frequency is controlled by a crystal or tank circuit. A disadvantage of harmonic oscillator VCOs is that they cannot be easily implemented in monolithic ICs. Relaxation oscillator VCOs are better suited for this technology. Relaxation VCOs are also tunable over a wider range of frequencies.
63
64
3.1.2 Control of frequency in VCOs
CHAPTER 3. APPLICATIONS • Where the oscillator drives equipment that may generate radio-frequency interference, adding a varying voltage to its control input can disperse the interference spectrum to make it less objectionable. See spread spectrum clock.
Voltage-controlled oscillator schematic - audio
A voltage-controlled capacitor is one method of making an LC oscillator vary its frequency in response to a control voltage. Any reverse-biased semiconductor diode displays a measure of voltage-dependent capacitance and can be used to change the frequency of an oscillator by varying a control voltage applied to the diode. Specialpurpose variable capacitance varactor diodes are available with well-characterized wide-ranging values of capacitance. Such devices are very convenient in the manufacture of voltage-controlled oscillators[note 1] For lowfrequency VCOs, other methods of varying the frequency (such as altering the charging rate of a capacitor by means of a voltage controlled current source) are used. See Function generator. The frequency of a ring oscillator is controlled by vary- A 26 MHz TCVCXO. ing either the supply voltage, the current available to each inverter stage, or the capacitive loading on each stage. A temperature-compensated VCXO (TCVCXO) incorporates components that partially correct the dependence on temperature of the resonant frequency of the 3.1.3 Voltage-controlled crystal oscillators crystal. A smaller range of voltage control then suffices to stabilize the oscillator frequency in applications A voltage-controlled crystal oscillator (VCXO) is used for where temperature varies, such as heat buildup inside a fine adjustment of the operating frequency. The fre- transmitter. quency of a voltage-controlled crystal oscillator can be varied a few tens of parts per million (ppm), because the Placing the oscillator in a temperature-controlled “oven” high Q factor of the crystals allows “pulling” over only a at a constant but higher-than-ambient temperature is another way to stabilize oscillator frequency. High stability small range of frequencies. crystal oscillator references often place the crystal in an There are two reasons for using a VCXO: oven and use a voltage input for fine control.[1] The temperature is selected to be the turnover temperature: the • To adjust the output frequency to match (or perhaps temperature where small changes do not affect the resbe some exact multiple of) an accurate external ref- onance. The control voltage can be used to occasionally erence. adjust the reference frequency to a NIST source. Sophis-
3.1. VOLTAGE-CONTROLLED OSCILLATOR
65
ticated designs may also adjust the control voltage over VCO freq-domain equations time to compensate for crystal aging.
VCO time-domain equations ftuning (t) = f∫quiescent + Ko · vin (t) ftuning (t) dt = θout (t) • fo is the quiescent frequency of the oscillator •
•
Ko is called the oscillator sensitivity, or gain. Its units are hertz per volt. ftuning (t) is the symbol for the time-domain waveform that is the VCO’s tunable frequency component.
• θout (t) is the symbol for the time-domain waveform that is the VCO’s output phase. •
vin (t) is the time-domain symbol of the control (input) voltage of the VCO; it is sometimes also represented as vtune (t)
VCOs used at radio frequency have a more complex relationship than the simplistic one shown here. There can be some non-linearity in the relationship.
Ftuning (s) = Ko · Vin (s) Ftuning (s) = Θout (s) s Analog applications such as frequency modulation and frequency-shift keying often need to control an oscillator frequency with an input — a voltage-controlled oscillator (VCO). The functional relationship between the control voltage and the output frequency may not be linear. Over small ranges, the relationship is approximately linear, and linear control theory can be used. There are devices called voltage-to-frequency converters (VFC). These devices are often designed to be very linear over a wide range of input voltages.
3.1.4 VCO design and circuits Tuning range, tuning gain and phase noise are the important characteristics of a VCO. Generally low phase noise is preferred in the VCO. The noise present in the control signal and the tuning gain affect the phase noise; high noise or high tuning gain imply more phase noise. Other important elements that determine the phase noise are the transistor’s flicker noise (1/f noise),[2] the output power level, and the loaded Q of the resonator.[3] See Leeson’s equation. The low frequency flicker noise affects the phase noise because the flicker noise is heterodyned to the oscillator output frequency due to the active devices non-linear transfer function. The effect of flicker noise can be reduced with negative feedback that linearizes the transfer function (for example, emitter degeneration). Leeson’s expression[4] for single-sideband (SSB) phase noise in dBc/Hz (decibels relative to output level per Hertz) is[5] [ (( L(fm ) = 10 log )( )] F kT 1 Ps
1 2
)2 f0 2Ql fm
)( +1
fc fm
+
where f 0 is the output frequency, Q is the loaded Q, f is the offset from the output frequency (Hz), f is the 1/f corner frequency, F is the noise factor of the amplifier, k is
66
CHAPTER 3. APPLICATIONS Boltzmann’s constant, T is absolute temperature in Kelvins, and P is the oscillator output power.
range, linearity, and distortion are often most important specs. Audio-frequency VCOs for use in musical contexts were largely superseded in the 1980s by their digital counterparts, DCOs, due to their output stability in the Commonly used VCO circuits are the Clapp and Colpitts face of temperature changes during operation. From the oscillators. The more widely used oscillator of the two is 1990s on, pure software is the primary sound-generating Colpitts and these oscillators are very similar in configu- method, but VCOs have become popular again often thanks to their imperfections. ration. VCOs generally have the lowest Q-factor of the used oscillators, and so suffer more jitter than the other types. The jitter can be made low enough for many applications (such as driving an ASIC), in which case VCOs enjoy the advantages of having no off-chip components (expensive) or on-chip inductors (low yields on generic CMOS processes). These oscillators also have larger tuning ranges than the other kinds, which improves yield and is sometimes a feature of the end product (for instance, the dot clock on a graphics card which drives a wide range of monitors).
3.1.5 Applications
3.1.6
Voltage-controlled crystal oscillator as a clock generator
A clock generator is an oscillator that provides a timing signal to synchronize operations in digital circuits. VCXO clock generators are used in many areas such as digital TV, modems, transmitters and computers. Design parameters for a VCXO clock generator are tuning voltage range, center frequency, frequency tuning range and the timing jitter of the output signal. Jitter is a form of phase noise that must be minimised in applications such as radio receivers, transmitters and measuring equipment.
The tuning range of a VCXO is typically a few parts per million over a control voltage range of typically 0 to 3 volts. When a wider selection of clock frequencies is needed the VCXO output can be passed through digiFunction generators, tal divider circuits to obtain lower frequency(ies) or be The production of electronic music, to generate fed to a PLL (Phase Locked Loop). ICs containing both variable tones in synthesizers, a VCXO (for external crystal) and a PLL are available. A typical application is to provide clock frequencies in a Phase-locked loops, range from 12 kHz to 96 kHz to an audio digital to analog Frequency synthesizers used in communication converter. equipment.
VCOs are used in: • • • •
Voltage-to-Frequency converters are voltage-controlled oscillators, with a highly linear relation between applied voltage and frequency. They are used to convert a slow analog signal (such as from a temperature transducer) to a digital signal for transmission over a long distance, since the frequency will not drift or be affected by noise. VCOs may have sine and/or square wave outputs. Function generators are low-frequency oscillators which feature multiple waveforms, typically sine, square, and triangle waves. Monolithic function generators are voltagecontrolled. Analog phase-locked loops typically contain VCOs. High-frequency VCOs are usually used in phaselocked loops for radio receivers. Phase noise is the most important specification for them. Low-frequency VCOs are used in analog music synthesizers. For these, sweep
3.1.7
See also
• VFO • VCF • VCA • LFO • modular synthesizer • Digitally controlled oscillator, DCO • Numerically controlled oscillator, NCO • Phase-locked loop, PLL
3.2. FREQUENCY-SHIFT KEYING
3.1.8
67
Notes
[1] A voltage-controlled inductor would be in principle as useful, but such devices are unsatisfactory at the frequencies usually desired.
3.1.9
Data
References
[1] For example, an HP/Agilent 10811 reference oscillator [2] Wideband VCO from Herley - General Microwave - “For optimum performance, the active element used is a silicon bipolar transistor. (This is in lieu of GaAs FETs which typically exhibit 10-20 dB poorer phase noise performance) extquotedbl
Carrier
[3] Rhea, Randall W. (1997), Oscillator Design & Computer Simulation (Second ed.), McGraw-Hill, ISBN 0-07052415-7 [4] Leeson, D. B. (February 1966), “A Simple Model of Feedback Oscillator Noise Spectrum”, Proceedings of the IEEE 54 (2): 329–330, doi:10.1109/PROC.1966.4682
Modulated Signal
An example of binary FSK
[5] Rhea 1997, p. 115
3.1.10
External links
FSK signal can be done using the Goertzel algorithm very efficiently, even on low-power microcontrollers.[4]
• schematics • Designing VCOs and Buffers Using the UPA family of Dual Transistors
3.2.2 Other forms of FSK
3.2 Frequency-shift keying Frequency-shift keying (FSK) is a frequency modulation scheme in which digital information is transmitted through discrete frequency changes of a carrier wave.[1] The simplest FSK is binary FSK (BFSK). BFSK uses a pair of discrete frequencies to transmit binary (0s and 1s) information.[2] With this scheme, the “1” is called the mark frequency and the “0” is called the space frequency. The time domain of an FSK modulated carrier is illustrated in the figures to the right.
Minimum-shift keying Main article: Minimum-shift keying
Minimum frequency-shift keying or minimum-shift keying (MSK) is a particular spectrally efficient form of coherent FSK. In MSK, the difference between the higher and lower frequency is identical to half the bit rate. Consequently, the waveforms that represent a 0 and a 1 bit differ by exactly half a carrier period. The maximum frequency deviation is δ = 0.25 fm, where fm is the maximum modulating frequency. As a result, the modulation index m is 0.5. This is the smallest FSK modulation index 3.2.1 Implementations of FSK Modems that can be chosen such that the waveforms for 0 and 1 Reference implementations of FSK modems exist and are are orthogonal. A variant of MSK called GMSK is used documented in detail.[3] The demodulation of a binary in the GSM mobile phone standard.
68
CHAPTER 3. APPLICATIONS
Audio FSK
cassettes . AFSK is still widely used in amateur radio, as it allows data transmission through unmodified voiceband Audio frequency-shift keying (AFSK) is a modulation equipment. Radio control gear uses FSK, but calls it FM technique by which digital data is represented by changes and PPM instead. in the frequency (pitch) of an audio tone, yielding an AFSK is also used in the United States' Emergency Alert encoded signal suitable for transmission via radio or System to transmit warning information . It is used at telephone. Normally, the transmitted audio alternates be- higher bitrates for Weathercopy used on Weatheradio by tween two tones: one, the “mark”, represents a binary NOAA in the U.S. one; the other, the “space”, represents a binary zero. The CHU shortwave radio station in Ottawa, Canada AFSK differs from regular frequency-shift keying in per- broadcasts an exclusive digital time signal encoded using forming the modulation at baseband frequencies. In radio AFSK modulation. applications, the AFSK-modulated signal normally is being used to modulate an RF carrier (using a conventional FSK is commonly used in Caller ID and remote metering applications: see FSK standards for use in Caller ID and technique, such as AM or FM) for transmission. remote metering for more details AFSK is not always used for high-speed data communications, since it is far less efficient in both power and bandwidth than most other modulation modes. In addi- 3.2.4 See also tion to its simplicity, however, AFSK has the advantage that encoded signals will pass through AC-coupled links, • Amplitude-shift keying (ASK) including most equipment originally designed to carry • Continuous-phase frequency-shift keying (CPFSK) music or speech. AFSK is used in the U.S. based Emergency Alert System to notify stations of the type of emergency, locations affected, and the time of issue without actually hearing the text of the alert.
• Dual-tone multi-frequency (DTMF), another encoding technique representing data by pairs of audio frequencies
3.2.3 Applications
• Multiple frequency-shift keying (MFSK)
In 1910, Reginald Fessenden invented a two-tone method of transmitting Morse code. Dots and dashes were different tones of equal length.[5] The intent was to minimize transmission time.
• Frequency-change signaling
• Orthogonal (OFDM)
frequency
division
multiplexing
• Phase-shift keying (PSK)
• Federal Standard 1037C Some early CW transmitters employed an arc converter that could not be conveniently keyed. Instead of turning • MIL-STD-188 the arc on and off, the key slightly changed the transmitter frequency in a technique known as the compensationwave method.[6] The compensation-wave was not used at 3.2.5 References the receiver. The method consumed a lot of bandwidth [1] Kennedy, G.; Davis, B. (1992). Electronic Communicaand caused interference, so it was discouraged by 1921.[7] Most early telephone-line modems used audio frequencyshift keying (AFSK) to send and receive data at rates up to about 1200 bits per second. The common Bell 103 and Bell 202 modems used this technique.[8] Even today, North American caller ID uses 1200 baud AFSK in the form of the Bell 202 standard. Some early microcomputers used a specific form of AFSK modulation, the Kansas City standard, to store data on audio
tion Systems (4th ed.). McGraw-Hill International. ISBN 0-07-112672-4., p 509
[2] FSK: Signals and Demodulation (B. Watson) http://www.xn--sten-cpa.se/share/text/tektext/ digital-modulation/FSK_signals_demod.pdf [3] Teaching DSP through the Practical Case Study of an FSK Modem (TI) http://www.ti.com/lit/an/spra347/ spra347.pdf
3.3. AMPLIFIER
69
[4] FSK Modulation and Demodulation With the MSP430 Microcontroller (TI) http://www.ti.com/lit/an/slaa037/ slaa037.pdf
shape but with a larger amplitude. In this sense, an amplifier modulates the output of the power supply to make the output signal stronger than the input signal.
[5] Morse 1925, p. 44; Morse cites British patent 2,617/11.
The four basic types of electronic amplifiers are voltage amplifiers, current amplifiers, transconductance amplifiers, and transresistance amplifiers. A further distinction is whether the output is a linear or nonlinear representation of the input. Amplifiers can also be categorized by their physical placement in the signal chain.[1]
[6] Bureau of Standards 1922, pp. 415–416 [7] Little 1921, p. 125 [8] Kennedy & Davis 1992, pp. 549–550
• Bureau of Standards (1922), The Principles Un- 3.3.1 Figures of merit derlying Radio Communication (Second ed.), U.S. Army Signal Corps, Radio Communications Pam- Main article: Amplifier figures of merit phlet No. 40. Revised to April 24, 1921. Amplifier quality is characterized by a list of specifica• Little, D. G. (April 1921), “Continuous Wave Radio tions that includes: Communication”, Electric Journal 18: 124–129 • Morse, A. H. (1925), Radio: Beam and Broadcast, London: Ernest Benn Limited
• Gain, the ratio between the magnitude of output and input signals • Bandwidth, the width of the useful frequency range
3.2.6
External links
• dFSK: Distributed Frequency Shift Keying Modulation in Dense Sensor Networks
For other uses, see Amplifier (disambiguation). An electronic amplifier, amplifier, or (informally)
R3
+V supply
R4
Q4
C1
D1 Q1
Q2 R7
R2
R5
Output
D2
Q5
R8
• Output dynamic range, the ratio of the largest and the smallest useful output levels • Slew rate, the maximum rate of change of the output • Rise time, settling time, ringing and overshoot that characterize the step response
Q3
Input
• Linearity, the degree of proportionality between input and output • Noise, a measure of undesired noise mixed into the output
3.3 Amplifier
R1
• Efficiency, the ratio between the power of the output and total power consumption
• Stability, the ability to avoid self-oscillation
C2
R6 0V (ground)
3.3.2 Amplifier types
Amplifiers are described according to their input and output properties.[2] They exhibit the property of gain, or multiplication factor that relates the magnitude of the amp is an electronic device that increases the power of output signal to the input signal. The gain may be specia signal. It does this by taking energy from a power sup- fied as the ratio of output voltage to input voltage (voltage ply and controlling the output to match the input signal gain), output power to input power (power gain), or some A practical bipolar transistor amplifier circuit
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CHAPTER 3. APPLICATIONS
combination of current, voltage, and power. In many and other instrument amplifiers. The essential compocases, with input and output in the same unit, gain is unit- nents include active devices, such as vacuum tubes or transistors. A brief introduction to the many types of less (though often expressed in decibels (dB)). electronic amplifiers follows. The four basic types of amplifiers are as follows:[1] • Voltage amplifier – This is the most common type of Power amplifier amplifier. An input voltage is amplified to a larger output voltage. The amplifier’s input impedance is The term power amplifier is a relative term with respect to the amount of power delivered to the load and/or prohigh and the output impedance is low. vided by the power supply circuit. In general the power • Current amplifier – This amplifier changes an input amplifier is the last 'amplifier' or actual circuit in a sigcurrent to a larger output current. The amplifier’s nal chain (the output stage) and is the amplifier stage that input impedance is low and the output impedance is requires attention to power efficiency. Efficiency conhigh. siderations lead to the various classes of power amplifier based on the biasing of the output transistors or tubes: • Transconductance amplifier – This amplifier resee power amplifier classes. sponds to a changing input voltage by delivering a related changing output current. Power amplifiers by application • Transresistance amplifier – This amplifier responds to a changing input current by delivering a related • Audio power amplifiers changing output voltage. Other names for the device are transimpedance amplifier and current-to-voltage • RF power amplifier, such as for transmitter final converter. stages (see also: Linear amplifier). • Servo motor controllers, where linearity is not imIn practice the power gain of an amplifier will depend on portant. the source and load impedances used as well as the inherent voltage/current gain; while an RF amplifier may • Piezoelectric audio amplifier includes a DC-tohave its impedances optimized for power transfer, auDC converter to generate the high voltage output redio and instrumentation amplifiers are normally designed quired to drive piezoelectric speakers.[3] with their input and output impedances optimized for least loading and highest signal integrity. An amplifier that is said to have a gain of 20 dB might have a voltage Power amplifier circuits Power amplifier circuits ingain of ten times and an available power gain of much clude the following types: more than 20 dB (power ratio of 100), yet actually be delivering a much lower power gain if, for example, the • Vacuum tube/valve, hybrid or transistor power aminput is from a 600 ohm microphone and the output is plifiers connected to a 47 kilohm input socket for a power am• Push-pull output or single-ended output stages plifier. In most cases an amplifier will be linear; that is, the gain is constant for any normal level of input and output signal. Vacuum-tube (valve) amplifiers If the gain is not linear, e.g., clipping of the signal, the output signal will be distorted. There are however cases Main article: Valve amplifier where variable gain is useful. Exponential gain amplifiers are used in certain signal processing applications.[1] According to Symons, while semiconductor amplifiers There are many differing types of electronic amplifiers have largely displaced valve amplifiers for low power apused in areas such as: radio and television transmitters plications, valve amplifiers are much more cost effecand receivers, high-fidelity (“hi-fi”) stereo equipment, tive in high power applications such as “radar, countermicrocomputers and other digital equipment, and guitar measures equipment, or communications equipment” (p.
3.3. AMPLIFIER
71 audiophile equipment) Transistor amplifiers See also: Transistor, Bipolar junction transistor, Fieldeffect transistor, JFET and MOSFET The essential role of this active element is to magnify an input signal to yield a significantly larger output signal. The amount of magnification (the “forward gain”) is determined by the external circuit design as well as the active device. Many common active devices in transistor amplifiers are bipolar junction transistors (BJTs) and metal oxide semiconductor field-effect transistors (MOSFETs). Applications are numerous, some common examples are audio amplifiers in a home stereo or PA system, RF high power generation for semiconductor equipment, to RF and Microwave applications such as radio transmitters. Transistor-based amplifier can be realized using various configurations: for example with a bipolar junction transistor we can realize common base, common collector or common emitter amplifier; using a MOSFET we can realize common gate, common source or common drain amplifier. Each configuration has different characteristic (gain, impedance...). Operational amplifiers (op-amps) Main articles: Operational amplifier and Instrumentation amplifier
An ECC83 tube glowing inside a preamp
56). Many microwave amplifiers are specially designed valves, such as the klystron, gyrotron, traveling wave tube, and crossed-field amplifier, and these microwave valves provide much greater single-device power output at microwave frequencies than solid-state devices (p. 59).[4]
An operational amplifier is an amplifier circuit with very high open loop gain and differential inputs that employs external feedback to control its transfer function, or gain. Though the term today commonly applies to integrated circuits, the original operational amplifier design used valves.
Valves/tube amplifiers also have niche uses in other areas, such as Fully differential amplifiers • electric guitar amplification • in Russian military aircraft, for their EMP tolerance
Main article: Fully differential amplifier
A fully differential amplifier is a solid state integrated cir• niche audio for their sound qualities (recording, and cuit amplifier that uses external feedback to control its
72
CHAPTER 3. APPLICATIONS These use transmission lines to temporally split the signal and amplify each portion separately to achieve higher bandwidth than possible from a single amplifier. The outputs of each stage are combined in the output transmission line. This type of amplifier was commonly used on oscilloscopes as the final vertical amplifier. The transmission lines were often housed inside the display tube glass envelope. Switched mode amplifiers These nonlinear amplifiers have much higher efficiencies than linear amps, and are used where the power saving justifies the extra complexity.
An LM741 general purpose op-amp
Negative resistance devices
Negative resistances can be used as amplifiers, such as the transfer function or gain. It is similar to the operational tunnel diode amplifier. amplifier, but also has differential output pins. These are usually constructed using BJTs or FETs. Microwave amplifiers Video amplifiers These deal with video signals and have varying bandwidths depending on whether the video signal is for SDTV, EDTV, HDTV 720p or 1080i/p etc.. The specification of the bandwidth itself depends on what kind of filter is used—and at which point (−1 dB or −3 dB for example) the bandwidth is measured. Certain requirements for step response and overshoot are necessary for an acceptable TV image. Oscilloscope vertical amplifiers
Travelling wave tube amplifiers Main article: Traveling wave tube Traveling wave tube amplifiers (TWTAs) are used for high power amplification at low microwave frequencies. They typically can amplify across a broad spectrum of frequencies; however, they are usually not as tunable as klystrons. Klystrons Main article: Klystron
These deal with video signals that drive an oscilloscope display tube, and can have bandwidths of about 500 MHz. The specifications on step response, rise time, overshoot, and aberrations can make designing these amplifiers difficult. One of the pioneers in high bandwidth vertical amplifiers was the Tektronix company.
Klystrons are specialized linear-beam vacuum-devices, designed to provide high power, widely tunable amplification of millimetre and sub-millimetre waves. Klystrons are designed for large scale operations and despite having a narrower bandwidth than TWTAs, they have the advantage of coherently amplifying a reference signal so its output may be precisely controlled in amplitude, frequency and phase.
Distributed amplifiers
Musical instrument amplifiers
Main article: Distributed Amplifier
Main article: Instrument amplifier
3.3. AMPLIFIER
73
An audio power amplifier is usually used to amplify signals such as music or speech. Several factors are especially important in the selection of musical instrument amplifiers (such as guitar amplifiers) and other audio amplifiers (although the whole of the sound system – components such as microphones to loudspeakers – affect these parameters): • Frequency response – not just the frequency range but the requirement that the signal level varies so little across the audible frequency range that the human ear notices no variation. A typical specification The four types of dependent source—control variable on left, for audio amplifiers may be 20 Hz to 20 kHz +/- 0.5 output variable on right dB. • Power output – the power level obtainable with little Each type of amplifier in its ideal form has an ideal indistortion, to obtain a sufficiently loud sound pres- put and output resistance that is the same as that of the sure level from the loudspeakers. corresponding dependent source:[5] • Low distortion – all amplifiers and transducers distort to some extent. They cannot be perfectly linear, but aim to pass signals without affecting the harmonic content of the sound more than the human ear can tolerate. That tolerance of distortion, and indeed the possibility that some “warmth” or second harmonic distortion (Tube sound) improves the “musicality” of the sound, are subjects of great debate.
3.3.3
Classification of amplifier stages and systems
Many alternative classifications address different aspects of amplifier designs, and they all express some particular perspective relating the design parameters to the objectives of the circuit. Amplifier design is always a compromise of numerous factors, such as cost, power consumption, real-world device imperfections, and a multitude of performance specifications. Below are several different approaches to classification: Input and output variables Electronic amplifiers use one variable presented as either a current and voltage. Either current or voltage can be used as input and either as output, leading to four types of amplifiers. In idealized form they are represented by each of the four types of dependent source used in linear analysis, as shown in the figure, namely:
In practice the ideal impedances are only approximated. For any particular circuit, a small-signal analysis is often used to find the impedance actually achieved. A smallsignal AC test current Ix is applied to the input or output node, all external sources are set to AC zero, and the corresponding alternating voltage Vx across the test current source determines the impedance seen at that node as R = Vx / Ix. Amplifiers designed to attach to a transmission line at input and/or output, especially RF amplifiers, do not fit into this classification approach. Rather than dealing with voltage or current individually, they ideally couple with an input and/or output impedance matched to the transmission line impedance, that is, match ratios of voltage to current. Many real RF amplifiers come close to this ideal. Although, for a given appropriate source and load impedance, RF amplifiers can be characterized as amplifying voltage or current, they fundamentally are amplifying power.[6]
Common terminal One set of classifications for amplifiers is based on which device terminal is common to both the input and the output circuit. In the case of bipolar junction transistors, the three classes are common emitter, common base, and common collector. For field-effect transistors, the corresponding configurations are common source, common gate, and common drain; for triode vacuum devices, common cathode, common grid, and common plate. The com-
74 mon emitter (or common source, or common cathode etc.) is most often configured to provide amplification of a voltage applied between base and emitter, and the output signal taken between collector and emitter will be inverted, relative to the input. The common collector arrangement applies the input voltage between base and collector, and to take the output voltage between emitter and collector. This results in negative feedback, and the output voltage will tend to 'follow' the input voltage (this arrangement is also used as the input presents a high impedance and does not load the signal source, although the voltage amplification will be less than 1 (unity)); the common-collector circuit is therefore better known as an emitter follower, source follower, or cathode follower.
CHAPTER 3. APPLICATIONS Inverting or non-inverting Another way to classify amplifiers is by the phase relationship of the input signal to the output signal. An 'inverting' amplifier produces an output 180 degrees out of phase with the input signal (that is, a polarity inversion or mirror image of the input as seen on an oscilloscope). A 'non-inverting' amplifier maintains the phase of the input signal waveforms. An emitter follower is a type of non-inverting amplifier, indicating that the signal at the emitter of a transistor is following (that is, matching with unity gain but perhaps an offset) the input signal. Voltage follower is also non inverting type of amplifier having unity gain. This description can apply to a single stage of an amplifier, or to a complete amplifier system.
Function Unilateral or bilateral Other amplifiers may be classified by their function or output characteristics. These functional descriptions usuWhen an amplifier has an output that exhibits no feed- ally apply to complete amplifier systems or sub-systems back to its input side, it is called 'unilateral'. The input and rarely to individual stages. impedance of a unilateral amplifier is independent of the load, and the output impedance is independent of the sig• A servo amplifier indicates an integrated feedback nal source impedance. loop to actively control the output at some desired If feedback connects part of the output back to the input level. A DC servo indicates use at frequencies down of the amplifier it is called a 'bilateral' amplifier. The into DC levels, where the rapid fluctuations of an audio put impedance of a bilateral amplifier is dependent upon or RF signal do not occur. These are often used in the load, and the output impedance is dependent upon the mechanical actuators, or devices such as DC motors signal source impedance. that must maintain a constant speed or torque. An AC servo amp can do this for some ac motors. All amplifiers are bilateral to some degree; however they may often be modeled as unilateral under operating con• A linear amplifier responds to different frequency ditions where feedback is small enough to neglect for components independently, and does not generate most purposes, simplifying analysis (see the common harmonic distortion or Intermodulation distortion. base article for an example). No amplifier can provide perfect linearity (even Negative feedback is often applied deliberately to tailor the most linear amplifier has some nonlinearities, amplifier behavior. Some feedback, which may be posisince the amplifying devices—transistors or vacuum tive or negative, is unavoidable and often undesirable, intubes—follow nonlinear power laws such as squaretroduced, for example, by parasitic elements such as the laws and rely on circuitry techniques to reduce those inherent capacitance between input and output of a deeffects). vice such as a transistor and capacitative coupling due to external wiring. Excessive frequency-dependent positive • A nonlinear amplifier generates significant distorfeedback may cause what is intended/expected to be an tion and so changes the harmonic content; there are amplifier to become an oscillator. situations where this is useful. Amplifier circuits inLinear unilateral and bilateral amplifiers can be represented as two-port networks.
tentionally providing a non-linear transfer function include:
3.3. AMPLIFIER --- a device like a Silicon Controlled Rectifier or a transistor used as a switch may be employed to turn either fully ON or OFF a load such as a lamp based on a threshold in a continuously variable input. --- a non-linear amplifier in an analog computer or true RMS converter for example can provide a special transfer function, such as logarithmic or square-law. --- a Class C RF amplifier may be chosen because it can be very efficient, but will be non-linear; following such an amplifier with a extquotedbltank extquotedbl tuned circuit can reduce unwanted harmonics (distortion) sufficiently to be useful in transmitters, or some desired harmonic may be selected by setting the resonant frequency of the tuned circuit to a higher frequency rather than fundamental frequency in frequency multiplier circuits. --- Automatic gain control circuits require an amplifier’s gain be controlled by the timeaveraged amplitude so that the output amplitude varies little when weak stations are being received. The non-linearities are assumed to be arranged so the relatively small signal amplitude suffers from little distortion (crosschannel interference or intermodulation) yet is still modulated by the relatively large gaincontrol DC voltage. --- AM detector circuits that use amplification such as Anode-bend detectors, Precision rectifiers and Infinite impedance detectors (so excluding unamplified detectors such as Cat’swhisker detectors), as well as peak detector circuits, rely on changes in amplification based on the signal's instantaneous amplitude to derive a direct current from an alternating current input. --- Operational amplifier comparator and detector circuits. • A wideband amplifier has a precise amplification factor over a wide frequency range, and is often used to boost signals for relay in communications systems. A narrowband amp amplifies a specific narrow range of frequencies, to the exclusion of other frequencies. • An RF amplifier amplifies signals in the radio frequency range of the electromagnetic spectrum, and
75 is often used to increase the sensitivity of a receiver or the output power of a transmitter.[7] • An audio amplifier amplifies audio frequencies. This category subdivides into small signal amplification, and power amps that are optimised to driving speakers, sometimes with multiple amps grouped together as separate or bridgeable channels to accommodate different audio reproduction requirements. Frequently used terms within audio amplifiers include: --- Preamplifier (preamp), which may include a phono preamp with RIAA equalization, or tape head preamps with CCIR equalisation filters. They may include filters or tone control circuitry. --- Power amplifier (normally drives loudspeakers), headphone amplifiers, and public address amplifiers. --- Stereo amplifiers imply two channels of output (left and right), though the term simply means “solid” sound (referring to threedimensional)—so quadraphonic stereo was used for amplifiers with four channels. 5.1 and 7.1 systems refer to Home theatre systems with 5 or 7 normal spacial channels, plus a subwoofer channel. • Buffer amplifiers, which may include emitter followers, provide a high impedance input for a device (perhaps another amplifier, or perhaps an energyhungry load such as lights) that would otherwise draw too much current from the source. Line drivers are a type of buffer that feeds long or interferenceprone interconnect cables, possibly with differential outputs through twisted pair cables. • A special type of amplifier - originally used in analog computers - is widely used in measuring instruments for signal processing, and many other uses. These are called operational amplifiers or op-amps. The “operational” name is because this type of amplifier can be used in circuits that perform mathematical algorithmic functions, or “operations” on input signals to obtain specific types of output signals. Modern op-amps are usually provided as integrated circuits, rather than constructed from discrete components. A typical modern op-amp has differential inputs (one “inverting”, one “non-inverting”) and one
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CHAPTER 3. APPLICATIONS output. An idealised op-amp has the following characteristics: --- Infinite input impedance (so it does not load the circuitry at its input) --- Zero output impedance --- Infinite gain --- Zero propagation delay
vacuum tube days when the anode (output) voltage was at greater than several hundred volts and the grid (input) voltage at a few volts minus. So they were only used if the gain was specified down to DC (e.g., in an oscilloscope). In the context of modern electronics developers are encouraged to use directly coupled amplifiers whenever possible. Frequency range
The performance of an op-amp with these characteristics Depending on the frequency range and other properties is entirely defined by the (usually passive) components amplifiers are designed according to different principles. that form a negative feedback loop around it. The amplifier itself does not effect the output. All real-world op• Frequency ranges down to DC are only used when amps fall short of the idealised specification above—but this property is needed. DC amplification leads to some modern components have remarkable performance specific complications that are avoided if possible; and come close in some respects. DC-blocking capacitors are added to remove DC and sub-sonic frequencies from audio amplifiers. Interstage coupling method • Depending on the frequency range specified differSee also: multistage amplifiers Amplifiers are sometimes classified by the coupling method of the signal at the input, output, or between stages. Different types of these include: Resistive-capacitive (RC) coupled amplifier, using a network of resistors and capacitors By design these amplifiers cannot amplify DC signals as the capacitors block the DC component of the input signal. RC-coupled amplifiers were used very often in circuits with vacuum tubes or discrete transistors. In the days of the integrated circuit a few more transistors on a chip are much cheaper and smaller than a capacitor.
ent design principles must be used. Up to the MHz range only “discrete” properties need be considered; e.g., a terminal has an input impedance. • As soon as any connection within the circuit gets longer than perhaps 1% of the wavelength of the highest specified frequency (e.g., at 100 MHz the wavelength is 3 m, so the critical connection length is approx. 3 cm) design properties radically change. For example, a specified length and width of a PCB trace can be used as a selective or impedancematching entity. • Above a few hundred MHz, it gets difficult to use discrete elements, especially inductors. In most cases, PCB traces of very closely defined shapes are used instead.
Inductive-capacitive (LC) coupled amplifier, using a The frequency range handled by an amplifier might be network of inductors and capacitors This kind of amplifier is most often used in selective specified in terms of bandwidth (normally implying a response that is 3 dB down when the frequency reaches the radio-frequency circuits. specified bandwidth), or by specifying a frequency reTransformer coupled amplifier, using a transformer sponse that is within a certain number of decibels beto match impedances or to decouple parts of the cir- tween a lower and an upper frequency (e.g. “20 Hz to 20 cuits kHz plus or minus 1 dB”). Quite often LC-coupled and transformer-coupled amplifiers cannot be distinguished as a transformer is some kind of inductor. 3.3.4 Power amplifier classes Direct coupled amplifier, using no impedance and Power amplifier circuits (output stages) are classified as bias matching components This class of amplifier was very uncommon in the A, B, AB and C for analog designs, and class D and E for
3.3. AMPLIFIER switching designs based on the proportion of each input cycle (conduction angle), during which an amplifying device is passing current. The image of the conduction angle is derived from amplifying a sinusoidal signal. If the device is always on, the conducting angle is 360°. If it is on for only half of each cycle, the angle is 180°. The angle of flow is closely related to the amplifier power efficiency. The various classes are introduced below, followed by a more detailed discussion under their individual headings further down.
77 are mainly used for specialized applications, such as very high-power units. Also, class-E and class-F amplifiers are commonly described in literature for radio-frequency applications where efficiency of the traditional classes is important, yet several aspects deviate substantially from their ideal values. These classes use harmonic tuning of their output networks to achieve higher efficiency and can be considered a subset of class C due to their conduction-angle characteristics.
In the illustrations below, a bipolar junction transistor is shown as the amplifying device. However the same at- Class A tributes are found with MOSFETs or vacuum tubes. Conduction angle classes Class A 100% of the input signal is used (conduction angle Θ = 360°). The active element remains conducting[8] all of the time. Class B 50% of the input signal is used (Θ = 180°); the active element carries current half of each cycle, and is turned off for the other half. Class AB Class AB is intermediate between class A and B, the two active elements conduct more than half Class-A amplifier of the time Amplifying devices operating in class A conduct over the Class C Less than 50% of the input signal is used (conentire range of the input cycle. A class-A amplifier is disduction angle Θ < 180°). tinguished by the output stage devices being biased for class A operation. Subclass A2 is sometimes used to refer A “Class D” amplifier uses some form of pulse-width to vacuum-tube class-A stages where the grid is allowed modulation to control the output devices; the conduction to be driven slightly positive on signal peaks, resulting in angle of each device is no longer related directly to the slightly more power than normal class A (A1; where the input signal but instead varies in pulse width. These are grid is always negative[9] ), but this incurs a higher distorsometimes called “digital” amplifiers because the output tion level. device is switched fully on or off, and not carrying current proportional to the signal amplitude. Advantages of class-A amplifiers Additional classes There are several other amplifier classes, although they are mainly variations of the previous classes. For example, class-G and classH amplifiers are marked by variation of the supply rails (in discrete steps or in a continuous fashion, respectively) following the input signal. Wasted heat on the output devices can be reduced as excess voltage is kept to a minimum. The amplifier that is fed with these rails itself can be of any class. These kinds of amplifiers are more complex, and
• Class-A designs are simpler than other classes; for example class -AB and -B designs require two connected devices in the circuit (push–pull output), each to handle one half of the waveform; class A can use a single device (single-ended). • The amplifying element is biased so the device is always conducting, the quiescent (small-signal) collector current (for transistors; drain current for FETs or anode/plate current for vacuum tubes) is close
78
CHAPTER 3. APPLICATIONS to the most linear portion of its transconductance curve.
• Because the device is never 'off' there is no “turn on” time, no problems with charge storage, and generally better high frequency performance and feedback loop stability (and usually fewer high-order harmonics). • The point at which the device comes closest to being 'off' is not at 'zero signal', so the problems of crossover distortion associated with class-AB and B designs is avoided. • Best for low signal levels of radio receivers due to low distortion. Disadvantage of class-A amplifiers • Class-A amplifiers are inefficient. A theoretical efficiency of 50% is obtainable with transformer output coupling and only 25% with capacitive coupling, unless deliberate use of nonlinearities is made (such as in square-law output stages). In a power amplifier, this not only wastes power and limits operation with batteries, but increases operating costs and requires higher-rated output devices. Inefficiency comes from the standing current that must be roughly half the maximum output current, and a large part of the power supply voltage is present across the output device at low signal levels. If high output power is needed from a class-A circuit, the power supply and accompanying heat becomes significant. For every watt delivered to the load, the amplifier itself, at best, uses an extra watt. For high power amplifiers this means very large and expensive power supplies and heat sinks.
• Single-ended output stages have an asymmetrical transfer function, meaning that even order harmonics in the created distortion tend not to be canceled (as they are in push–pull output stages); for tubes, or FETs, most of the distortion is second-order harmonics, from the square law transfer characteristic, which to some produces a “warmer” and more pleasant sound.[11][12] • For those who prefer low distortion figures, the use of tubes with class A (generating little odd-harmonic distortion, as mentioned above) together with symmetrical circuits (such as push–pull output stages, or balanced low-level stages) results in the cancellation of most of the even distortion harmonics, hence the removal of most of the distortion. • Historically, valve amplifiers often used a class-A power amplifier simply because valves are large and expensive; many class-A designs use only a single device. Transistors are much cheaper, and so more elaborate designs that give greater efficiency but use more parts are still cost-effective. A classic application for a pair of class-A devices is the long-tailed pair, which is exceptionally linear, and forms the basis of many more complex circuits, including many audio amplifiers and almost all op-amps.
Class-A amplifiers are often used in output stages of high quality op-amps (although the accuracy of the bias in low cost op-amps such as the 741 may result in class A or class AB or class B, varying from device to device or with temperature). They are sometimes used as medium-power, low-efficiency, and high-cost audio power amplifiers. The power consumption is unrelated to the output power. At idle (no input), the power consumption is essentially the same as at high output volume. The result is low effiClass-A power amplifier designs have largely been su- ciency and high heat dissipation. perseded by more efficient designs, though they remain popular with some hobbyists, mostly for their simplicity. There is a market for expensive high fidelity class- Class B A amps considered a “cult item” amongst audiophiles[10] mainly for their absence of crossover distortion and re- Class-B amplifiers only amplify half of the input wave cyduced odd-harmonic and high-order harmonic distortion. cle, thus creating a large amount of distortion, but their efficiency is greatly improved and is much better than class A. Class-B amplifiers are also favoured in batterySingle-ended and triode class-A amplifiers Some operated devices, such as transistor radios. Class B has a hobbyists who prefer class-A amplifiers also prefer the maximum theoretical efficiency of π/4. (≈ 78.5%) This use of thermionic valve (or “tube”) designs instead of is because the amplifying element is switched off altotransistors, for several reasons: gether half of the time, and so cannot dissipate power. A
3.3. AMPLIFIER
79 Class AB
Class-B amplifier
Class-B push–pull amplifier
single class-B element is rarely found in practice, though it has been used for driving the loudspeaker in the early IBM Personal Computers with beeps, and it can be used in RF power amplifier where the distortion levels are less important. However, class C is more commonly used for this. A practical circuit using class-B elements is the push–pull stage, such as the very simplified complementary pair arrangement shown below. Here, complementary or quasicomplementary devices are each used for amplifying the opposite halves of the input signal, which is then recombined at the output. This arrangement gives excellent efficiency, but can suffer from the drawback that there is a small mismatch in the cross-over region – at the “joins” between the two halves of the signal, as one output device has to take over supplying power exactly as the other finishes. This is called crossover distortion. An improvement is to bias the devices so they are not completely off when they're not in use. This approach is called class AB operation.
Class AB is widely considered a good compromise for amplifiers, since much of the time the music signal is quiet enough that the signal stays in the “class A” region, where it is amplified with good fidelity, and by definition if passing out of this region, is large enough that the distortion products typical of class B are relatively small. The crossover distortion can be reduced further by using negative feedback. In class-AB operation, each device operates the same way as in class B over half the waveform, but also conducts a small amount on the other half. As a result, the region where both devices simultaneously are nearly off (the “dead zone”) is reduced. The result is that when the waveforms from the two devices are combined, the crossover is greatly minimised or eliminated altogether. The exact choice of quiescent current (the standing current through both devices when there is no signal) makes a large difference to the level of distortion (and to the risk of thermal runaway, that may damage the devices); often the bias voltage applied to set this quiescent current has to be adjusted with the temperature of the output transistors (for example in the circuit at the beginning of the article the diodes would be mounted physically close to the output transistors, and chosen to have a matched temperature coefficient). Another approach (often used as well as thermally tracking bias voltages) is to include small value resistors in series with the emitters. Class AB sacrifices some efficiency over class B in favor of linearity, thus is less efficient (below 78.5% for fullamplitude sinewaves in transistor amplifiers, typically; much less is common in class-AB vacuum-tube amplifiers). It is typically much more efficient than class A. Sometimes a numeral is added for vacuum-tube stages. If the grid voltage is always negative with respect to the cathode the class is AB1 . If the grid is allowed to go slightly positive (hence drawing grid current, adding more distortion, but giving slightly higher output power) on signal peaks the class is AB2 . Class C Class-C amplifiers conduct less than 50% of the input signal and the distortion at the output is high, but high efficiencies (up to 90%) are possible. The usual application for class-C amplifiers is in RF transmitters operating at a single fixed carrier frequency, where the distortion
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CHAPTER 3. APPLICATIONS input signal. Power can be coupled to a load by transformer action with a secondary coil wound on the inductor. The average voltage at the drain is then equal to the supply voltage, and the signal voltage appearing across the tuned circuit varies from near zero to near twice the supply voltage during the rf cycle. The input circuit is biased so that the active element (e.g. transistor) conducts for only a fraction of the RF cycle, usually one third (120 degrees) or less.[14]
Class-C amplifier
is controlled by a tuned load on the amplifier. The input signal is used to switch the active device causing pulses of current to flow through a tuned circuit forming part of the load. The class-C amplifier has two modes of operation: tuned and untuned.[13] The diagram shows a waveform from a simple class-C circuit without the tuned load. This is called untuned operation, and the analysis of the waveforms shows the massive distortion that appears in the signal. When the proper load (e.g., an inductive-capacitive filter plus a load resistor) is used, two things happen. The first is that the output’s bias level is clamped with the average output voltage equal to the supply voltage. This is why tuned operation is sometimes called a clamper. This allows the waveform to be restored to its proper shape despite the amplifier having only a one-polarity supply. This is directly related to the second phenomenon: the waveform on the center frequency becomes less distorted. The residual distortion is dependent upon the bandwidth of the tuned load, with the center frequency seeing very little distortion, but greater attenuation the farther from the tuned frequency that the signal gets.
The active element conducts only while the drain voltage is passing through its minimum. By this means, power dissipation in the active device is minimised, and efficiency increased. Ideally, the active element would pass only an instantaneous current pulse while the voltage across it is zero: it then dissipates no power and 100% efficiency is achieved. However practical devices have a limit to the peak current they can pass, and the pulse must therefore be widened, to around 120 degrees, to obtain a reasonable amount of power, and the efficiency is then 60-70%.[14] Class D Main article: Class D amplifier In the class-D amplifier the active devices (transistors)
Input
C Low-pass filter Switching controller and output stage Triangular wave generator
Block diagram of a basic switching or PWM (class-D) amplifier.
function as electronic switches instead of linear gain devices; they are either on or off. The analog signal is converted to a stream of pulses that represents the signal by pulse width modulation, pulse density modulation, deltasigma modulation or a related modulation technique before being applied to the amplifier. The time average power value of the pulses is directly proportional to the analog signal, so after amplification the signal can be conIn practical class-C amplifiers a tuned load is invariably verted back to an analog signal by a passive low-pass filused. In one common arrangement the resistor shown in ter. the circuit above is replaced with a parallel-tuned circuit The purpose of the output filter is to smooth the pulse consisting of an inductor and capacitor in parallel, whose stream to an analog signal, removing the high frequency components are chosen to resonate the frequency of the spectral components of the pulses. The frequency of the
The tuned circuit resonates at one frequency, the fixed carrier frequency, and so the unwanted frequencies are suppressed, and the wanted full signal (sine wave) is extracted by the tuned load. The signal bandwidth of the amplifier is limited by the Q-factor of the tuned circuit but this is not a serious limitation. Any residual harmonics can be removed using a further filter.
3.3. AMPLIFIER
81 lated signal. Switching power supplies have even been modified into crude class-D amplifiers (although typically these can only reproduce low-frequencies with an acceptable level of accuracy).
Boss Audio class-D mono amplifier with a low pass filter for powering subwoofers
output pulses is typically ten or more times the highest frequency in the input signal to be amplified, so that the filter can adequately reduce the unwanted harmonics, reproducing an accurate reproduction of the input. The main advantage of a class-D amplifier is power efficiency. Because the output pulses have a fixed amplitude, the switching elements (usually MOSFETs, but valves (vacuum tubes) and bipolar transistors were once used) are switched either completely on or completely off, rather than operated in linear mode. A MOSFET operates with the lowest resistance when fully on and thus (excluding when fully off) has the lowest power dissipation when in that condition. Compared to an equivalent classAB device, a class-D amplifier’s lower losses permit the use of a smaller heat sink for the MOSFETs while also reducing the amount of input power required, allowing for a lower-capacity power supply design. Therefore, class-D amplifiers are typically smaller than an equivalent classAB amplifier.
High quality class-D audio power amplifiers have now appeared on the market. These designs have been said to rival traditional AB amplifiers in terms of quality. An early use of class-D amplifiers was high-power subwoofer amplifiers in cars. Because subwoofers are generally limited to a bandwidth of no higher than 150 Hz, the switching speed for the amplifier does not have to be as high as for a full range amplifier, allowing simpler designs. Class-D amplifiers for driving subwoofers are relatively inexpensive in comparison to class-AB amplifiers. The letter D used to designate this amplifier class is simply the next letter after C and, although occasionally used as such, does not stand for digital. Class-D and class-E amplifiers are sometimes mistakenly described as “digital” because the output waveform superficially resembles a pulse-train of digital symbols, but a class-D amplifier merely converts an input waveform into a continuously pulse-width modulated analog signal. (A digital waveform would be pulse-code modulated.) Additional classes
Class E The class-E/F amplifier is a highly efficient switching power amplifier, typically used at such high frequencies that the switching time becomes comparable to the duty time. As said in the class-D amplifier, the transistor is connected via a serial LC circuit to the load, and connected via a large L (inductor) to the supply voltage. The supply voltage is connected to ground via a large capacitor to prevent any RF signals leaking into the supply. The class-E amplifier adds a C (capacitor) between the transistor and ground and uses a defined L1 to connect to Another advantage of the class-D amplifier is that it can the supply voltage. operate from a digital signal source without requiring a The following description ignores DC, which can be digital-to-analog converter (DAC) to convert the signal added easily afterwards. The above-mentioned C and L to analog form first. If the signal source is in digital form, are in effect a parallel LC circuit to ground. When the such as in a digital media player or computer sound card, transistor is on, it pushes through the serial LC circuit into the digital circuitry can convert the binary digital signal the load and some current begins to flow to the parallel directly to a pulse width modulation signal to be applied LC circuit to ground. Then the serial LC circuit swings to the amplifier, simplifying the circuitry considerably. back and compensates the current into the parallel LC Class-D amplifiers have been widely used to control motors, but they are now also used as power amplifiers, with some extra circuitry to allow analogue to be converted to a much higher frequency pulse width modu-
circuit. At this point the current through the transistor is zero and it is switched off. Both LC circuits are now filled with energy in C and L0 . The whole circuit performs a damped oscillation. The damping by the load has been
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CHAPTER 3. APPLICATIONS
+Vcc L1
in 1975.[15] Some earlier reports on this operating class have been published in Russian.
L
L0
C0
Class F In push–pull amplifiers and in CMOS, the even harmonics of both transistors just cancel. Experishows that a square wave can be generated by those R L ment T1 C amplifiers. Theoretically square waves consist of odd harmonics only. In a class-D amplifier, the output filter blocks all harmonics; i.e., the harmonics see an open load. So even small currents in the harmonics suffice to generate a voltage square wave. The current is in phase Class-E amplifier with the voltage applied to the filter, but the voltage across the transistors is out of phase. Therefore, there is a minimal overlap between current through the transistors and adjusted so that some time later the energy from the Ls voltage across the transistors. The sharper the edges, the is gone into the load, but the energy in both C0 peaks at lower the overlap. the original value to in turn restore the original voltage so that the voltage across the transistor is zero again and it While in class D, transistors and the load exist as two separate modules, class F admits imperfections like the parcan be switched on. asitics of the transistor and tries to optimise the global With load, frequency, and duty cycle (0.5) as given pa- system to have a high impedance at the harmonics. Of rameters and the constraint that the voltage is not only course there has to be a finite voltage across the tranrestored, but peaks at the original voltage, the four pa- sistor to push the current across the on-state resistance. rameters (L, L0 , C and C0 ) are determined. The class-E Because the combined current through both transistors is amplifier takes the finite on resistance into account and mostly in the first harmonic, it looks like a sine. That tries to make the current touch the bottom at zero. This means that in the middle of the square the maximum of means that the voltage and the current at the transistor current has to flow, so it may make sense to have a dip are symmetric with respect to time. The Fourier trans- in the square or in other words to allow some overswing form allows an elegant formulation to generate the com- of the voltage square wave. A class-F load network by plicated LC networks and says that the first harmonic is definition has to transmit below a cutoff frequency and passed into the load, all even harmonics are shorted and reflect above. all higher odd harmonics are open. Any frequency lying below the cutoff and having its secClass E uses a significant amount of second-harmonic ond harmonic above the cutoff can be amplified, that is voltage. The second harmonic can be used to reduce the an octave bandwidth. On the other hand, an inductiveoverlap with edges with finite sharpness. For this to work, capacitive series circuit with a large inductance and a tunenergy on the second harmonic has to flow from the load able capacitance may be simpler to implement. By reducinto the transistor, and no source for this is visible in the ing the duty cycle below 0.5, the output amplitude can circuit diagram. In reality, the impedance is mostly re- be modulated. The voltage square waveform degrades, active and the only reason for it is that class E is a class but any overheating is compensated by the lower overall F (see below) amplifier with a much simplified load net- power flowing. Any load mismatch behind the filter can work and thus has to deal with imperfections. only act on the first harmonic current waveform, clearly In many amateur simulations of class-E amplifiers, sharp only a purely resistive load makes sense, then the lower current edges are assumed nullifying the very motivation the resistance, the higher the current. for class E and measurements near the transit frequency Class F can be driven by sine or by a square wave, for of the transistors show very symmetric curves, which look a sine the input can be tuned by an inductor to increase much similar to class-F simulations. gain. If class F is implemented with a single transistor, The class-E amplifier was invented in 1972 by Nathan O. the filter is complicated to short the even harmonics. All Sokal and Alan D. Sokal, and details were first published previous designs use sharp edges to minimise the overlap.
3.3. AMPLIFIER
U (V)
83
Ampli class G
+ Vss
+ Vs
0
t
- Vs
- Vss
U (V)
Ampli class H
+ Vss
+ Vs
0
t
- Vs
- Vss
Basic schematic of a class-H configuration
increases. The terms “class G” and “class H” are used interchangeably to refer to different designs, varying in definition from one manufacturer or paper to another.
Rail voltage modulation
Classes G and H There are a variety of amplifier designs that enhance class-AB output stages with more efficient techniques to achieve greater efficiencies with low distortion. These designs are common in large audio amplifiers since the heatsinks and power transformers would be prohibitively large (and costly) without the efficiency
Class-G amplifiers (which use “rail switching” to decrease power consumption and increase efficiency) are more efficient than class-AB amplifiers. These amplifiers provide several power rails at different voltages and switch between them as the signal output approaches each level. Thus, the amplifier increases efficiency by reducing the wasted power at the output transistors. Class-G amplifiers are more efficient than class AB but less efficient when compared to class D, however, they do not have the electromagnetic interference effects of class D.
84 Class-H amplifiers take the idea of class G one step further creating an infinitely variable supply rail. This is done by modulating the supply rails so that the rails are only a few volts larger than the output signal at any given time. The output stage operates at its maximum efficiency all the time. Switched-mode power supplies can be used to create the tracking rails. Significant efficiency gains can be achieved but with the drawback of more complicated supply design and reduced THD performance. In common designs, a voltage drop of about 10V is maintained over the output transistors in Class H circuits. The picture above shows positive supply voltage of the output stage and the voltage at the speaker output. The boost of the supply voltage is shown for a real music signal. The voltage signal shown is thus a larger version of the input, but has been changed in sign (inverted) by the amplification. Other arrangements of amplifying device are possible, but that given (that is, common emitter, common source or common cathode) is the easiest to understand and employ in practice. If the amplifying element is linear, the output is a faithful copy of the input, only larger and inverted. In practice, transistors are not linear, and the output only approximates the input. nonlinearity from any of several sources is the origin of distortion within an amplifier. The class of amplifier (A, B, AB or C) depends on how the amplifying device is biased. The diagrams omit the bias circuits for clarity. Any real amplifier is an imperfect realization of an ideal amplifier. An important limitation of a real amplifier is that the output it generates is ultimately limited by the power available from the power supply. An amplifier saturates and clips the output if the input signal becomes too large for the amplifier to reproduce or exceeds operational limits for the device.
Doherty amplifiers The Doherty, a hybrid configuration, is currently receiving renewed attention. It was invented in 1934 by William H. Doherty for Bell Laboratories—whose sister company, Western Electric, manufactured radio transmitters. The Doherty amplifier consists of a class-B primary or carrier stages in parallel with a class-C auxiliary or peak stage. The input signal splits to drive the two amplifiers, and a combining network sums the two output signals. Phase shifting networks are used in inputs and outputs. During periods of low signal level, the class-B amplifier efficiently operates on the signal and the class-C amplifier is cutoff and consumes little power.
CHAPTER 3. APPLICATIONS During periods of high signal level, the class-B amplifier delivers its maximum power and the class-C amplifier delivers up to its maximum power. The efficiency of previous AM transmitter designs was proportional to modulation but, with average modulation typically around 20%, transmitters were limited to less than 50% efficiency. In Doherty’s design, even with zero modulation, a transmitter could achieve at least 60% efficiency.[16] As a successor to Western Electric for broadcast transmitters, the Doherty concept was considerably refined by Continental Electronics Manufacturing Company of Dallas, TX. Perhaps, the ultimate refinement was the screengrid modulation scheme invented by Joseph B. Sainton. The Sainton amplifier consists of a class-C primary or carrier stage in parallel with a class-C auxiliary or peak stage. The stages are split and combined through 90degree phase shifting networks as in the Doherty amplifier. The unmodulated radio frequency carrier is applied to the control grids of both tubes. Carrier modulation is applied to the screen grids of both tubes. The bias point of the carrier and peak tubes is different, and is established such that the peak tube is cutoff when modulation is absent (and the amplifier is producing rated unmodulated carrier power) whereas both tubes contribute twice the rated carrier power during 100% modulation (as four times the carrier power is required to achieve 100% modulation). As both tubes operate in class C, a significant improvement in efficiency is thereby achieved in the final stage. In addition, as the tetrode carrier and peak tubes require very little drive power, a significant improvement in efficiency within the driver stage is achieved as well (317C, et al.).[17] The released version of the Sainton amplifier employs a cathode-follower modulator, not a push–pull modulator. Previous Continental Electronics designs, by James O. Weldon and others, retained most of the characteristics of the Doherty amplifier but added screen-grid modulation of the driver (317B, et al.). The Doherty amplifier remains in use in very-high-power AM transmitters, but for lower-power AM transmitters, vacuum-tube amplifiers in general were eclipsed in the 1980s by arrays of solid-state amplifiers, which could be switched on and off with much finer granularity in response to the requirements of the input audio. However, interest in the Doherty configuration has been revived by cellular-telephone and wireless-Internet applications where the sum of several constant envelope users creates an aggregate AM result. The main challenge of the Doherty amplifier for digital transmission modes is in aligning the two stages and getting the class-C amplifier to turn
3.3. AMPLIFIER
85
on and off very quickly. Recently, Doherty amplifiers have found widespread use in cellular base station transmitters for GHz frequencies. Implementations for transmitters in mobile devices have also been demonstrated.
R1
R3
+V supply
R4 Q3 Q4
Input C1
D1 Q1
Q2 R7
3.3.5
Implementation
R2
Output
D2
R5
Q5
R8
C2
R6 0V (ground)
Amplifiers are implemented using active elements of different kinds: A practical amplifier circuit • The first active elements were relays. They were for example used in transcontinental telegraph lines: a weak current was used to switch the voltage of a bat- typical (though substantially simplified) design as found tery to the outgoing line. in modern amplifiers, with a class-AB push–pull output stage, and uses some overall negative feedback. Bipolar • For transmitting audio, carbon microphones were transistors are shown, but this design would also be realused as the active element. This was used to moduizable with FETs or valves. late a radio-frequency source in one of the first AM audio transmissions, by Reginald Fessenden on Dec. The input signal is coupled through capacitor C1 to the base of transistor Q1. The capacitor allows the AC sig24, 1906.[18] nal to pass, but blocks the DC bias voltage established • Amplifiers used vacuum tubes exclusively until the by resistors R1 and R2 so that any preceding circuit is 1960s. Today, tubes are used for specialist audio ap- not affected by it. Q1 and Q2 form a differential ampliplications such as guitar amplifiers and audiophile fier (an amplifier that multiplies the difference between amplifiers. Many broadcast transmitters still use two inputs by some constant), in an arrangement known vacuum tubes. as a long-tailed pair. This arrangement is used to conve• In the 1960s, the transistor started to take over. niently allow the use of negative feedback, which is fed These days, discrete transistors are still used in high- from the output to Q2 via R7 and R8. power amplifiers and in specialist audio devices. • Beginning in the 1970s, more and more transistors were connected on a single chip therefore creating the integrated circuit. A large number of amplifiers commercially available today are based on integrated circuits. For special purposes, other active elements have been used. For example, in the early days of the satellite communication, parametric amplifiers were used. The core circuit was a diode whose capacity was changed by an RF signal created locally. Under certain conditions, this RF signal provided energy that was modulated by the extremely weak satellite signal received at the earth station. Amplifier circuit The practical amplifier circuit to the right could be the basis for a moderate-power audio amplifier. It features a
The negative feedback into the difference amplifier allows the amplifier to compare the input to the actual output. The amplified signal from Q1 is directly fed to the second stage, Q3, which is a common emitter stage that provides further amplification of the signal and the DC bias for the output stages, Q4 and Q5. R6 provides the load for Q3 (A better design would probably use some form of active load here, such as a constant-current sink). So far, all of the amplifier is operating in class A. The output pair are arranged in class-AB push–pull, also called a complementary pair. They provide the majority of the current amplification (while consuming low quiescent current) and directly drive the load, connected via DCblocking capacitor C2. The diodes D1 and D2 provide a small amount of constant voltage bias for the output pair, just biasing them into the conducting state so that crossover distortion is minimized. That is, the diodes push the output stage firmly into class-AB mode (assuming that the base-emitter drop of the output transistors is reduced by heat dissipation).
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This design is simple, but a good basis for a practical design because it automatically stabilises its operating point, since feedback internally operates from DC up through the audio range and beyond. Further circuit elements would probably be found in a real design that would roll off the frequency response above the needed range to prevent the possibility of unwanted oscillation. Also, the use of fixed diode bias as shown here can cause problems if the diodes are not both electrically and thermally matched to the output transistors – if the output transistors turn on too much, they can easily overheat and destroy themselves, as the full current from the power supply is not limited at this stage. A common solution to help stabilise the output devices is to include some emitter resistors, typically an ohm or so. Calculating the values of the circuit’s resistors and capacitors is done based on the components employed and the intended use of the amp. For the basics of radio frequency amplifiers using valves, see Valved RF amplifiers. Notes on implementation Real world amplifiers are imperfect. • One consequence is that the power supply itself may influence the output, and must itself be considered when designing the amplifier • a power amplifier is effectively an input signal controlled power regulator - regulating the power sourced from the power supply or mains to the amplifier’s load. The power output from a power amplifier cannot exceed the power input to it.
output needed - e.g. short-time or continuous, and dynamic range required - e.g. recorded program or live • In the case of high-powered audio applications requiring long cables to the load - e.g. cinemas and shipping centres - instead of using heavy gauge cables it may be more efficient to connect to the load at line output voltage with matching transformers at source and loads. • To prevent instability and/or overheating, care is need to ensure solid state amplifiers are adequately loaded. Most have a rated minimum load impedance. • All amplifiers generate heat through electrical losses. This heat must be dissipated via natural or forced air cooling. Heat can damage or reduce service life of electronic components. Consideration should be given to the heating effects of or upon adjacent equipment. Different methods of supplying power result in many different methods of bias. Bias is a technique by which the active devices are set up to operate in a particular region, or by which the DC component of the output signal is set to the midpoint between the maximum voltages available from the power supply. Most amplifiers use several devices at each stage; they are typically matched in specifications except for polarity. Matched inverted polarity devices are called complementary pairs. Class-A amplifiers generally use only one device, unless the power supply is set to provide both positive and negative voltages, in which case a dual device symmetrical design may be used. Class-C amplifiers, by definition, use a single polarity supply.
• The amplifier circuit has an “open loop” performance, that can be described by various parame- Amplifiers often have multiple stages in cascade to inters (gain, slew rate, output impedance, distortion, crease gain. Each stage of these designs may be a difbandwidth, signal to noise ratio, etc.) ferent type of amp to suit the needs of that stage. For • Many modern amplifiers use negative feedback instance, the first stage might be a class-A stage, feedtechniques to hold the gain at the desired value and ing a class-AB push–pull second stage, which then drives to reduce distortion. Negative loop feedback has the a class-G final output stage, taking advantage of the intended effect of electrically damping loudspeaker strengths of each type, while minimizing their weakmotion, thereby damping the mechanical dynamic nesses. performance of the loudspeaker. • When assessing rated amplifier power output it is 3.3.6 See also useful to consider the load to be applied, the form • Charge transfer amplifier of signal - i.e. speech or music, duration of power
3.3. AMPLIFIER
87
• Distributed amplifier
[8] RCA Receiving Tube Manual, RC-14 (1940) p 12
• Faithful amplification
[9] ARRL Handbook, 1968; page 65
• Guitar amplifier • Instrument amplifier
[10] Jerry Del Colliano (20 February 2012), Pass Labs XA30.5 Class-A Stereo Amp Reviewed, Home Theater Review, Luxury Publishing Group Inc.
• Instrumentation amplifier
[11] Ask the Doctors: Tube vs. Solid-State Harmonics
• Low noise amplifier
[12] Volume cranked up in amp debate
• Negative feedback amplifier • Operational amplifier • Optical amplifier • Power added efficiency • Programmable gain amplifier • RF power amplifier • Valve audio amplifier
3.3.7
References
[1] Patronis, Gene (1987). “Amplifiers”. In Glen Ballou. Handbook for Sound Engineers: The New Audio Cyclopedia. Howard W. Sams & Co. p. 493. ISBN 0-67221983-2. [2] Robert Boylestad and Louis Nashelsky (1996). Electronic Devices and Circuit Theory, 7th Edition. Prentice Hall College Division. ISBN 978-0-13-375734-7. [3]
• Mark Cherry, Maxim Engineering journal, volume 62, Amplifier Considerations in Ceramic Speaker Applications, p.3, accessed 2012-10-01
[4] Robert S. Symons (1998). “Tubes: Still vital after all these years”. IEEE Spectrum 35 (4): 52–63. doi:10.1109/6.666962. [5] It is a curiosity to note that this table is a “Zwicky box”; in particular, it encompasses all possibilities. See Fritz Zwicky. [6] John Everett (1992). Vsats: Very Small Aperture Terminals. IET. ISBN 0-86341-200-9. [7] Roy, Apratim; Rashid, S. M. S. (5 June 2012). “A power efficient bandwidth regulation technique for a low-noise high-gain RF wideband amplifier”. Central European Journal of Engineering 2 (3): 383–391. Bibcode:2012CEJE....2..383R. doi:10.2478/s13531012-0009-1.
[13] A.P. Malvino, Electronic Principles (2nd Ed.1979. ISBN 0-07-039867-4) p.299. [14] Electronic and Radio Engineering, R.P.Terman, McGraw Hill, 1964 [15] N. O. Sokal and A. D. Sokal, “Class E – A New Class of High-Efficiency Tuned Single-Ended Switching Power Amplifiers”, IEEE Journal of Solid-State Circuits, vol. SC10, pp. 168–176, June 1975. HVK [16] US patent 2210028, William H. Doherty, “Amplifier”, issued 1940-08-06, assigned to Bell Telephone Laboratories [17] US patent 3314034, Joseph B. Sainton, “High Efficiency Amplifier and Push–Pull Modulator”, issued 1967-04-11, assigned to Continental Electronics Manufacturing Company [18] Lee, Thomas (2004). The Design of CMOS RadioFrequency Integrated Circuits. New York, NY: Cambridge University Press. p. 8. ISBN 978-0-521-83539-8.
3.3.8 External links • Rane audio’s guide to amplifier classes • Design and analysis of a basic class D amplifier • Conversion: distortion factor to distortion attenuation and THD • An alternate topology called the grounded bridge amplifier - pdf • Contains an explanation of different amplifier classes - pdf • Reinventing the power amplifier - pdf • Anatomy of the power amplifier, including information about classes
88 • Tons of Tones - Site explaining non linear distortion stages in Amplifier Models • Class D audio amplifiers, white paper - pdf • Class E Radio Transmitters - Tutorials, Schematics, Examples, and Construction Details
CHAPTER 3. APPLICATIONS
Chapter 4
Background Theory 4.1 Electron hole
Electrons: Protons: Neutrons:
An electron hole is the conceptual and mathematical opposite of an electron, useful in the study of physics, chemistry, and electronic engineering. The concept describes the lack of an electron at a position where one could exist in an atom or atomic lattice. It is different from the positron, which is an actual particle of antimatter.
-
1 2 2
Electron Hole
-
He +
Charge: +1
The electron hole was introduced into calculations for the following situations: • If an electron is excited into a higher state it leaves a hole in its old state. This meaning is used in Auger electron spectroscopy (and other x-ray techniques), in computational chemistry, and to explain the low electron-electron scattering-rate in crystals (metals, semiconductors). • In crystals, electronic band structure calculations lead to an effective mass for the electrons, which typically is negative at the top of a band. The negative mass is an unintuitive concept,[1] and in these situations a more familiar picture is found by considering a positive charge with a positive mass.
4.1.1
Solid-state physics
In solid-state physics, an electron hole (usually referred to simply as a hole) is the absence of an electron from an otherwise full valence band. A hole is essentially a way to conceptualize the interactions of the electrons within a nearly full system, which is missing just a few electrons. In some ways, the behavior of a hole within a semiconductor crystal lattice is comparable to that of the bubble
When an electron leaves a helium atom, it leaves an electron hole in its place. This causes the helium atom to become positively charged.
in an otherwise full bottle of water.[2]
Simplified analogy: Empty seat in an auditorium Hole conduction in a valence band can be explained by the following analogy. Imagine a row of people seated in an auditorium, where there are no spare chairs. Someone in the middle of the row wants to leave, so he jumps over the back of the seat into an empty row, and walks out. The empty row is analogous to the conduction band, and the person walking out is analogous to a free electron. Now imagine someone else comes along and wants to sit down. The empty row has a poor view; so he does not want to sit there. Instead, a person in the crowded row moves into the empty seat the first person left behind. The empty seat moves one spot closer to the edge and the person waiting to sit down. The next person follows, and the next, et cetera. One could say that the empty seat
89
90
CHAPTER 4. BACKGROUND THEORY
moves towards the edge of the row. Once the empty seat The analogy above is quite simplified, and cannot explain reaches the edge, the new person can sit down. why holes create an opposite effect to electrons in the Hall and Seebeck effect. A more precise and detailed effect In the process everyone in the row has moved along. explanation follows.[3] If those people were negatively charged (like electrons), this movement would constitute conduction. If the seats themselves were positively charged, then only the vacant seat would be positive. This is a very simple model of how hole conduction works. In reality, due to the crystal structure properties, the hole is not localized to a single position as described in the previous example. Rather, the hole spans an area in the crystal lattice covering many hundreds of unit cells. This is equivalent to being unable to tell which broken bond corresponds to the “missing” electron. Instead of analyzing the movement of an empty state in the valence band as the movement of many separate electrons, a single equivalent imaginary particle called a “hole” is considered. In an applied electric field, the electrons move in one direction, corresponding to the hole moving in the other. If a hole associates itself with a neutral atom, that atom loses an electron and becomes positive. Therefore the hole is taken to have positive charge of +e, precisely the opposite of the electron charge.
Detailed picture: A hole is the absence of a negativemass electron
• The dispersion relation determines how electrons respond to forces (via the concept of effective mass).[3] A dispersion relation is the relationship between wavevector (k-vector) and energy in a band, part of the electronic band structure. In quantum mechanics, the electrons are waves, and energy is the wave frequency. A localized electron is a wavepacket, and the motion of an electron is given by the formula for the group velocity of a wave. An electric field affects an electron by gradually shifting all the wavevectors in the wavepacket, and the electron moves because its wave group velocity changes. Therefore, again, the way an electron responds to forces is entirely determined by its dispersion relation. An electron floating in space has the dispersion relation E=ℏ2 k2 /(2m), where m is the (real) electron mass and ℏ is reduced Planck constant. In the conduction band of a semiconductor, the dispersion relation is instead E=ℏ2 k2 /(2m* ) (m* is the effective mass), so a conductionband electron responds to forces as if it had the mass m* . • Electrons near the top of the valence band behave as if they have negative mass.[3] The dispersion relation near the top of the valence band is E=ℏ2 k2 /(2m* ) with negative effective mass. So electrons near the top of the valence band behave like they have negative mass. When a force pulls the electrons to the right, these electrons actually move left. This is solely due to the shape of the valence band, and is unrelated to whether the band is full or empty. If you could somehow empty out the valence band and just put one electron near the valence band maximum (an unstable situation), this electron would move the “wrong way” in response to forces.
A semiconductor electronic band structure (right) includes the dispersion relation of each band, i.e. the energy of an electron E as a function of the electron’s wavevector k. The “unfilled band” is the semiconductor’s conduction band; it curves upward indicating positive effective mass. The “filled band” is the semiconductor’s valence band; it curves downward indicating negative effective mass.
• Positively-charged holes as a shortcut for calculating the total current of an almost-full band.[3] A perfectly-full band always has zero current. One way to think about this fact is that the electron states near the top of the band have negative effective mass, and those near the bottom of the band have positive effective mass,
4.1. ELECTRON HOLE so the net motion is exactly zero. If an otherwise-almostfull valence band has a state without an electron in it, we say that this state is occupied by a hole. There is a mathematical shortcut for calculating the current due to every electron in the whole valence band: Start with zero current (the total if the band were full), and subtract the current due to the electrons that would be in each hole state if it wasn't a hole. Since subtracting the current caused by a negative charge in motion is the same as adding the current caused by a positive charge moving on the same path, the mathematical shortcut is to pretend that each hole state is carrying a positive charge, while ignoring every other electron state in the valence band. • A hole near the top of the valence band moves the same way as an electron near the top of the valence band would move.[3]
91 mobility for holes under the influence of an electric field and this may slow down the speed of the electronic device made of that semiconductor. This is one major reason for adopting electrons as the primary charge carriers, whenever possible in semiconductor devices, rather than holes. That said, in many semiconductor devices, both electrons and holes play an essential role. Examples include p–n diodes and bipolar transistors.
4.1.2 Holes in quantum chemistry An alternate meaning for the term electron hole is used in computational chemistry. In coupled cluster methods, the ground (or lowest energy) state of a molecule is interpreted as the “vacuum state”—conceptually, in this state there are no electrons. In this scheme, the absence of an electron from a normally-filled state is called a “hole” and is treated as a particle, and the presence of an electron in a normally-empty state is simply called an “electron”. This terminology is almost identical to that used in solid-state physics.
This fact follows from the discussion and definition above. This is an example where the auditorium analogy above is misleading. When a person moves left in a full auditorium, an empty seat moves right. But in this section we are imagining how electrons move through kspace, not real space, and the effect of a force is to move all the electrons through k-space in the same direction at the same time. So a better analogy is a bubble underwa- 4.1.3 See also ter in a river: The bubble moves the same direction as the • Band gap water, not opposite. • Conclusion: Hole as a positive-charge, positive-mass quasiparticle.
• Carrier generation and recombination • Effective mass
From the above, a hole (A) carries a positive charge, and • Electrical resistivity and conductivity (B) responds to electric and magnetic fields as if it had a • Semiconductor positive charge and positive mass. (The latter is because a particle with positive charge and positive mass responds to electric and magnetic fields in the same way as a particle with negative charge and negative mass.) That ex- 4.1.4 References plains why holes can be treated in all situations as ordi[1] For these negative mass electrons, momentum is opposite nary positively-charged quasiparticles. to velocity, so forces acting on these electrons cause their Role in semiconductor technology
velocity to change in the 'wrong' direction. As these electrons gain energy (moving towards the top of the band), they slow down.
In some semiconductors, such as silicon, the hole’s effective mass is dependent on direction (anisotropic), however a value averaged over all directions can be used for some macroscopic calculations.
[2] Weller, Paul F. (1967). “An analogy for elementary band theory concepts in solids”. J. Chem. Educ 44 (7): 391. Bibcode:1967JChEd..44..391W. doi:10.1021/ed044p391.
In most semiconductors, the effective mass of a hole is much larger than that of an electron. This results in lower
[3] Kittel, Introduction to Solid State Physics 8th edition, page 194-196
92
4.2 P–n junction
CHAPTER 4. BACKGROUND THEORY in one direction but not in the other (opposite) direction. This property is explained in terms of forward bias and reverse bias, where the term bias refers to an application of electric voltage to the p–n junction.
4.2.2
Equilibrium (zero bias)
In a p–n junction, without an external applied voltage, an equilibrium condition is reached in which a potential A p–n junction. The circuit symbol is shown: the triangle corre- difference is formed across the junction. This potential sponds to the p side. difference is called built-in potential Vbi . See also: p–n diode and Diode § Semiconductor diodes A p–n junction is a boundary or interface between two types of semiconductor material, p-type and n-type, inside a single crystal of semiconductor. It is created by doping, for example by ion implantation, diffusion of dopants, or by epitaxy (growing a layer of crystal doped with one type of dopant on top of a layer of crystal doped with another type of dopant). If two separate pieces of material were used, this would introduce a grain boundary between the semiconductors that would severely inhibit its utility by scattering the electrons and holes.
After joining p-type and n-type semiconductors, electrons from the n region near the p–n interface tend to diffuse into the p region. As electrons diffuse, they leave positively charged ions (donors) in the n region. Likewise, holes from the p-type region near the p–n interface begin to diffuse into the n-type region, leaving fixed ions (acceptors) with negative charge. The regions nearby the p–n interfaces lose their neutrality and become charged, forming the space charge region or depletion layer (see figure A).
p–n junctions are elementary “building blocks” of most semiconductor electronic devices such as diodes, transistors, solar cells, LEDs, and integrated circuits; they are the active sites where the electronic action of the device takes place. For example, a common type of transistor, the bipolar junction transistor, consists of two p–n junctions in series, in the form n–p–n or p–n–p. The discovery of the p–n junction is usually attributed to American physicist Russell Ohl of Bell Laboratories.[1] A Schottky junction is a special case of a p–n junction, Figure A. A p–n junction in thermal equilibrium with zero-bias where metal serves the role of the p-type semiconductor. voltage applied. Electron and hole concentration are reported
4.2.1 Properties of a p–n junction The p–n junction possesses some interesting properties that have useful applications in modern electronics. A pdoped semiconductor is relatively conductive. The same is true of an n-doped semiconductor, but the junction between them can become depleted of charge carriers, and hence non-conductive, depending on the relative voltages of the two semiconductor regions. By manipulating this non-conductive layer, p–n junctions are commonly used as diodes: circuit elements that allow a flow of electricity
with blue and red lines, respectively. Gray regions are chargeneutral. Light-red zone is positively charged. Light-blue zone is negatively charged. The electric field is shown on the bottom, the electrostatic force on electrons and holes and the direction in which the diffusion tends to move electrons and holes.
The electric field created by the space charge region opposes the diffusion process for both electrons and holes. There are two concurrent phenomena: the diffusion process that tends to generate more space charge, and the electric field generated by the space charge that tends to counteract the diffusion. The carrier concentration profile at equilibrium is shown in figure A with blue and red
4.2. P–N JUNCTION
93
lines. Also shown are the two counterbalancing phenomena that establish equilibrium.
PN junction operation in forward-bias mode, showing reducing depletion width. Both p and n junctions are doped at a 1e15/cm3 doping level, leading to built-in potential of ~0.59 V. Reducing depletion width can be inferred from the shrinking charge profile, as fewer dopants are exposed with increasing forward bias.
Figure B. A p–n junction in thermal equilibrium with zero-bias voltage applied. Under the junction, plots for the charge density, the electric field, and the voltage are reported.
The space charge region is a zone with a net charge provided by the fixed ions (donors or acceptors) that have been left uncovered by majority carrier diffusion. When equilibrium is reached, the charge density is approximated by the displayed step function. In fact, the region is completely depleted of majority carriers (leaving a charge density equal to the net doping level), and the edge between the space charge region and the neutral region is quite sharp (see figure B, Q(x) graph). The space charge region has the same magnitude of charge on both sides of the p–n interfaces, thus it extends farther on the less doped side in this example (the n side in figures A and B).
P-type material repels the holes, while the negative potential applied to the N-type material repels the electrons. As electrons and holes are pushed toward the junction, the distance between them decreases. This lowers the barrier in potential. With increasing forward-bias voltage, the depletion zone eventually becomes thin enough that the zone’s electric field cannot counteract charge carrier motion across the p–n junction, as a consequence reducing electrical resistance. The electrons that cross the p–n junction into the P-type material (or holes that cross into the N-type material) will diffuse in the near-neutral region. Therefore, the amount of minority diffusion in the near-neutral zones determines the amount of current that may flow through the diode.
Only majority carriers (electrons in N-type material or holes in P-type) can flow through a semiconductor for a macroscopic length. With this in mind, consider the flow of electrons across the junction. The forward bias causes a force on the electrons pushing them from the N side toward the P side. With forward bias, the depletion region is narrow enough that electrons can cross the junction and inject into the P-type material. However, they do not continue to flow through the P-type material indefinitely, because it is energetically favorable for them to recombine with holes. The average length an electron 4.2.3 Forward bias travels through the P-type material before recombining is In forward bias, the p-type is connected with the positive called the diffusion length, and it is typically on the order terminal and the n-type is connected with the negative of micrometers.[2] terminal. Although the electrons penetrate only a short distance With a battery connected this way, the holes in the Ptype region and the electrons in the N-type region are pushed toward the junction. This reduces the width of the depletion zone. The positive potential applied to the
into the P-type material, the electric current continues uninterrupted, because holes (the majority carriers) begin to flow in the opposite direction. The total current (the sum of the electron and hole currents) is constant in
94 space, because any variation would cause charge buildup over time (this is Kirchhoff’s current law). The flow of holes from the P-type region into the N-type region is exactly analogous to the flow of electrons from N to P (electrons and holes swap roles and the signs of all currents and voltages are reversed).
CHAPTER 4. BACKGROUND THEORY does so increasingly with increasing reverse-bias voltage. This increases the voltage barrier causing a high resistance to the flow of charge carriers, thus allowing minimal electric current to cross the p–n junction. The increase in resistance of the p–n junction results in the junction behaving as an insulator.
Therefore, the macroscopic picture of the current flow through the diode involves electrons flowing through the N-type region toward the junction, holes flowing through the P-type region in the opposite direction toward the junction, and the two species of carriers constantly recombining in the vicinity of the junction. The electrons and holes travel in opposite directions, but they also have opposite charges, so the overall current is in the same direction on both sides of the diode, as required.
The strength of the depletion zone electric field increases as the reverse-bias voltage increases. Once the electric field intensity increases beyond a critical level, the p– n junction depletion zone breaks down and current begins to flow, usually by either the Zener or the avalanche breakdown processes. Both of these breakdown processes are non-destructive and are reversible, as long as the amount of current flowing does not reach levels that cause the semiconductor material to overheat and cause The Shockley diode equation models the forward-bias thermal damage. operational characteristics of a p–n junction outside the This effect is used to one’s advantage in Zener diode regavalanche (reverse-biased conducting) region. ulator circuits. Zener diodes have a certain – low – breakdown voltage. A standard value for breakdown voltage is for instance 5.6 V. This means that the voltage at the cath4.2.4 Reverse bias ode can never be more than 5.6 V higher than the voltage at the anode, because the diode will break down – and therefore conduct – if the voltage gets any higher. This in effect regulates the voltage over the diode. Another application of reverse biasing is Varicap diodes, where the width of the depletion zone (controlled with the reverse bias voltage) changes the capacitance of the diode.
4.2.5
Governing Equations
A silicon p–n junction in reverse bias.
Size of depletion region Connecting the P-type region to the negative terminal of the battery and the N-type region to the positive terminal corresponds to reverse bias. If a diode is reverse-biased, the voltage at the cathode is comparatively higher than the anode. Therefore, no current will flow until the diode breaks down. Reverse-bias usually refers to how a diode is used in a circuit. The connections are illustrated in the diagram to the right. Because the p-type material is now connected to the negative terminal of the power supply, the 'holes' in the Ptype material are pulled away from the junction, causing the width of the depletion zone to increase. Likewise, because the N-type region is connected to the positive terminal, the electrons will also be pulled away from the junction. Therefore, the depletion region widens, and
See also: Band bending For a p–n junction, letting CA (x) and CD (x) be the concentrations of acceptor and donor atoms respectively, and letting N0 (x) and P0 (x) be the equilibrium concentrations of electrons and holes respectively, yields, by Poisson’s equation: 2
− ddxV2 =
ρ ε
=
q ε
[(N0 − P0 ) + (CD − CA )]
where V is the electric potential, ρ is the charge density, ε is permittivity and q is the magnitude of the electron charge. Letting dp be the width of the depletion region within the p-side, and letting dn be the width of the depletion region within the n-side, it must be that
4.2. P–N JUNCTION
dp CA = dn CD
95
4.2.6 Summary
because the total charge on either side of the depletion region must cancel out. Therefore, letting D and ∆V represent the entire depletion region and the potential difference across it, ∫ ∫ ∆V = D qε [(N0 − P0 ) + (CD − CA )] dx dx
The forward-bias and the reverse-bias properties of the p–n junction imply that it can be used as a diode. A p–n junction diode allows electric charges to flow in one direction, but not in the opposite direction; negative charges (electrons) can easily flow through the junction from n to p but not from p to n, and the reverse is true for holes. CA CD 2q = CA +CD ε (dp + dn )2 When the p–n junction is forward-biased, electric charge Where P0 = N0 = 0 , because we are in the depletion flows freely due to reduced resistance of the p–n juncregion. And thus, letting d be the total width of the de- tion. When the p–n junction is reverse-biased, however, pletion region, we get the junction barrier (and therefore resistance) becomes √ greater and charge flow is minimal. CA +CD d = 2ε q CA CD ∆V
Where ∆V can be written as ∆V0 + ∆Vext , where we have broken up the voltage difference into the equilibrium plus external components. The equilibrium potential results from diffusion forces, and thus we can calculate ∆V0 by implementing the Einstein relation and assuming the semiconductor is nondegenerate (i.e. the product P0 N0 is independent of the Fermi energy): ( ) CA CD ∆V0 = kT q ln P0 N0
4.2.7 Non-rectifying junctions
In the above diagrams, contact between the metal wires and the semiconductor material also creates metal– semiconductor junctions called Schottky diodes. In a simplified ideal situation a semiconductor diode would never function, since it would be composed of several diodes connected back-to-front in series. But, in practice, surface impurities within the part of the semiconwhere T is the temperature of the semiconductor and k is ductor that touches the metal terminals will greatly re[3] Boltzmann constant. duce the width of those depletion layers to such an extent that the metal-semiconductor junctions do not act as diodes. These non-rectifying junctions behave as ohmic Current across depletion region contacts regardless of applied voltage polarity.
The Shockley ideal diode equation characterizes the current across a p-n junction as a function of external voltage 4.2.8 See also and ambient conditions (temperature, choice of semicon• Diode and junction diode ductor, etc.). To see how it can be derived, we must examine the various reasons for current. The convention • Diode modelling is that the forward (+) direction be pointed against the diode’s built-in potential gradient at equilibrium. • Semiconductor • Forward Current ( JF ) --- Diffusion Current: current due to local imbalances in carrier concentration n , via the equation JD ∝ −q∇n
--- Semiconductor device --- n-type semiconductor --- p-type semiconductor • Transistor --- Field-effect transistor
• Reverse Current ( JR ) --- Field Current --- Generation Current
--- Bipolar junction transistor ∗ Alloy-junction transistor ∗ p–n–p transistor ∗ n–p–n transistor
96
CHAPTER 4. BACKGROUND THEORY --- Transistor–transistor logic
• Capacitance–voltage profiling • Deep-level transient spectroscopy • p–n diode • Solar cell • Semiconductor detector
4.2.9 References
• Understanding the PN Junction - Explains PN junction in a very easy to understand language.
4.3 Bipolar transistor biasing Bipolar transistor amplifiers must be properly biased to operate correctly. In circuits made with individual devices (discrete circuits), biasing networks consisting of resistors are commonly employed. Much more elaborate biasing arrangements are used in integrated circuits, for example, bandgap voltage references and current mirrors.
[1] Riordan, Michael; Lillian Hoddeson (1988). Crystal fire: the invention of the transistor and the birth of the information age. USA: W. W. Norton & Company. pp. 88–97. ISBN 0-393-31851-6.
The operating point of a device, also known as bias point, quiescent point, or Q-point, is the point on the output characteristics that shows the DC collector–emitter voltage (V ₑ) and the collector current (I ) with no input signal [2] Hook, J. R.; H. E. Hall (2001). Solid State Physics. John applied. The term is normally used in connection with Wiley & Sons. ISBN 0-471-92805-4. devices such as transistors. [3] Luque, Antonio; Steven Hegedus (29 March 2011). Handbook of Photovoltaic Science and Engineering. John Wiley & Sons. ISBN 978-0-470-97612-8.
4.3.1
Bias circuit requirements
Signal requirements for Class A amplifiers
4.2.10 Further reading For analog operation of a Class A amplifier, the Q-point is placed so the transistor stays in active mode (does not shift to operation in the saturation region or cut-off region) when input is applied. For digital operation, the Q-point is placed so the transistor does the contrary switches from the “on” (saturation) to the “off” (cutoff) state. Often, the Q-point is established near the center of the active region of a transistor characteristic to allow 4.2.11 External links similar signal swings in positive and negative directions. The Q-point should be stable; in particular, it should be • http://www.youtube.com/watch?v=JBtEckh3L9Q insensitive to variations in transistor parameters (for exEducational video on the P-N junction. ample, should not shift if transistor is replaced by another of the same type), variations in temperature, variations in • “P-N Junction” - PowerGuru, August, 2012. power supply voltage and so forth. The circuit must also • Olav Torheim, Elementary Physics of P-N Junctions, be practical; both easily implemented and cost-effective. 2007. • Shockley, William (1949). “The Theory of p-n Junctions in Semiconductors and p-n Junction Transistors”. Bell System Technical Journal 28 (3): 435– 489. doi:10.1002/j.1538-7305.1949.tb03645.x. Retrieved 12 June 2013.
• PN Junction Properties Calculator • PN Junction Lab free to use on nanoHUB.org allows simulation and study of a P-N junction diode with different doping and materials. Users can calculate current-voltage (I-V) & capacitance-voltage (C-V) outputs, as well. • Theory of P-N Diodes – Dr. Vasileska (2009)
Thermal considerations At constant current, the voltage across the emitter–base junction VBE of a bipolar transistor decreases 2 mV (silicon) and 1.8mV (germanium) for each 1 °C rise in temperature (reference being 25 °C). By the Ebers–Moll model, if the base–emitter voltage VBE is held constant and the temperature rises, the current through the base–
4.3. BIPOLAR TRANSISTOR BIASING
97
emitter diode IB will increase, and thus the collector current IC will also increase. Depending on the bias point, the power dissipated in the transistor may also increase, which will further increase its temperature and exacerbate the problem. This deleterious positive feedback results in thermal runaway.[1] There are several approaches to mitigate bipolar transistor thermal runaway. For example, • Negative feedback can be built into the biasing circuit so that increased collector current leads to decreased base current. Hence, the increasing collector current throttles its source. • Heat sinks can be used that carry away extra heat and prevent the base–emitter temperature from rising. • The transistor can be biased so that its collector is normally less than half of the power supply voltage, which implies that collector–emitter power dissipation is at its maximum value. Runaway is then impossible because increasing collector current leads to a decrease in dissipated power; this notion is Fixed bias (Base bias) known as the half-voltage principle. The circuits below primarily demonstrate the use of negative feedback to prevent thermal runaway.
V = IBRB + V ₑ Therefore,
4.3.2
Types of bias circuit for Class A amplifiers
IB = (V - V ₑ)/RB
The following discussion treats five common biasing cir- For a given transistor, V ₑ does not vary significantly durcuits used with Class A bipolar transistor amplifiers: ing use. As V is of fixed value, on selection of RB, the base current IB is fixed. Therefore this type is called fixed 1. Fixed bias bias type of circuit. 2. Collector-to-base bias 3. Fixed bias with emitter resistor 4. Voltage divider bias 5. Emitter bias Fixed bias (base bias)
Also for given circuit, V = ICRC + V ₑ Therefore, V ₑ = V - ICRC
This form of biasing is also called base bias. In the example image on the right, the single power source (for example, a battery) is used for both collector and base of a transistor, although separate batteries can also be used.
The common-emitter current gain of a transistor is an important parameter in circuit design, and is specified on the data sheet for a particular transistor. It is denoted as β on this page.
In the given circuit,
Because
98
CHAPTER 4. BACKGROUND THEORY IC = βIB
we can obtain IC as well. In this manner, operating point given as (V ₑ,IC) can be set for given transistor. Merits: • It is simple to shift the operating point anywhere in the active region by merely changing the base resistor (RB). • A very small number of components are required. Demerits: • The collector current does not remain constant with variation in temperature or power supply voltage. Collector-to-base bias Therefore the operating point is unstable. Collector Feedback Bias • Changes in V ₑ will change IB and thus cause IE to change. This in turn will alter the gain of the stage. This configuration employs negative feedback to prevent thermal runaway and stabilize the operating point. In this • When the transistor is replaced with another one, form of biasing, the base resistor R is connected to the B considerable change in the value of β can be ex- collector instead of connecting it to the DC source V . cc pected. Due to this change the operating point will So any thermal runaway will induce a voltage drop across shift. the RC resistor that will throttle the transistor’s base current. • For small-signal transistors (e.g., not power transistors) with relatively high values of β (i.e., between From Kirchhoff’s voltage law, the voltage VRb across the 100 and 200), this configuration will be prone to base resistor Rb is thermal runaway. In particular, the stability factor, which is a measure of the change in collector curacross drop VoltageRc base at Voltage rent with changes in reverse saturation current, is z }| { z}|{ approximately β+1. To ensure absolute stability of VRb = Vcc − (Ic + Ib )Rc − Vbe . the amplifier, a stability factor of less than 25 is preferred, and so small-signal transistors have large sta- By the Ebers–Moll model, Ic = βIb , and so bility factors. Ic
Usage:
z}|{ = Vcc −( βIb +Ib )Rc −Vbe = Vcc −Ib (β+1)Rc −Vbe .
VRb Due to the above inherent drawbacks, fixed bias is rarely used in linear circuits (i.e., those circuits which use the From Ohm’s law, the base current Ib = VRb /Rb , and so transistor as a current source). Instead, it is often used in circuits where transistor is used as a switch. However, VRb one application of fixed bias is to achieve crude automatic z}|{ gain control in the transistor by feeding the base resistor Ib Rb = Vcc − Ib (β + 1)Rc − Vbe . from a DC signal derived from the AC output of a later Hence, the base current Ib is stage.
4.3. BIPOLAR TRANSISTOR BIASING
99
Usage: The feedback also decreases the input impedance of the amplifier as seen from the base, which can be adVcc − Vbe Ib = vantageous. Due to the gain reduction from feedback, Rb + (β + 1)Rc this biasing form is used only when the trade-off for staIf Vbe is held constant and temperature increases, then the bility is warranted. collector current Ic increases. However, a larger Ic causes the voltage drop across resistor Rc to increase, which in Fixed bias with emitter resistor turn reduces the voltage VRb across the base resistor Rb . A lower base-resistor voltage drop reduces the base current Ib , which results in less collector current Ic . Because an increase in collector current with temperature is opposed, the operating point is kept stable. Merits: • Circuit stabilizes the operating point against variations in temperature and β (i.e. replacement of transistor) Demerits: • In this circuit, to keep Ic independent of β , the following condition must be met:
Ic = βIb =
β(Vcc − Vbe ) (Vcc − Vbe ) ≈ Rb + Rc + βRc Rc
which is the case when Fixed bias with emitter resistor
βRc ≫ Rb .
The fixed bias circuit is modified by attaching an external resistor to the emitter. This resistor introduces negative • As β -value is fixed (and generally unknown) for a feedback that stabilizes the Q-point. From Kirchhoff’s given transistor, this relation can be satisfied either voltage law, the voltage across the base resistor is by keeping Rc fairly large or making Rb very low. --- If Rc is large, a high Vcc is necessary, which increases cost as well as precautions necessary while handling.
VRb = VCC − Ie Re − Vbe
--- If Rb is low, the reverse bias of the collector– From Ohm’s law, the base current is base region is small, which limits the range of collector voltage swing that leaves the transistor in active mode. VRb Ib = Rb • The resistor Rb causes an AC feedback, reducing the voltage gain of the amplifier. This undesirable The way feedback controls the bias point is as follows. effect is a trade-off for greater Q-point stability. If V ₑ is held constant and temperature increases, emitter
100
CHAPTER 4. BACKGROUND THEORY
current increases. However, a larger Iₑ increases the emitter voltage Vₑ = IₑRₑ, which in turn reduces the voltage VR across the base resistor. A lower base-resistor voltage drop reduces the base current, which results in less collector current because I = β IB. Collector current and emitter current are related by I = α Iₑ with α ≈ 1, so the increase in emitter current with temperature is opposed, and the operating point is kept stable.
• In addition to the above, RE causes ac feedback which reduces the voltage gain of the amplifier. Usage:
The feedback also increases the input impedance of the amplifier when seen from the base, which can be advantageous. Due to the above disadvantages, this type of biasing circuit is used only with careful consideration of Similarly, if the transistor is replaced by another, there the trade-offs involved. may be a change in IC (corresponding to change in β- Collector-Stabilized Biasing value, for example). By similar process as above, the change is negated and operating point kept stable. Voltage divider biasing For the given circuit,
IB =
VCC − Vbe RB + (β + 1)RE
Merits: The circuit has the tendency to stabilize operating point against changes in temperature and β-value. Demerits: • In this circuit, to keep IC independent of β the following condition must be met:
IC = βIB =
(VCC − Vbe ) β(VCC − Vbe ) ≈ RB + (β + 1)RE RE
which is approximately the case if
(β + 1)RE ≫ RB Voltage divider bias
• As β-value is fixed for a given transistor, this relation can be satisfied either by keeping RE very large, or The voltage divider is formed using external resistors R1 and R2 . The voltage across R2 forward biases the emitmaking RB very low. ter junction. By proper selection of resistors R1 and R2 , --- If RE is of large value, high VCC is necessary. the operating point of the transistor can be made indeThis increases cost as well as precautions nec- pendent of β. In this circuit, the voltage divider holds the essary while handling. base voltage fixed independent of base current provided --- If RB is low, a separate low voltage supply the divider current is large compared to the base current. should be used in the base circuit. Using two However, even with a fixed base voltage, collector cursupplies of different voltages is impractical. rent varies with temperature (for example) so an emitter
4.3. BIPOLAR TRANSISTOR BIASING
101
resistor is added to stabilize the Q-point, similar to the above circuits with emitter resistor. In this circuit the base voltage is given by:
• As β-value is fixed for a given transistor, this relation can be satisfied either by keeping RE fairly large, or making R1 ||R2 very low.
R2 2 VB = voltage across R2 = Vcc (R1R+R − IB (RR11+R 2) 2)
--- If RE is of large value, high VCC is necessary. This increases cost as well as precautions necessary while handling.
2 ≈ Vcc (R1R+R provided IB << I2 = 2) VB /R2 .
--- If R1 || R2 is low, either R1 is low, or R2 is low, or both are low. A low R1 raises VB closer to VC, reducing the available swing in collector voltage, and limiting how large RC can be made without driving the transistor out of active mode. A low R2 lowers V ₑ, reducing the allowed collector current. Lowering both resistor values draws more current from the power supply and lowers the input resistance of the amplifier as seen from the base.
Also VB = Vbe + IE RE For the given circuit,
IB =
VCC 1+R1 /R2
− Vbe
(β + 1)RE + R1 ∥ R2
. • AC as well as DC feedback is caused by RE, which reduces the AC voltage gain of the amplifier. A method to avoid AC feedback while retaining DC feedback is discussed below.
Merits:
• Unlike above circuits, only one dc supply is necessary. Usage:
• Operating point is almost independent of β varia- The circuit’s stability and merits as above make it widely used for linear circuits. tion. • Operating point stabilized against shift in temperaVoltage divider with AC bypass capacitor The stanture. dard voltage divider circuit discussed above faces a drawback - AC feedback caused by resistor RE reduces the Demerits: gain. This can be avoided by placing a capacitor (CE) in parallel with RE, as shown in circuit diagram. • In this circuit, to keep IC independent of β the following condition must be met: Emitter bias
IC = βIB = β
VCC 1+R1 /R2
− Vbe
(β + 1)RE + R1 ∥ R2
which is approximately the case if
≈
When a split supply (dual power supply) is available, this − Vbebiasing circuit is the most effective, and provides zero bias , voltage at the emitter or collector for load. The RE negative supply VEE is used to forward-bias the emitter junction through RE. The positive supply VCC is used to reverse-bias the collector junction. Only two resistors are necessary for the common collector stage and four resistors for the common emitter or common base stage.
VCC 1+R1 /R2
(β + 1)RE >> R1 ∥ R2 where R1 || R2 denotes the equivalent resistance of R1 and R2 connected in parallel.
We know that, VB - VE = V ₑ If RB is small enough, base voltage will be approximately zero. Therefore emitter current is,
102
Voltage divider with capacitor
CHAPTER 4. BACKGROUND THEORY
Emitter bias
IE = (VEE - V ₑ)/RE The operating point is independent of β if RE >> RB/β Merit: Good stability of operating point similar to voltage divider bias. (about 1% of maximum possible value). Class AB bias is when the collector current I is about 1/4 of maximum Demerit: possible value. The class AB push–pull output amplifier This type can only be used when a split (dual) power sup- circuit below could be the basis for a moderate-power auply is available. dio amplifier.
4.3.3 Class B and AB amplifiers Signal requirements Class B and AB amplifiers employ 2 active devices to cover the complete 360 deg of input signal flow. Each transistor is therefore biased to perform over approximately 180 deg of the input signal. Class B bias is when the collector current I with no signal is just conducting
4.3. BIPOLAR TRANSISTOR BIASING
103 • Bipolar junction transistor
R1
R3
• MOSFET
R4
+V supply
Q3
4.3.5 References Input C1
D1 Q1
Q2
D2 R7
R2
R8
R5
Q4 [1] A.S. Sedra and K.C. Smith (2004). Microelectronic Circuits (5th ed.). New York: Oxford University Press. Output p. 397, Figure 5.17, and p.&nb₡sp;1245. ISBN 0-19514251-9. Q5 C2
4.3.6 Further reading R6
• Patil, P.K.; Chitnis, M.M. (2005). Basic Electricity 0VDevices. (ground) and Semiconductor Phadke Prakashan.
A practical amplifier circuit Q3 is a common emitter stage that provides amplification of the signal and the DC bias current through D1 and D2 to generate a bias voltage for the output devices. The output pair are arranged in Class AB push–pull, also called a complementary pair. The diodes D1 and D2 provide a small amount of constant voltage bias for the output pair, just biasing them into the conducting state so that crossover distortion is minimized. That is, the diodes push the output stage into class-AB mode (assuming that the base-emitter drop of the output transistors is reduced by heat dissipation). This design automatically stabilizes its operating point, since overall feedback internally operates from DC up through the audio range and beyond. The use of fixed diode bias requires the diodes to be both electrically and thermally matched to the output transistors. If the output transistors conduct too much, they can easily overheat and destroy themselves, as the full current from the power supply is not limited at this stage. A common solution to help stabilize the output device operating point is to include some emitter resistors, typically an ohm or so. Calculating the values of the circuit’s resistors and capacitors is done based on the components employed and the intended use of the amplifier.
4.3.4
See also
• Biasing (electronics) • Small signal model
4.3.7 External links • Bias – from Sci-Tech Encyclopedia • Electrical Engineering Training Series: Types of bias
Chapter 5
Common Integrated Circuits 5.1 555 timer IC
tions. The 555 can be used to provide time delays, as an oscillator, and as a flip-flop element. Derivatives provide up to four timing circuits in one package. Introduced in 1971 by Signetics, the 555 is still in widespread use due to its ease of use, low price, and stability. It is now made by many companies in the original bipolar and also in low-power CMOS types. As of 2003, it was estimated that 1 billion units are manufactured every year.[1]
5.1.1
Design
VCC
NE555 from Signetics in dual-in-line package
CONT THRES
THRES
6
VCC 8 CONT 5
RESET 4
OUT
TRIG RESET DISCH
R1 R S
3
OUT
GND
Internal schematic TRIG
2
7
DISCH
The IC was designed in 1971 by Hans Camenzind under contract to Signetics, which was later acquired by Philips (now NXP).
Depending on the manufacturer, the standard 555 package includes 25 transistors, 2 diodes and 15 resistors on a silicon chip installed in an 8-pin mini dual-in-line packInternal block diagram age (DIP-8).[2] Variants available include the 556 (a 14pin DIP combining two 555s on one chip), and the two The 555 timer IC is an integrated circuit (chip) used in a 558 & 559s (both a 16-pin DIP combining four slightly variety of timer, pulse generation, and oscillator applica- modified 555s with DIS & THR connected internally, and 1 GND
104
5.1. 555 TIMER IC
105
VCC
RESET
GND 1
8 VCC
OUT
TRIG 2
7 DIS
THRES CONT TRIG DISCH
OUT 3
555
6 THR
GND
Internal schematic (CMOS version)
TR is falling edge sensitive instead of level sensitive).
RESET 4
5 CTRL
Pinout diagram
The NE555 parts were commercial temperature range, 0 °C to +70 °C, and the SE555 part number designated the military temperature range, −55 °C to +125 Modes °C. These were available in both high-reliability metal can (T package) and inexpensive epoxy plastic (V pack- The 555 has three operating modes: age) packages. Thus the full part numbers were NE555V, NE555T, SE555V, and SE555T. It has been hypothe• Monostable mode: In this mode, the 555 funcsized that the 555 got its name from the three 5 kΩ resistions as a “one-shot” pulse generator. Applications tors used within,[3] but Hans Camenzind has stated that include timers, missing pulse detection, bouncethe number was arbitrary.[1] free switches, touch switches, frequency divider, capacitance measurement, pulse-width modulation Low-power versions of the 555 are also available, such as (PWM) and so on. [4] the 7555 and CMOS TLC555. The 7555 is designed to cause less supply noise than the classic 555 and the manufacturer claims that it usually does not require a “control” capacitor and in many cases does not require a decoupling capacitor on the power supply. Those parts should generally be included, however, because noise produced by the timer or variation in power supply voltage might interfere with other parts of a circuit or influence its threshold voltages.
Pins The connection of the pins for a DIP package is as follows:
• Astable (free-running) mode: The 555 can operate as an oscillator. Uses include LED and lamp flashers, pulse generation, logic clocks, tone generation, security alarms, pulse position modulation and so on. The 555 can be used as a simple ADC, converting an analog value to a pulse length. E.g. selecting a thermistor as timing resistor allows the use of the 555 in a temperature sensor: the period of the output pulse is determined by the temperature. The use of a microprocessor based circuit can then convert the pulse period to temperature, linearize it and even provide calibration means. • Bistable mode or Schmitt trigger: The 555 can operate as a flip-flop, if the DIS pin is not connected and no capacitor is used. Uses include bounce-free latched switches.
Pin 5 is also sometimes called the CONTROL VOLTAGE pin. By applying a voltage to the CONTROL VOLTAGE input one can alter the timing characteristics of the device. In most applications, the CONTROL VOLTAGE input is not used. It is usual to connect a Monostable 10 nF capacitor between pin 5 and 0 V to prevent interference. The CONTROL VOLTAGE input can be used See also: RC circuit to build an astable multivibrator with a frequency modu- In the monostable mode, the 555 timer acts as a “oneshot” pulse generator. The pulse begins when the 555 lated output.
106
CHAPTER 5. COMMON INTEGRATED CIRCUITS VCC
The output pulse width of time t, which is the time it takes to charge C to 2/3 of the supply voltage, is given by R
4
RESET 7 6
C
2
Trigger
8
VCC
t = RC ln(3) ≈ 1.1RC
DIS THR
OUT
3
Out
TRIG GND CTRL 1
5 10nF
where t is in seconds, R is in ohms (resistance) and C is in farads(capacitance). While using the timer IC in monostable mode, the main disadvantage is that the time span between any two triggering pulses must be greater than the RC time constant.[6]
GND
Bistable Schematic of a 555 in monostable mode
VCC
Reset
4
RESET 2
Trigger
6 7
8
VCC
TRIG THR
OUT
3
Out
DIS GND CTRL 1
5 10nF
GND Schematic of a 555 in bistable mode The relationships of the trigger signal, the voltage on C and the pulse width in monostable mode
timer receives a signal at the trigger input that falls below a third of the voltage supply. The width of the output pulse is determined by the time constant of an RC network, which consists of a capacitor (C) and a resistor (R). The output pulse ends when the voltage on the capacitor equals 2/3 of the supply voltage. The output pulse width can be lengthened or shortened to the need of the specific application by adjusting the values of R and C.[5]
In bistable (also called Schmitt trigger) mode, the 555 timer acts as a basic flip-flop. The trigger and reset inputs (pins 2 and 4 respectively on a 555) are held high via Pull-up resistors while the threshold input (pin 6) is simply floating. Thus configured, pulling the trigger momentarily to ground acts as a 'set' and transitions the output pin (pin 3) to Vcc (high state). Pulling the reset input to ground acts as a 'reset' and transitions the output pin to ground (low state). No timing capacitors are required in a bistable configuration. Pin 5 (control voltage) is connected to ground via a small-value capacitor (usually 0.01 to 0.1 uF); pin 7 (discharge) is left floating.[7]
5.1. 555 TIMER IC
107
VCC
The power capability of R1 must be greater than R1
4
RESET 7 6
R2
2
8
VCC
DIS THR
OUT
3
Out
TRIG GND CTRL 1
5
C
10nF
GND Standard 555 astable circuit
Astable In astable mode, the 555 timer puts out a continuous stream of rectangular pulses having a specified frequency. Resistor R1 is connected between VCC and the discharge pin (pin 7) and another resistor (R2 ) is connected between the discharge pin (pin 7), and the trigger (pin 2) and threshold (pin 6) pins that share a common node. Hence the capacitor is charged through R1 and R2 , and discharged only through R2 , since pin 7 has low impedance to ground during output low intervals of the cycle, therefore discharging the capacitor.
2 Vcc R1
.
Particularly with bipolar 555s, low values of R1 must be avoided so that the output stays saturated near zero volts during discharge, as assumed by the above equation. Otherwise the output low time will be greater than calculated above. The first cycle will take appreciably longer than the calculated time, as the capacitor must charge from 0V to 2/3 of VCC from power-up, but only from 1/3 of VCC to 2/3 of VCC on subsequent cycles. To achieve a duty cycle of less than 50% a small diode (that is fast enough for the application) can be placed in parallel with R2 , with the cathode on the capacitor side. This bypasses R2 during the high part of the cycle so that the high interval depends approximately only on R1 and C. The presence of the diode is a voltage drop that slows charging on the capacitor so that the high time is longer than the expected and often-cited ln(2)*R1 C = 0.693 R1 C. The low time will be the same as without the diode as shown above. With a diode, the high time is ( high = R1 C · ln
2Vcc − 3Vdiode Vcc − 3Vdiode
)
where V ᵢₒ ₑ is when the diode has a current of 1/2 of V /R1 which can be determined from its datasheet or by testing. As an extreme example, when V = 5 and V ᵢₒ ₑ= 0.7, high time = 1.00 R1 C which is 45% longer than the “expected” 0.693 R1 C. At the other extreme, when V = 15 and V ᵢₒ ₑ= 0.3, the high time = 0.725 R1 C which is closer to the expected 0.693 R1 C. The equation reduces In the astable mode, the frequency of the pulse stream to the expected 0.693 R1 C if V ᵢₒ ₑ= 0. depends on the values of R1 , R2 and C: The operation of RESET in this mode is not well defined, some manufacturers’ parts will hold the output state to 1 [8] f = ln(2)·C·(R what it was when RESET is taken low, others will send +2R ) 1 2 the output either high or low.
The high time from each pulse is given by:
5.1.2 Specifications high = ln(2) · (R1 + R2 ) · C and the low time from each pulse is given by:
low = ln(2) · R2 · C
These specifications apply to the NE555. Other 555 timers can have different specifications depending on the grade (military, medical, etc.).
5.1.3 Derivatives
where R1 and R2 are the values of the resistors in ohms Many pin-compatible variants, including CMOS verand C is the value of the capacitor in farads. sions, have been built by various companies. Bigger
108
CHAPTER 5. COMMON INTEGRATED CIRCUITS
packages also exist with two or four timers on the same “game paddles” or two joysticks to the host computer. It chip. The 555 is also known under the following type also used a single 555 for flashing the display cursor. numbers: A similar circuit was used in the IBM PC.[11] In the joystick interface circuit of the IBM PC, the capacitor (C) of the RC network (see Monostable Mode above) was 556 Dual timer generally a 10 nF capacitor. The resistor (R) of the RC network consisted of the potentiometer inside the joystick along with an external resistor of 2.2 kilohms.[12] The joystick potentiometer acted as a variable resistor. By moving the joystick, the resistance of the joystick increased from a small value up to about 100 kilohms. The joystick operated at 5 V.[13] Software running in the host computer started the process of determining the joystick position by writing to a special address (ISA bus I/O address 201h).[13][14] This would result in a trigger signal to the quad timer, which would cause the capacitor (C) of the RC network to begin charging and cause the quad timer to output a pulse. The width of the pulse was determined by how long it took the C to charge up to 2/3 of 5 V (or about 3.33 V), which was in turn determined by the joystick position.[13][15] The Die of a 556 dual timer manufactured by STMicroelectronics. software then measured the pulse width to determine the joystick position. A wide pulse represented the full-right The dual version is called 556. It features two complete joystick position, for example, while a narrow pulse rep555s in a 14 pin DIL package. resented the full-left joystick position.[13] 558 Quad timer The quad version is called 558 and has 16 pins. To fit four 555s into a 16 pin package the power, control voltage, and reset lines are shared by all four modules. Each module’s discharge and threshold circuits are wired together internally.
5.1.5
• Counter • OpAmp • Oscillator • RC circuit
XTR650/651 extended functionality hirel hitemp 5.1.6 (−60°C to 250+ °C) This version includes non-overlapped complementary outputs, coarse temperature sensor and on-chip 200pF timing capacitance.[10]
See also
References
[1] Ward, Jack (2004). The 555 Timer IC – An Interview with Hans Camenzind. The Semiconductor Museum. Retrieved 2010-04-05 [2] van Roon, Fig 3 & related text.
5.1.4 Example applications Joystick interface circuit using the 558 quad timer The Apple II microcomputer used a quad timer 558 in monostable (or “one-shot”) mode to interface up to four
[3] Scherz, Paul (2000) “Practical Electronics for Inventors”, p. 589. McGraw-Hill/TAB Electronics. ISBN 978-0-07058078-7. Retrieved 2010-04-05. [4] Jung, Walter G. (1983) “IC Timer Cookbook, Second Edition”, pp. 40–41. Sams Technical Publishing; 2nd ed. ISBN 978-0-672-21932-0. Retrieved 2010-04-05.
5.2. OPERATIONAL AMPLIFIER
[5] van Roon, Chapter “Monostable Mode”. (Using the 555 timer as a logic clock)
109
5.1.8 External links
[6] http://www.national.com/ds/LM/LM555.pdf
• 555 Timer Circuits – the Astable, Monostable and Bistable
[7] http://www.555-timer-circuits.com/operating-modes. html
• Simple 555 timer circuits
[8] van Roon Chapter: “Astable operation”. [9] http://www.customsiliconsolutions.com/ products-for-ASIC-solutions/standard-IC-products. aspx
• Java simulation of 555 oscillator circuit • NE555 Frequency and duty cycle calculator for astable multivibrators • Using NE555 as a Temperature DSP
[10] 15 X-REL Semiconductor Data Sheet, 38100 Grenoble France
• 555 Timer Tutorial
[11] Engdahl, pg 1.
• Common Mistakes When Using a 555 Timer
[12] Engdahl, “Circuit diagram of PC joystick interface”
• 555 and 556 Timer Circuits
[13] http://www.epanorama.net/documents/joystick/pc_ joystick.html [14] Eggebrecht, p. 197.
• 555 using areas and examples circuits • Working with 555 Timer Circuits Engineers Garage
[15] Eggebrecht, pp. 197-99
• Analysis and synthesis of a 555 astable multivibrator circuit - online calculator
5.1.7
• Online simulations of a 555 astable multivibrator circuit - online simulator
Further reading
• 555 Timer Applications Sourcebook Experiments; H. IC Datasheets Berlin; BPB Publications; 218 pages; 2008; ISBN 978-8176567909. • NE555, Single Bipolar Timer, Texas Instruments • Timer, Op Amp, and Optoelectronic Circuits and Projects; Forrest Mims III; Master Publishing; 128 pages; 2004; ISBN 978-0-945053-29-3. • Engineer’s Mini-Notebook – 555 Timer IC Circuits; Forrest Mims III; Radio Shack; 33 pages; 1989; ASIN B000MN54A6. • IC Timer Cookbook; 2nd Ed; Walter G Jung; Sams Publishing; 384 pages; 1983; ISBN 978-0-67221932-0. • 555 Timer Applications Sourcebook with Experiments; Howard M Berlin; Sams Publishing; 158 pages; 1979; ISBN 978-0-672-21538-4. • IC 555 Projects; E.A. Parr; Bernard Babani Publishing; 144 pages; 1978; ISBN 978-0-85934-047-2.
• NE556, Dual Bipolar Timer, Texas Instruments • NE558, Quad Bipolar Timer, NXP • LMC555, Single CMOS Timer, Texas Instruments (operates down to 1.5 Volt at 50 uAmp) • ICM755x, Single / Dual CMOS Timer, Intersil (operates down to 2.0 Volt at 60 uAmp) • ZSCT1555, Single CMOS Timer, Diodes Inc (operates down to 0.9 Volt at 74 uAmp) • TS300x, Single CMOS Timers, Touchstone (operates down to 0.9 Volt at 1.0 uAmp) • XTR65x, HiRel HiTemp Timer, X-REL (operates from −60°C to 230°C)
110
CHAPTER 5. COMMON INTEGRATED CIRCUITS mode voltages that would destroy an ordinary op-amp), and negative feedback amplifier (usually built from one or more op-amps and a resistive feedback network).
5.2.1
Circuit notation
VS+ A Signetics μa741 operational amplifier, one of the most successful op-amps.
5.2 Operational amplifier
V+
Vout
V−
An operational amplifier (op-amp) is a DC-coupled high-gain electronic voltage amplifier with a differential S− input and, usually, a single-ended output.[1] In this configuration, an op-amp produces an output potential (relative to circuit ground) that is typically hundreds of thousands Circuit diagram symbol for an op-amp of times larger than the potential difference between its input terminals.[2] The circuit symbol for an op-amp is shown to the right, Operational amplifiers had their origins in analog com- where: puters, where they were used to do mathematical operations in many linear, non-linear and frequency-dependent • V₊: non-inverting input circuits. Characteristics of a circuit using an op-amp are set by external components with little dependence on • V₋: inverting input temperature changes or manufacturing variations in the op-amp itself, which makes op-amps popular building • Vₒᵤ : output blocks for circuit design. • VS₊: positive power supply Op-amps are among the most widely used electronic devices today, being used in a vast array of consumer, in• VS₋: negative power supply dustrial, and scientific devices. Many standard IC opamps cost only a few cents in moderate production volThe power supply pins (VS₊ and VS₋) can be labeled in ume; however some integrated or hybrid operational amdifferent ways (See IC power supply pins). Often these plifiers with special performance specifications may cost pins are left out of the diagram for clarity, and the power over $100 US in small quantities.[3] Op-amps may be configuration is described or assumed from the circuit. packaged as components, or used as elements of more complex integrated circuits.
V
The op-amp is one type of differential amplifier. Other types of differential amplifier include the fully differential amplifier (similar to the op-amp, but with two outputs), the instrumentation amplifier (usually built from three op-amps), the isolation amplifier (similar to the instrumentation amplifier, but with tolerance to common-
5.2.2
Operation
The amplifier’s differential inputs consist of a noninverting input (+) with voltage V₊ and an inverting input (–) with voltage V₋; ideally the op-amp amplifies only the difference in voltage between the two, which is called the
5.2. OPERATIONAL AMPLIFIER
V in
111
V out
Rg
from the output to either input, this is an open loop circuit acting as a comparator. The circuit’s gain is just the AOL of the op-amp. Closed loop
V in
V out
An op-amp without negative feedback (a comparator)
differential input voltage. The output voltage of the opamp Vₒᵤ is given by the equation:
Rg
Rf
Vout = AOL (V+ − V− ) An op-amp with negative feedback (a non-inverting amplifier)
where AOL is the open-loop gain of the amplifier (the term “open-loop” refers to the absence of a feedback loop If predictable operation is desired, negative feedback is from the output to the input). used, by applying a portion of the output voltage to the inverting input. The closed loop feedback greatly reduces the gain of the circuit. When negative feedback Open loop amplifier is used, the circuit’s overall gain and response becomes The magnitude of AOL is typically very large—100,000 determined mostly by the feedback network, rather than or more for integrated circuit op-amps—and therefore by the op-amp characteristics. If the feedback network is even a quite small difference between V₊ and V₋ drives made of components with values small relative to the op the amplifier output nearly to the supply voltage. Situ- amp’s input impedance, the value of the op-amp’s open ations in which the output voltage is equal to or greater loop response AOL does not seriously affect the circuit’s than the supply voltage are referred to as saturation of the performance. The response of the op-amp circuit with its amplifier. The magnitude of AOL is not well controlled input, output, and feedback circuits to an input is characby the manufacturing process, and so it is impractical to terized mathematically by a transfer function; designing use an operational amplifier as a stand-alone differential an op-amp circuit to have a desired transfer function is amplifier. in the realm of electrical engineering. The transfer funcWithout negative feedback, and perhaps with positive tions are important in most applications of op-amps, such feedback for regeneration, an op-amp acts as a as in analog computers. High input impedance at the incomparator. If the inverting input is held at ground (0 put terminals and low output impedance at the output terV) directly or by a resistor R , and the input voltage Vᵢ minal(s) are particularly useful features of an op-amp. applied to the non-inverting input is positive, the output In the non-inverting amplifier on the right, the presence will be maximum positive; if Vᵢ is negative, the output of negative feedback via the voltage divider R , R deterwill be maximum negative. Since there is no feedback mines the closed-loop gain ACL = Vₒᵤ / Vᵢ . Equilibrium
112
CHAPTER 5. COMMON INTEGRATED CIRCUITS
will be established when Vₒᵤ is just sufficient to “reach around and pull” the inverting input to the same voltage as Vᵢ . The voltage gain of the entire circuit is thus 1 + R /R . As a simple example, if Vᵢ = 1 V and R = R , Vₒᵤ will be 2 V, exactly the amount required to keep V₋ at 1 V. Because of the feedback provided by the R , R network, this is a closed loop circuit. Another way to analyze this circuit proceeds by making the following (usually valid) assumptions:[4] • When an op-amp operates in linear (i.e., not saturated) mode, the difference in voltage between the non-inverting (+) pin and the inverting (−) pin is negligibly small. • The input impedance between (+) and (−) pins is much larger than other resistances in the circuit. The input signal Vᵢ appears at both (+) and (−) pins, resulting in a current i through R equal to Vᵢ /R .
i=
VS+
v+ R in
vin
Rout
vout
Gvin
v−
VS− An equivalent circuit of an operational amplifier that models some resistive non-ideal parameters.
• Infinite input impedance Rᵢ , and so zero input current • Zero input offset voltage • Infinite voltage range available at the output
Vin Rg
Since Kirchhoff’s current law states that the same current must leave a node as enter it, and since the impedance into the (−) pin is near infinity, we can assume practically all of the same current i flows through R , creating an output voltage
• Infinite bandwidth with zero phase shift and infinite slew rate • Zero output impedance Rₒᵤ • Zero noise • Infinite Common-mode rejection ratio (CMRR)
• Infinite Power ( ) ( ) supply rejection ratio. Vin Vin × Rf Rf Vout = Vin +i×Rf = Vin + × Rf = Vin + = Vin 1 + Rg Rg These ideals can Rg be summarized by the two “golden rules By combining terms, we determine the closed-loop gain extquotedbl: ACL:
ACL =
Rf Vout =1+ Vin Rg
I. The output attempts to do whatever is necessary to make the voltage difference between the inputs zero. II. The inputs draw no current.[5]:177
The first rule only applies in the usual case where the opamp is used in a closed-loop design (negative feedback, where there is a signal path of some sort feeding back Ideal op-amps from the output to the inverting input). These rules are for analyzAn ideal op-amp is usually considered to have the follow- commonly used as a good first approximation [5]:177 ing or designing op-amp circuits. ing properties:
5.2.3 Op-amp characteristics
• Infinite open-loop gain G = vₒᵤ / 'vin
None of these ideals can be perfectly realized. A real op-amp may be modeled with non-infinite or non-zero
5.2. OPERATIONAL AMPLIFIER parameters using equivalent resistors and capacitors in the op-amp model. The designer can then include these effects into the overall performance of the final circuit. Some parameters may turn out to have negligible effect on the final design while others represent actual limitations of the final performance that must be evaluated. Real op-amps Real op-amps differ from the ideal model in various aspects. DC imperfections Real operational amplifiers suffer from several non-ideal effects:
113 the amplifier will be significant. Hence, the output impedance of the amplifier limits the maximum power that can be provided. In configurations with a voltage-sensing negative feedback, the output impedance of the amplifier is effectively lowered; thus, in linear applications, op-amps usually exhibit a very low output impedance indeed. Negative feedback can not, however, reduce the limitations that R ₒₐ in conjunction with Rₒᵤ place on the maximum and minimum possible output voltages; it can only reduce output errors within that range. Low-impedance outputs typically require high quiescent (i.e., idle) current in the output stage and will dissipate more power, so low-power designs may purposely sacrifice low output impedance.
Finite gain Open-loop gain is infinite in the ideal oper- Input current Due to biasing requirements or leakage, a small amount of current (typically ~10 nanoamperes ational amplifier but finite in real operational amfor bipolar op-amps, tens of picoamperes (pA) for plifiers. Typical devices exhibit open-loop DC gain JFET input stages, and only a few pA for MOSFET ranging from 100,000 to over 1 million. So long input stages) flows into the inputs. When large reas the loop gain (i.e., the product of open-loop and sistors or sources with high output impedances are feedback gains) is very large, the circuit gain will be used in the circuit, these small currents can produce determined entirely by the amount of negative feedlarge unmodeled voltage drops. If the input curback (i.e., it will be independent of open-loop gain). rents are matched, and the impedance looking out In cases where closed-loop gain must be very high, of both inputs are matched, then the voltages prothe feedback gain will be very low, and the low feedduced at each input will be equal. Because the operback gain causes low loop gain; in these cases, the ational amplifier operates on the difference between operational amplifier will cease to behave ideally. its inputs, these matched voltages will have no effect (unless the operational amplifier has poor CMRR, Finite input impedances The differential input which is described below). It is more common for impedance of the operational amplifier is defined as the input currents (or the impedances looking out the impedance between its two inputs; the commonof each input) to be slightly mismatched, and so a mode input impedance is the impedance from small offset voltage (different from the input offset each input to ground. MOSFET-input operational voltage below) can be produced. This offset voltamplifiers often have protection circuits that efage can create offsets or drifting in the operational fectively short circuit any input differences greater amplifier. It can often be nulled externally; howthan a small threshold, so the input impedance can ever, many operational amplifiers include offset null appear to be very low in some tests. However, as or balance pins and some procedure for using them long as these operational amplifiers are used in a to remove this offset. Some operational amplifiers typical high-gain negative feedback application, attempt to nullify this offset automatically these protection circuits will be inactive. The input bias and leakage currents described below Input offset voltage This voltage, which is what is reare a more important design parameter for typical quired across the op-amp’s input terminals to drive operational amplifier applications. the output voltage to zero,[6][nb 1] is related to the Non-zero output impedance Low output impedance is important for low-impedance loads; for these loads, the voltage drop across the output impedance of
mismatches in input bias current. In the perfect amplifier, there would be no input offset voltage. However, it exists in actual op-amps because of imperfections in the differential amplifier that constitutes
114
CHAPTER 5. COMMON INTEGRATED CIRCUITS the input stage of the vast majority of these devices. Input offset voltage creates two problems: First, due to the amplifier’s high voltage gain, it virtually assures that the amplifier output will go into saturation if it is operated without negative feedback, even when the input terminals are wired together. Second, in a closed loop, negative feedback configuration, the input offset voltage is amplified along with the signal and this may pose a problem if high precision DC amplification is required or if the input signal is very small.[nb 2]
Common-mode gain A perfect operational amplifier amplifies only the voltage difference between its two inputs, completely rejecting all voltages that are common to both. However, the differential input stage of an operational amplifier is never perfect, leading to the amplification of these common voltages to some degree. The standard measure of this defect is called the common-mode rejection ratio (denoted CMRR). Minimization of common mode gain is usually important in non-inverting amplifiers (described below) that operate at high amplification. Power-supply rejection The output of a perfect operational amplifier will be completely independent from ripples that arrive on its power supply inputs. Every real operational amplifier has a specified power supply rejection ratio (PSRR) that reflects how well the op-amp can reject changes in its supply voltage. Copious use of bypass capacitors can improve the PSRR of many devices, including the operational amplifier. Temperature effects All parameters change with temperature. Temperature drift of the input offset voltage is especially important. Drift Real op-amp parameters are subject to slow change over time and with changes in temperature, input conditions, etc. Noise Amplifiers generate random voltage at the output even when there is no signal applied. This can be due to thermal noise and flicker noise of the devices. For applications with high gain or high bandwidth, noise becomes a very important consideration.
AC imperfections The op-amp gain calculated at DC does not apply at higher frequencies. Thus, for highspeed operation, more sophisticated considerations must be used in an op-amp circuit design. Finite bandwidth All amplifiers have finite bandwidth. To a first approximation, the op-amp has the frequency response of an integrator with gain. That is, the gain of a typical op-amp is inversely proportional to frequency and is characterized by its gain– bandwidth product (GBWP). For example, an opamp with a GBWP of 1 MHz would have a gain of 5 at 200 kHz, and a gain of 1 at 1 MHz. This dynamic response coupled with the very high DC gain of the op-amp gives it the characteristics of a firstorder low-pass filter with very high DC gain and low cutoff frequency given by the GBWP divided by the DC gain. The finite bandwidth of an op-amp can be the source of several problems, including: • Stability. Associated with the bandwidth limitation is a phase difference between the input signal and the amplifier output that can lead to oscillation in some feedback circuits. For example, a sinusoidal output signal meant to interfere destructively with an input signal of the same frequency will interfere constructively if delayed by 180 degrees forming positive feedback. In these cases, the feedback circuit can be stabilized by means of frequency compensation, which increases the gain or phase margin of the open-loop circuit. The circuit designer can implement this compensation externally with a separate circuit component. Alternatively, the compensation can be implemented within the operational amplifier with the addition of a dominant pole that sufficiently attenuates the high-frequency gain of the operational amplifier. The location of this pole may be fixed internally by the manufacturer or configured by the circuit designer using methods specific to the op-amp. In general, dominant-pole frequency compensation reduces the bandwidth of the op-amp even further. When
5.2. OPERATIONAL AMPLIFIER the desired closed-loop gain is high, opamp frequency compensation is often not needed because the requisite open-loop gain is sufficiently low; consequently, applications with high closed-loop gain can make use of op-amps with higher bandwidths. • Noise, Distortion, and Other Effects. Reduced bandwidth also results in lower amounts of feedback at higher frequencies, producing higher distortion, noise, and output impedance and also reduced output phase linearity as the frequency increases. Typical low-cost, general-purpose op-amps exhibit a GBWP of a few megahertz. Specialty and high-speed op-amps exist that can achieve a GBWP of hundreds of megahertz. For very high-frequency circuits, a currentfeedback operational amplifier is often used. Input capacitance Most important for high frequency operation because it further reduces the open-loop bandwidth of the amplifier. Common-mode gain See DC imperfections, above.
The input (yellow) and output (green) of a saturated op amp in an inverting amplifier
Non-linear imperfections Saturation Output voltage is limited to a minimum and maximum value close to the power supply voltages.[nb 3] Saturation occurs when the output of the amplifier reaches this value and is usually due to:
115 • In the case of an op-amp using a bipolar power supply, a voltage gain that produces an output that is more positive or more negative than that maximum or minimum; or • In the case of an op-amp using a single supply voltage, either a voltage gain that produces an output that is more positive than that maximum, or a signal so close to ground that the amplifier’s gain is not sufficient to raise it above the lower threshold.[nb 4] Slewing The amplifier’s output voltage reaches its maximum rate of change, the slew rate, usually specified in volts per microsecond. When slewing occurs, further increases in the input signal have no effect on the rate of change of the output. Slewing is usually caused by the input stage saturating; the result is a constant current i driving a capacitance C in the amplifier (especially those capacitances used to implement its frequency compensation); the slew rate is limited by dv/dt=i/C. Slewing is associated with the large-signal performance of an op-amp. Consider for, example an op-amp configured for a gain of 10. Let the input be a 1 V, 100 kHz sawtooth wave. That is, the amplitude is 1 V and the period is 10 microseconds. Accordingly, the rate of change (i.e., the slope) of the input is 0.1 V per microsecond. After 10x amplification, the output should be a 10 V, 100 kHz sawtooth, with a corresponding slew rate of 1 V per microsecond. However, the classic 741 op-amp has a 0.5 V per microsecond slew rate specification, so that its output can rise to no more than 5 V in the sawtooth’s 10 microsecond period. Thus, if one were to measure the output, it would be a 5 V, 100 kHz sawtooth, rather than a 10 V, 100 kHz sawtooth. Next consider the same amplifier and 100 kHz sawtooth, but now the input amplitude is 100 mV rather than 1 V. After 10x amplification the output is a 1 V, 100 kHz sawtooth with a corresponding slew rate of 0.1 V per microsecond. In this instance the 741 with its 0.5 V per microsecond slew rate will amplify the input properly.
116
CHAPTER 5. COMMON INTEGRATED CIRCUITS Modern high speed op-amps can have slew rates in excess of 5,000 V per microsecond. However, it is more common for op-amps to have slew rates in the range 5-100 V per microsecond. For example, the general purpose TL081 op-amp has a slew rate of 13 V per microsecond. As a general rule, low power and small bandwidth op-amps have low slew rates. As an example, the LT1494 micropower opamp consumes 1.5 microamp but has a 2.7 kHz gain-bandwidth product and a 0.001 V per microsecond slew rate.
Limited dissipated power The output current flows through the op-amp’s internal output impedance, dissipating heat. If the op-amp dissipates too much power, then its temperature will increase above some safe limit. The op-amp may enter thermal shutdown, or it may be destroyed.
Modern integrated FET or MOSFET op-amps approximate more closely the ideal op-amp than bipolar ICs when it comes to input impedance and input bias currents. Bipolars are generally better when it comes to input voltage offset, and often have lower noise. Generally, Non-linear input-output relationship The output at room temperature, with a fairly large signal, and limvoltage may not be accurately proportional to ited bandwidth, FET and MOSFET op-amps now offer the difference between the input voltages. It is better performance. commonly called distortion when the input signal is a waveform. This effect will be very small in a practical circuit where substantial negative 5.2.4 Internal circuitry of 741-type opfeedback is used.
amp Phase reversal In some integrated op-amps, when the published common mode voltage is violated (e.g. by one of the inputs being driven to one of the supply voltages), the output may slew to the opposite polarity from what is expected in normal operation.[7][8] Under such conditions, negative feedback becomes positive, likely causing the circuit to “lock up” in that state.
Q8
Q12
Q9
Q14 Non-inverting input
Q1
Q2
Inverting input
3
4.5 kΩ Q16
2 Q3
Q4
30 pF
Output sink current The output sink current is the maximum current allowed to sink into the output stage. Some manufacturers show the output voltage vs. the output sink current plot, which gives an idea of the output voltage when it is sinking current from another source into the output pin.
Q6
Q5 50 kΩ 1 kΩ
Output 50 Ω
Q7
Offset null
Limited output current The output current must be finite. In practice, most op-amps are designed to limit the output current so as not to exceed a specified level – around 25 mA for a type 741 IC op-amp – thus protecting the op-amp and associated circuitry from damage. Modern designs are electronically more rugged than earlier implementations and some can sustain direct short circuits on their outputs without damage.
6 7.5 kΩ
1
7 VS+
Q17 25 Ω
39 kΩ
1 kΩ
Q22
5 Offset null
Q20
Q15
Q10
Power considerations
Q13
Q19
Q11 5 kΩ
50 kΩ
50 Ω 4 VS−
A component-level diagram of the common 741 op-amp. Dotted lines outline: current mirrors (red); differential amplifier (blue); class A gain stage (magenta); voltage level shifter (green); output stage (cyan).
Sourced by many manufacturers, and in multiple similar products, an example of a bipolar transistor operational amplifier is the 741 integrated circuit designed by Dave Fullagar at Fairchild Semiconductor after Bob Widlar's LM301 integrated circuit design.[9] In this discussion, we use the parameters of the Hybrid-pi model to characterize the small-signal, grounded emitter characteristics of a transistor. In this model, the current gain of a transistor is denoted h ₑ, more commonly called the β.[10]
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Architecture
output sink transistor Q20 receives its base drive from the common collectors of Q15 and Q19; the level-shifter A small-scale integrated circuit, the 741 op-amp shares Q16 provides base drive for the output source transistor with most op-amps an internal structure consisting of Q14. Note the similarity between the transistors Q15 and three gain stages: Q7. The transistor Q22 prevents this stage from saturating 1. Differential amplifier (outlined blue) — provides by diverting the excessive Q15 base current (it acts as a high differential amplification (gain), with rejec- Baker clamp). tion of common-mode signal, low noise, high input impedance, and drives a Output amplifier The output stage (Q14, Q20, out2. Voltage amplifier (outlined magenta) — provides lined in cyan) is a Class AB push-pull emitter follower high voltage gain, a single-pole frequency roll-off, amplifier. It provides an output drive with impedance of and in turn drives the ≈50Ω, in essence, current gain. Transistor Q16 (outlined 3. Output amplifier (outlined cyan and green) — pro- in green) provides the quiescent current for the output vides high current gain (low output impedance), transistors, and Q17 provides output current limiting. along with output current limiting, and output shortcircuit protection. Biasing circuits Additionally, it contains current mirror (outlined red) bias Provide appropriate quiescent current for each stage of circuitry and a gain-stabilization capacitor (30 pF). the op-amp. Differential amplifier A cascaded differential amplifier followed by a current-mirror active load, the input stage (outlined in blue) is a transconductance amplifier, turning a differential voltage signal at the bases of Q1, Q2 into a current signal into the base of Q15. It entails two cascaded transistor pairs, satisfying conflicting requirements. The first stage consists of the matched NPN emitter follower pair Q1, Q2 that provide high input impedance. The second is the matched PNP commonbase pair Q3, Q4 that eliminates the undesirable Miller effect; it drives an active load Q7 plus matched pair Q5, Q6. That active load is implemented as a modified Wilson current mirror; its role is to convert the (differential) input current signal to a single-ended signal without the attendant 50% losses (increasing the op-amp’s open-loop gain by 3dB).[nb 5] Thus, a small-signal differential current in Q3 versus Q4 appears summed (doubled) at the base of Q15, the input of the voltage gain stage.
The resistor (39 kΩ) connecting the (diode-connected) Q11 and Q12, and the given supply voltage (VS₊−VS₋), determine the current in the current mirrors, (matched pairs) Q10/Q11 and Q12/Q13. The collector current of Q11, i11 * 39 kΩ = VS₊ − VS₋ − 2 VBE. For the typical VS = ±20 V, the standing current in Q11/Q12 (as well as in Q13) would be ≈1 mA. A supply current for a typical 741 of about 2 mA agrees with the notion that these two bias currents dominate the quiescent supply current. Transistors Q11 and Q10 form a Widlar current mirror, with quiescent current in Q10 i10 such that ln( i11 / i10 ) = i10 * 5 kΩ / 28 mV, where 5 kΩ represents the emitter resistor of Q10, and 28 mV is VT, the thermal voltage at room temperature. In this case i10 ≈ 20 μA. Differential amplifier The biasing circuit of this stage is set by a feedback loop that forces the collector currents of Q10 and Q9 to (nearly) match. The small difference in these currents provides the drive for the common base of Q3/Q4 (note that the base drive for input transistors Q1/Q2 is the input bias current and must be sourced externally). The summed quiescent currents of Q1/Q3 plus Q2/Q4 is mirrored from Q8 into Q9, where it is summed with the collector current in Q10, the result being applied to the bases of Q3/Q4.
Voltage amplifier The (class-A) voltage gain stage (outlined in magenta) consists of the two NPN transistors Q15/Q19 connected in a Darlington configuration and uses the output side of current mirror Q12/Q13 as its collector (dynamic) load to achieve its high voltage gain. The The quiescent currents of Q1/Q3 (resp., Q2/Q4) i1 will
118 thus be half of i10 , of order ≈ 10 μA. Input bias current for the base of Q1 (resp. Q2) will amount to i1 / β; typically ≈50 nA, implying a current gain h ₑ ≈ 200 for Q1(Q2). This feedback circuit tends to draw the common base node of Q3/Q4 to a voltage V ₒ − 2 * VBE, where V ₒ is the input common-mode voltage. At the same time, the magnitude of the quiescent current is relatively insensitive to the characteristics of the components Q1–Q4, such as h ₑ, that would otherwise cause temperature dependence or part-to-part variations. Transistor Q7 drives Q5 and Q6 into conduction until their (equal) collector currents match that of Q1/Q3 and Q2/Q4. The quiescent current in Q7 is VBE / 50 kΩ, about 35μA, as is the quiescent current in Q15, with its matching operating point. Thus, the quiescent currents are pairwise matched in Q1/Q2, Q3/Q4, Q5/Q6, and Q7/Q15.
Voltage amplifier Quiescent currents in Q16 and Q19 are set by the current mirror Q12/Q13, which is running at ≈ 1 mA. Through some (?) mechanism, the collector current in Q19 tracks that standing current.
CHAPTER 5. COMMON INTEGRATED CIRCUITS Input impedance Because Q1 and Q3 (resp. Q2 and Q4) form a Darlington pair, the small-signal differential input impedance is of order 2hᵢₑh ₑ, where hᵢₑ is the small-signal input impedance (common emitter) of Q1 and Q3 (resp. Q2 and Q4) and where h ₑ is the transistor small-signal current gain (or β). This contrasts with what would be the case with a simpler emitter-coupled pair (long-tailed pair) input stage, where the differential input impedance is 2hᵢₑ, a factor of β lower. A typical 741 op amp has an input impedance 2–8 MΩ. Differential amplifier A differential voltage VI at the op-amp inputs (pins 3 and 2, respectively) gives rise to a small differential current in the bases of Q1 and Q2 iI ≈ VI / ( 2 hᵢₑ * h ₑ). This differential base current causes a change in the differential collector current in each leg by iI * h ₑ. Introducing the transconductance of Q1, gm = h ₑ / hᵢₑ, the (small-signal) current at the base of Q15 (the input of the voltage gain stage) is VI * gm / 2. This portion of the op amp cleverly changes a differential signal at the op amp inputs to a single-ended signal at the base of Q15, and in a way that avoids wastefully discarding the signal in either leg. To see how, notice that a small negative change in voltage at the inverting input (Q2 base) drives it out of conduction, and this incremental decrease in current passes directly from Q4 collector to its emitter, resulting in an decrease in base drive for Q15. On the other hand, a small positive change in voltage at the non-inverting input (Q1 base) drives this transistor into conduction, reflected in an increase in current at the collector of Q3. This current drives Q7 further into conduction, which turns on current mirror Q5/Q6. Thus, the increase in Q3 emitter current is mirrored in an increase in Q6 collector current, resulting also in a decrease in base drive for Q15. Besides avoiding wasting 3dB of gain here, this technique decreases common-mode gain and feedthrough of power supply noise.
Output amplifier In the circuit involving Q16 (variously named rubber diode or VBE multiplier), the 4.5 kΩ resistor must be conducting about 100 μA, with the Q16 VBE roughly 700 mV. Then the VCB must be about 0.45 V and VCE at about 1.0 V. Because the Q16 collector is driven by a current source and the Q16 emitter drives into the Q19 collector current sink, the Q16 transistor establishes a voltage difference between Q14 base and Q20 base of ≈ 1 V, regardless of the common-mode voltage of Q14/Q20 base. The standing current in Q14/Q20 will be a factor exp(100 mV / VT ) ≈ 36 smaller than the 1 mA quiescent current in the class A portion of the op amp. This (small) standing current in the output transisQ15’s base tors establishes the output stage in class AB operation and Voltage amplifier A current signal i at 2 gives rise to a current in Q19 of order i * β (the product reduces the crossover distortion of this stage. of the h ₑ of each of Q15 and Q19, which are connected in a Darlington pair). This current signal develops a voltage at the bases of output transistors Q14/Q20 proportional Small-signal differential mode to the hᵢₑ of the respective transistor.
A small differential input voltage signal gives rise, through multiple stages of current amplification, to a Output amplifier Output transistors Q14 and Q20 are each configured as an emitter follower, so no voltage gain much larger voltage signal on output.
5.2. OPERATIONAL AMPLIFIER
119
occurs there; instead, this stage provides current gain, reactive and the closed loop gain is unity or higher. equal to the h ₑ of Q14 (resp. Q20). By contrast, amplifiers requiring external compensation, The output impedance is not zero, as it would be in an such as the μA748, may require external compensation ideal op-amp, but with negative feedback it approaches or closed-loop gains significantly higher than unity. zero at low frequencies. Overall open-loop voltage gain The net open-loop small-signal voltage gain of the op amp involves the product of the current gain h ₑ of some 4 transistors. In practice, the voltage gain for a typical 741-style op amp is of order 200,000, and the current gain, the ratio of input impedance (≈2−6 MΩ) to output impedance (≈50Ω) provides yet more (power) gain.
Input offset voltage The “offset null” pins may be used to place external resistors (typically in the form of the two ends of a potentiometer, with the slider connected to VS–) in parallel with the emitter resistors of Q5 and Q6, to adjust the balance of the Q5/Q6 current mirror. The potentiometer is adjusted such that the output is null (midrange) when the inputs are shorted together. Non-linear characteristics
Other linear characteristics
Input breakdown voltage The transistors Q3, Q4 Small-signal common mode gain The ideal op help to increase the reverse VBE rating: the base-emitter amp has infinite common-mode rejection ratio, or zero junctions of the NPN transistors Q1 and Q2 break down at around 7V, but the PNP transistors Q3 and Q4 have common-mode gain. VBE breakdown voltages around 50 V.[11] In the present circuit, if the input voltages change in the same direction, the negative feedback makes Q3/Q4 base voltage follow (with 2VBE below) the input voltage vari- Output-stage voltage swing and current limiting ations. Now the output part (Q10) of Q10-Q11 current Variations in the quiescent current with temperature, or mirror keeps up the common current through Q9/Q8 con- between parts with the same type number, are common, stant in spite of varying voltage. Q3/Q4 collector cur- so crossover distortion and quiescent current may be subrents, and accordingly the output current at the base of ject to significant variation. Q15, remain unchanged. The output range of the amplifier is about one volt less In the typical 741 op amp, the common-mode rejection than the supply voltage, owing in part to VBE of the outratio is 90dB, implying an open-loop common-mode volt- put transistors Q14 and Q20. age gain of about 6. The 25 Ω resistor at the Q14 emitter, along with Q17, acts to limit Q14 current to about 25 mA; otherwise, Q17 Frequency compensation The innovation of the conducts no current. Fairchild μA741 was the introduction of frequency compensation via an on-chip (monolithic) capacitor, simplifying application of the op amp by eliminating the need for external components for this function. The 30 pF capacitor stabilizes the amplifier via Miller compensation and functions in a manner similar to an op-amp integrator circuit. Also known as 'dominant pole compensation' because it introduces a pole that masks (dominates) the effects of other poles into the open loop frequency response; in a 741 op amp this pole can be as low as 10 Hz (where it causes a −3 dB loss of open loop voltage gain).
Current limiting for Q20 is performed in the voltage gain stage: Q22 senses the voltage across Q19’s emitter resistor (50Ω); as it turns on, it diminishes the drive current to Q15 base. Later versions of this amplifier schematic may show a somewhat different method of output current limiting. Applicability considerations
Note: while the 741 was historically used in audio and This internal compensation is provided to achieve un- other sensitive equipment, such use is now rare because conditional stability of the amplifier in negative feed- of the improved noise performance of more modern opback configurations where the feedback network is non- amps. Apart from generating noticeable hiss, 741s and
120 other older op-amps may have poor common-mode rejection ratios and so will often introduce cable-borne mains hum and other common-mode interference, such as switch 'clicks’, into sensitive equipment. The “741” has come to often mean a generic op-amp IC (such as μA741, LM301, 558, LM324, TBA221 — or a more modern replacement such as the TL071). The description of the 741 output stage is qualitatively similar for many other designs (that may have quite different input stages), except: • Some devices (μA748, LM301, LM308) are not internally compensated (require an external capacitor from output to some point within the operational amplifier, if used in low closed-loop gain applications). • Some modern devices have “rail-to-rail output” capability, meaning that the output can range from within a few millivolts of the positive supply voltage to within a few millivolts of the negative supply voltage.
5.2.5 Classification Op-amps may be classified by their construction:
CHAPTER 5. COMMON INTEGRATED CIRCUITS • Classification by internal compensation: op-amps may suffer from high frequency instability in some negative feedback circuits unless a small compensation capacitor modifies the phase and frequency responses. Op-amps with a built-in capacitor are termed extquotedblcompensated extquotedbl, or perhaps compensated for closed-loop gains down to (say) 5. All others are considered uncompensated. • Single, dual and quad versions of many commercial op-amp IC are available, meaning 1, 2 or 4 operational amplifiers are included in the same package. • Rail-to-rail input (and/or output) op-amps can work with input (and/or output) signals very close to the power supply rails. • CMOS op-amps (such as the CA3140E) provide extremely high input resistances, higher than JFETinput op-amps, which are normally higher than bipolar-input op-amps. • other varieties of op-amp include programmable opamps (simply meaning the quiescent current, gain, bandwidth and so on can be adjusted slightly by an external resistor). • manufacturers often tabulate their op-amps according to purpose, such as low-noise pre-amplifiers, wide bandwidth amplifiers, and so on.
• discrete (built from individual transistors or 5.2.6 tubes/valves)
Applications
• IC (fabricated in an Integrated circuit) — most common • hybrid IC op-amps may be classified in many ways, including: • Military, Industrial, or Commercial grade (for exDIP pinout for 741-type operational amplifier ample: the LM301 is the commercial grade version of the LM101, the LM201 is the industrial version). Main article: Operational amplifier applications This may define operating temperature ranges and other environmental or quality factors. • Classification by package type may also affect envi- Use in electronics system design ronmental hardiness, as well as manufacturing options; DIP, and other through-hole packages are The use of op-amps as circuit blocks is much easier and clearer than specifying all their individual circuit eletending to be replaced by surface-mount devices.
5.2. OPERATIONAL AMPLIFIER
121
ments (transistors, resistors, etc.), whether the amplifiers mains interference and current spikes. used are integrated or discrete. In the first approximation op-amps can be used as if they were ideal differential gain blocks; at a later stage limits can be placed on the accept- Positive feedback applications able range of parameters for each op-amp. Another typical configuration of op-amps is with posiCircuit design follows the same lines for all electronic cir- tive feedback, which takes a fraction of the output signal cuits. A specification is drawn up governing what the back to the non-inverting input. An important applicacircuit is required to do, with allowable limits. For ex- tion of it is the comparator with hysteresis, the Schmitt ample, the gain may be required to be 100 times, with a trigger. Some circuits may use Positive feedback and Negtolerance of 5% but drift of less than 1% in a specified ative feedback around the same amplifier, for example temperature range; the input impedance not less than one Triangle wave oscillators and active filters. megohm; etc. Because of the wide slew-range and lack of positive feedA basic circuit is designed, often with the help of circuit back, the response of all the open-loop level detectors modeling (on a computer). Specific commercially avail- described above will be relatively slow. External overable op-amps and other components are then chosen that all positive feedback may be applied but (unlike internal meet the design criteria within the specified tolerances at positive feedback that may be applied within the latter acceptable cost. If not all criteria can be met, the speci- stages of a purpose-designed comparator) this markedly fication may need to be modified. affects the accuracy of the zero-crossing detection point. A prototype is then built and tested; changes to meet or Using a general-purpose op-amp, for example, the freimprove the specification, alter functionality, or reduce quency of Eᵢ for the sine to square wave converter should probably be below 100 Hz. the cost, may be made. Applications without using any feedback That is, the op-amp is being used as a voltage comparator. Note that a device designed primarily as a comparator may be better if, for instance, speed is important or a wide range of input voltages may be found, since such devices can quickly recover from full on or full off (“saturated”) states. A voltage level detector can be obtained if a reference voltage Vᵣₑ is applied to one of the op-amp’s inputs. This means that the op-amp is set up as a comparator to detect a positive voltage. If the voltage to be sensed, Eᵢ, is applied to op amp’s (+) input, the result is a noninverting positive-level detector: when Eᵢ is above Vᵣₑ , VO equals +V ₐ ; when Eᵢ is below Vᵣₑ , VO equals −V ₐ . If Eᵢ is applied to the inverting input, the circuit is an inverting positive-level detector: When Eᵢ is above Vᵣₑ , VO equals −V ₐ . A zero voltage level detector (Eᵢ = 0) can convert, for example, the output of a sine-wave from a function generator into a variable-frequency square wave. If Eᵢ is a sine wave, triangular wave, or wave of any other shape that is symmetrical around zero, the zero-crossing detector’s output will be square. Zero-crossing detection may also be useful in triggering TRIACs at the best time to reduce
Negative feedback applications
Vin
R1
Vout
R2
An op-amp connected in the non-inverting amplifier configuration
Non-inverting amplifier In a non-inverting amplifier, the output voltage changes in the same direction as the input voltage. The gain equation for the op-amp is:
Vout = AOL (V+ − V− ) However, in this circuit V₋ is a function of Vₒᵤ because of the negative feedback through the R1 R2 network. R1 and R2 form a voltage divider, and as V₋ is a high-impedance input, it does not load it appreciably. Consequently:
122
CHAPTER 5. COMMON INTEGRATED CIRCUITS
Rf V− = β · Vout where
β=
Vin
Rin Vout
R1 R1 + R2
Substituting this into the gain equation, we obtain: An op-amp connected in the inverting amplifier configuration
Vout = AOL (Vin − β · Vout ) Solving for Vout : ( Vout = Vin
1 β + 1/AOL
)
If AOL is very large, this simplifies to
Vout ≈
Vin = β
Vin R1 R1 +R2
This time, V₋ is a function of both Vₒᵤ and Vᵢ due to the voltage divider formed by R and Rᵢ . Again, the op-amp input does not apply an appreciable load, so:
( ) R2 = Vin 1 + R1
The non-inverting input of the operational amplifier needs a path for DC to ground; if the signal source does not supply a DC path, or if that source requires a given load impedance, then the circuit will require another resistor from the non-inverting input to ground. When the operational amplifier’s input bias currents are significant, then the DC source resistances driving the inputs should be balanced.[12] The ideal value for the feedback resistors (to give minimum offset voltage) will be such that the two resistances in parallel roughly equal the resistance to ground at the non-inverting input pin. That ideal value assumes the bias currents are well-matched, which may not be true for all op-amps.[13]
V− =
1 (Rf Vin + Rin Vout ) Rf + Rin
Substituting this into the gain equation and solving for Vout :
Vout = −Vin ·
AOL Rf Rf + Rin + AOL Rin
If AOL is very large, this simplifies to
Vout ≈ −Vin
Rf Rin
A resistor is often inserted between the non-inverting input and ground (so both inputs “see” similar resistances), reducing the input offset voltage due to different voltage drops due to bias current, and may reduce distortion in some op-amps.
A DC-blocking capacitor may be inserted in series with the input resistor when a frequency response down to DC is not needed and any DC voltage on the input is unwanted. That is, the capacitive component of the input Inverting amplifier In an inverting amplifier, the out- impedance inserts a DC zero and a low-frequency pole put voltage changes in an opposite direction to the input that gives the circuit a bandpass or high-pass characterisvoltage. tic. As with the non-inverting amplifier, we start with the gain The potentials at the operational amplifier inputs remain equation of the op-amp: virtually constant (near ground) in the inverting configuVout = AOL (V+ − V− )
ration. The constant operating potential typically results in distortion levels that are lower than those attainable with the non-inverting topology.
5.2. OPERATIONAL AMPLIFIER
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Other applications • audio- and video-frequency pre-amplifiers and buffers • differential amplifiers • differentiators and integrators • filters • precision rectifiers • precision peak detectors • voltage and current regulators • analog calculators • analog-to-digital converters • digital-to-analog converters • Voltage clamping • oscillators and waveform generators Most single, dual and quad op-amps available have a standardized pin-out which permits one type to be substituted for another without wiring changes. A specific op-amp may be chosen for its open loop gain, bandwidth, noise performance, input impedance, power consumption, or a compromise between any of these factors.
5.2.7
Historical timeline
1941: A vacuum tube op-amp. An op-amp, defined as a general-purpose, DC-coupled, high gain, inverting feedback amplifier, is first found in U.S. Patent 2,401,779 “Summing Amplifier” filed by Karl D. Swartzel Jr. of Bell Labs in 1941. This design used three vacuum tubes to achieve a gain of 90 dB and operated on voltage rails of ±350 V. It had a single inverting input rather than differential inverting and non-inverting inputs, as are common in today’s op-amps. Throughout World War II, Swartzel’s design proved its value by being liberally used in the M9 artillery director designed at Bell Labs. This artillery director worked with the SCR584 radar system to achieve extraordinary hit rates (near 90%) that would not have been possible otherwise.[14]
GAP/R’s K2-W: a vacuum-tube op-amp (1953)
R. Ragazzini of Columbia University. In this same paper a footnote mentioned an op-amp design by a student that would turn out to be quite significant. This op-amp, designed by Loebe Julie, was superior in a variety of ways. It had two major innovations. Its input stage used a longtailed triode pair with loads matched to reduce drift in the output and, far more importantly, it was the first op-amp design to have two inputs (one inverting, the other non1947: An op-amp with an explicit non-inverting in- inverting). The differential input made a whole range put. In 1947, the operational amplifier was first for- of new functionality possible, but it would not be used mally defined and named in a paper by Professor John for a long time due to the rise of the chopper-stabilized
124 amplifier.[14] 1949: A chopper-stabilized op-amp. In 1949, Edwin A. Goldberg designed a chopper-stabilized op-amp.[15] This set-up uses a normal op-amp with an additional AC amplifier that goes alongside the op-amp. The chopper gets an AC signal from DC by switching between the DC voltage and ground at a fast rate (60 Hz or 400 Hz). This signal is then amplified, rectified, filtered and fed into the op-amp’s non-inverting input. This vastly improved the gain of the op-amp while significantly reducing the output drift and DC offset. Unfortunately, any design that used a chopper couldn't use their non-inverting input for any other purpose. Nevertheless, the much improved characteristics of the chopper-stabilized op-amp made it the dominant way to use op-amps. Techniques that used the non-inverting input regularly would not be very popular until the 1960s when op-amp ICs started to show up in the field.
CHAPTER 5. COMMON INTEGRATED CIRCUITS transistor in 1947, and the silicon transistor in 1954, the concept of ICs became a reality. The introduction of the planar process in 1959 made transistors and ICs stable enough to be commercially useful. By 1961, solid-state, discrete op-amps were being produced. These op-amps were effectively small circuit boards with packages such as edge connectors. They usually had hand-selected resistors in order to improve things such as voltage offset and drift. The P45 (1961) had a gain of 94 dB and ran on ±15 V rails. It was intended to deal with signals in the range of ±10 V.
1961: A varactor bridge op-amp. There have been many different directions taken in op-amp design. Varactor bridge op-amps started to be produced in the early 1960s.[16][17] They were designed to have extremely small input current and are still amongst the best op-amps available in terms of common-mode rejection with the ability to correctly deal with hundreds of volts at their in1953: A commercially available op-amp. In 1953, vac- puts. uum tube op-amps became commercially available with the release of the model K2-W from George A. Philbrick Researches, Incorporated. The designation on the devices shown, GAP/R, is an acronym for the complete company name. Two nine-pin 12AX7 vacuum tubes were mounted in an octal package and had a model K2-P chopper add-on available that would effectively “use up” the non-inverting input. This op-amp was based on a descendant of Loebe Julie’s 1947 design and, along with its successors, would start the widespread use of op-amps in industry.
GAP/R’s model PP65: a solid-state op-amp in a potted module (1962)
GAP/R’s model P45: a solid-state, discrete op-amp (1961).
1962: An op-amp in a potted module. By 1962, several companies were producing modular potted packages that could be plugged into printed circuit boards. These packages were crucially important as they made the operational amplifier into a single black box which could be easily treated as a component in a larger circuit.
1963: A monolithic IC op-amp. In 1963, the first 1961: A discrete IC op-amp. With the birth of the monolithic IC op-amp, the μA702 designed by Bob Wid-
5.2. OPERATIONAL AMPLIFIER
125
lar at Fairchild Semiconductor, was released. Monolithic ICs consist of a single chip as opposed to a chip and discrete parts (a discrete IC) or multiple chips bonded and connected on a circuit board (a hybrid IC). Almost all modern op-amps are monolithic ICs; however, this first IC did not meet with much success. Issues such as an uneven supply voltage, low gain and a small dynamic range held off the dominance of monolithic op-amps until 1965 when the μA709[18] (also designed by Bob Widlar) was released. 1968: Release of the μA741. The popularity of monolithic op-amps was further improved upon the release of the LM101 in 1967, which solved a variety of issues, and the subsequent release of the μA741 in 1968. The μA741 was extremely similar to the LM101 except that Fairchild’s facilities allowed them to include a 30 pF compensation capacitor inside the chip instead of requiring external compensation. This simple difference has made ADI’s HOS-050: a high speed hybrid IC op-amp (1979) the 741 the canonical op-amp and many modern amps base their pinout on the 741s. The μA741 is still in production, and has become ubiquitous in electronics— tems. many manufacturers produce a version of this classic chip, recognizable by part numbers containing 741. The same part is manufactured by several companies. 1970: First high-speed, low-input current FET design. In the 1970s high speed, low-input current designs started to be made by using FETs. These would be largely replaced by op-amps made with MOSFETs in the 1980s. During the 1970s single sided supply op-amps also became available. 1972: Single sided supply op-amps being produced. A single sided supply op-amp is one where the input and output voltages can be as low as the negative power supply voltage instead of needing to be at least two volts above it. The result is that it can operate in many applications with the negative supply pin on the op-amp being connected to the signal ground, thus eliminating the need for a separate negative power supply. The LM324 (released in 1972) was one such op-amp that came in a quad package (four separate op-amps in one package) and became an industry standard. In addition to packaging multiple op-amps in a single package, the 1970s also saw the birth of op-amps in hybrid packages. These op-amps were generally improved versions of existing monolithic op-amps. As the properties of monolithic op-amps improved, the more complex hybrid ICs were quickly relegated to systems that are required to have extremely long service lives or other specialty sys-
An op-amp in a modern mini DIP
Recent trends. Recently supply voltages in analog circuits have decreased (as they have in digital logic) and low-voltage op-amps have been introduced reflecting this. Supplies of ±5 V and increasingly 3.3 V (sometimes as low as 1.8 V) are common. To maximize the signal range modern op-amps commonly have rail-to-rail output (the output signal can range from the lowest supply voltage to the highest) and sometimes rail-to-rail inputs.
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5.2.8 See also • Operational amplifier applications • Differential amplifier • Instrumentation amplifier • Active filter • Current-feedback operational amplifier • Operational transconductance amplifier • George A. Philbrick • Bob Widlar • Analog computer • Negative feedback amplifier • Current conveyor
5.2.9 Notes [1] This definition hews to the convention of measuring opamp parameters with respect to the zero voltage point in the circuit, which is usually half the total voltage between the amplifier’s positive and negative power rails. [2] Many older designs of operational amplifiers have offset null inputs to allow the offset to be manually adjusted away. Modern precision op-amps can have internal circuits that automatically cancel this offset using choppers or other circuits that measure the offset voltage periodically and subtract it from the input voltage. [3] That the output cannot reach the power supply voltages is usually the result of limitations of the amplifier’s output stage transistors. See Output stage. [4] The output of older op-amps can reach to within one or two volts of the supply rails. The output of newer so-called “rail to rail” op-amps can reach to within millivolts of the supply rails when providing low output currents. [5] Widlar used this same trick in μA702 and μA709
5.2.10 References [1] Maxim Application Note 1108: Understanding SingleEnded, Pseudo-Differential and Fully-Differential ADC Inputs – Retrieved November 10, 2007 [2] Analog devices MT-044 Tutorial
CHAPTER 5. COMMON INTEGRATED CIRCUITS
[3] “Burson Opamp”. Parts Connexion. Retrieved 24 September 2012. “BURSON-71484 Dual Discrete Op Amp Modules, pair pcX Selling Price: $179.95/pr BURSON-71485 Dual Discrete OpAmp Module, single pcX Selling Price: $89.95 each. BURSON-71486 Single Discrete Op Amp Modules, pair pcX Selling Price: $114.95/pr. Quantity discounts for Modifiers and OEM’s” [4] Jacob Millman, Microelectronics: Digital and Analog Circuits and Systems, McGraw-Hill, 1979, ISBN 0-07042327-X, pp. 523-527 [5] Horowitz, Paul; Hill, Winfield (1989). The Art of Electronics. Cambridge, UK: Cambridge University Press. ISBN 0-521-37095-7. [6] D.F. Stout Handbook of Operational Amplifier Circuit Design (McGraw-Hill, 1976, ISBN 0-07-061797-X ) pp. 1– 11. [7] {{cite web |url=http://www.analog.com/static/ imported-files/tutorials/MT-036.pdf |title=Op Amp Output Phase-Reversal and Input Over-Voltage Protection |year=2009 |publisher=Analog Devices |accessdate=2012-12-27}} [8] {{cite web |url=http://www.edn.com/contents/images/ 45890.pdf |title=Bootstrapping your op amp yields wide voltage swings |last1=King |first1=Grayson |last2=Watkins |first2=Tim |date=13 May 1999 |publisher=Electronic Design News |accessdate=2012-1227}} [9] Lee, Thomas H. (November 18, 2002). “IC Op-Amps Through the Ages”. Stanford UniversityHandout #18: EE214 Fall 2002. [10] Lu, Liang-Hung. “Electronics 2, Chapter 10”. National Taiwan University, Graduate Institute of Electronics Engineering. Retrieved 2014-02-22. [11] The μA741 Operational Amplifier [12] An input bias current of 1 µA through a DC source resistance of 10 kΩ produces a 10 mV offset voltage. If the other input bias current is the same and sees the same source resistance, then the two input offset voltages will cancel out. Balancing the DC source resistances may not be necessary if the input bias current and source resistance product is small. [13] http://www.analog.com/static/imported-files/tutorials/ MT-038.pdf [14] Jung, Walter G. (2004). “Chapter 8: Op Amp History”. Op Amp Applications Handbook. Newnes. p. 777. ISBN 978-0-7506-7844-5. Retrieved 2008-11-15.
5.3. PHASE-LOCKED LOOP
[15] http://www.analog.com/library/analogDialogue/ archives/39-05/Web_ChH_final.pdf [16] http://www.philbrickarchive.org/ [17] June 1961 advertisement for Philbrick P2, http://www.philbrickarchive.org/p2%20and%206033% 20ad%20rsi%20vol32%20no6%20june1961.pdf [18] A.P. Malvino, Electronic Principles (2nd Ed. 1979. ISBN 0-07-039867-4) p. 476.
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5.2.12 External links • Simple Op Amp Measurements How to measure offset voltage, offset and bias current, gain, CMRR, and PSRR. • Introduction to op-amp circuit stages, second order filters, single op-amp bandpass filters, and a simple intercom • MOS op amp design: A tutorial overview
5.2.11
Further reading
• Design with Operational Amplifiers and Analog Integrated Circuits; 4th Ed; Sergio Franco; McGraw Hill; 672 pages; 2014; ISBN 978-0078028168. • Op Amps For Everyone; 4th Ed; Ron Mancini; Newnes; 304 pages; 2013; ISBN 978-0123914958. (Free PDF download of older version)
• Operational Amplifier Noise Prediction (All Op Amps) using spot noise • Operational Amplifier Basics • History of the Op-amp from vacuum tubes to about 2002. Lots of detail, with schematics. IC part is somewhat ADI-centric.
• Small Signal Audio Design; Douglas Self; Focal Press; 556 pages; 2010; ISBN 978-0-240-52177-0.
• Loebe Julie historical OpAmp interview by Bob Pease
• Op Amp Applications Handbook; Walt G. Jung; Newnes; 896 pages; 2004; ISBN 978-0750678445.
• www.PhilbrickArchive.org – A free repository of materials from George A Philbrick / Researches Operational Amplifier Pioneer
(Free PDF download)
• Op Amps and Linear Integrated Circuits; James M. Fiore; Cengage Learning; 616 pages; 2000; ISBN 978-0766817937.
• What’s The Difference Between Operational Amplifiers And Instrumentation Amplifiers?, Electronic Design Magazine
• Operational Amplifiers and Linear Integrated Circuits; 6th Ed; Robert F Coughlin; Prentice Hall; 529 IC Datasheets pages; 2000; ISBN 978-0130149916. • LM301, Single BJT OpAmp, Texas Instruments • Op-Amps and Linear Integrated Circuits; 4th Ed; Ram Gayakwad; Prentice Hall; 543 pages; 1999; ISBN 978-0132808682. • Basic Operational Amplifiers and Linear Integrated Circuits; 2nd Ed; Thomas L Floyd and David Buchla; Prentice Hall; 593 pages; 1998; ISBN 9780130829870. • Troubleshooting Analog Circuits; Bob Pease; Newnes; 217 pages; 1991; ISBN 978-0750694995. • IC Op-Amp Cookbook; 3rd Ed; Walter G. Jung; Prentice Hall; 433 pages; 1986; ISBN 9780138896010.
• LM324, Quad BJT OpAmp, Texas Instruments • LM741, Single BJT OpAmp, Texas Instruments • NE5532, Dual BJT OpAmp, Texas Instruments (NE5534 is Quad) • TL072, Dual JFET OpAmp, Texas Instruments (TL074 is Quad)
5.3 Phase-locked loop
• Engineer’s Mini-Notebook – OpAmp IC Circuits; “PLL” redirects here. For other uses, see PLL (disamForrest Mims III; Radio Shack; 49 pages; 1985; biguation). ASIN B000DZG196.
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A phase-locked loop or phase lock loop (PLL) is a control system that generates an output signal whose phase is related to the phase of an input signal. While there are several differing types, it is easy to initially visualize as an electronic circuit consisting of a variable frequency oscillator and a phase detector. The oscillator generates a periodic signal. The phase detector compares the phase of that signal with the phase of the input periodic signal and adjusts the oscillator to keep the phases matched. Bringing the output signal back toward the input signal for comparison is called a feedback loop since the output is 'fed back' toward the input forming a loop.
However, if there is an accident, a pace car comes out to set a safe speed. None of the race cars are permitted to pass the pace car (or the race cars in front of them), but each of the race cars wants to stay as close to the pace car as it can. While it is on the track, the pace car is a reference, and the race cars become phase-locked loops. Each driver will measure the phase difference (a distance in laps) between him and the pace car. If the driver is far away, he will increase his engine speed to close the gap. If he’s too close to the pace car, he will slow down. The result is all the race cars lock on to the phase of the pace car. The cars travel around the track in a tight group that Keeping the input and output phase in lock step also is a small fraction of a lap. implies keeping the input and output frequencies the same. Consequently, in addition to synchronizing signals, Clock analogy a phase-locked loop can track an input frequency, or it can generate a frequency that is a multiple of the input Phase can be proportional to time,[1] so a phase differfrequency. These properties are used for computer clock ence can be a time difference. Clocks are, with varysynchronization, demodulation, and frequency synthesis. ing degrees of accuracy, phase-locked (time-locked) to a Phase-locked loops are widely employed in radio, master clock. telecommunications, computers and other electronic ap- Left on its own, each clock will mark time at slightly difplications. They can be used to demodulate a signal, re- ferent rates. A wall clock, for example, might be fast by cover a signal from a noisy communication channel, gen- a few seconds per hour compared to the reference clock erate a stable frequency at multiples of an input frequency at NIST. Over time, that time difference would become (frequency synthesis), or distribute precisely timed clock substantial. pulses in digital logic circuits such as microprocessors. Since a single integrated circuit can provide a complete To keep his clock in sync, each week the owner compares phase-locked-loop building block, the technique is widely the time on his wall clock to a more accurate clock (a used in modern electronic devices, with output frequen- phase comparison), and he resets his clock. Left alone, the wall clock will continue to diverge from the reference cies from a fraction of a hertz up to many gigahertz. clock at the same few seconds per hour rate. Some clocks have a timing adjustment (a fast-slow control). When the owner compared his wall clock’s time to 5.3.1 Practical analogies the reference time, he noticed that his clock was too fast. Consequently, he could turn the timing adjust a small Automobile race analogy amount to make the clock run a little slower. If things work out right, his clock will be more accurate. Over a For a practical idea of what is going on, consider an auto series of weekly adjustments, the wall clock’s notion of a race. There are many cars, and the driver of each of them second would agree with the reference time (within the wants to go around the track as fast as possible. Each lap wall clock’s stability). corresponds to a complete cycle, and each car will complete dozens of laps per hour. The number of laps per An early electromechanical version of a phase-locked hour (a speed) corresponds to an angular velocity (i.e. loop was used in 1921 in the Shortt-Synchronome clock. a frequency), but the number of laps (a distance) corresponds to a phase (and the conversion factor is the dis5.3.2 History tance around the track loop). During most of the race, each car is on its own and the Spontaneous synchronization of weakly coupled pendudriver of the car is trying to beat the driver of every other lum clocks was noted by the Dutch physicist Christiaan car on the course, and the phase of each car varies freely. Huygens as early as 1673.[2] Around the turn of the
5.3. PHASE-LOCKED LOOP
129
19th century, Lord Rayleigh observed synchronization of • feedback path (which may include a frequency diweakly coupled organ pipes and tuning forks.[3] In 1919, vider). W. H. Eccles and J. H. Vincent found that two electronic oscillators that had been tuned to oscillate at slightly different frequencies but that were coupled to a resonant cir- Variations cuit would soon oscillate at the same frequency.[4] Automatic synchronization of electronic oscillators was de- There are several variations of PLLs. Some terms that are used are analog phase-locked loop (APLL) also rescribed in 1923 by Edward Victor Appleton.[5] ferred to as a linear phase-locked loop (LPLL), digital Earliest research towards what became known as the phase-locked loop (DPLL), all digital phase-locked loop phase-locked loop goes back to 1932, when British (ADPLL), and software phase-locked loop (SPLL).[11] researchers developed an alternative to Edwin Armstrong's superheterodyne receiver, the Homodyne or Analog or linear PLL (APLL) Phase detector is an direct-conversion receiver. In the homodyne or synchroanalog multiplier. Loop filter is active or passive. dyne system, a local oscillator was tuned to the desired Uses a Voltage-controlled oscillator (VCO). input frequency and multiplied with the input signal. The resulting output signal included the original modulation Digital PLL (DPLL) An analog PLL with a digital phase detector (such as XOR, edge-trigger JK, information. The intent was to develop an alternative phase frequency detector). May have digital divider receiver circuit that required fewer tuned circuits than in the loop. the superheterodyne receiver. Since the local oscillator would rapidly drift in frequency, an automatic corAll digital PLL (ADPLL) Phase detector, filter and rection signal was applied to the oscillator, maintaining oscillator are digital. Uses a numerically controlled it in the same phase and frequency as the desired sigoscillator (NCO). nal. The technique was described in 1932, in a paper by Henri de Bellescize, in the French journal L'Onde Élec- Software PLL (SPLL) Functional blocks are impletrique.[6][7][8] mented by software rather than specialized hardware. In analog television receivers since at least the late 1930s, phase-locked-loop horizontal and vertical sweep circuits Neuronal PLL (NPLL) Phase detector, filter and osare locked to synchronization pulses in the broadcast cillator are neurons or small neuronal pools. Uses signal.[9] a rate controlled oscillator (RCO). Used for tracking and decoding low frequency modulations (< 1 When Signetics introduced a line of monolithic kHz), such as those occurring during mammalianintegrated circuits such as the NE565 that were complete [10] like active sensing. phase-locked loop systems on a chip in 1969, applications for the technique multiplied. A few years later RCA introduced the extquotedblCD4046 extquotedbl Performance parameters CMOS Micropower Phase-Locked Loop, which became a popular integrated circuit. • Type and order
5.3.3
Structure and function
Phase-locked loop mechanisms may be implemented as either analog or digital circuits. Both implementations use the same basic structure. Both analog and digital PLL circuits include four basic elements: • Phase detector, • Low-pass filter, • Variable-frequency oscillator, and
• Lock range: The frequency range the PLL is able to stay locked. Mainly defined by the VCO range. • Capture range: The frequency range the PLL is able to lock-in, starting from unlocked condition. This range is usually smaller than the lock range and will depend, for example, on phase detector. • Loop bandwidth: Defining the speed of the control loop. • Transient response: Like overshoot and settling time to a certain accuracy (like 50ppm).
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CHAPTER 5. COMMON INTEGRATED CIRCUITS
• Steady-state errors: Like remaining phase or timing Clock recovery error Some data streams, especially high-speed serial data • Output spectrum purity: Like sidebands generated streams (such as the raw stream of data from the magnetic from a certain VCO tuning voltage ripple. head of a disk drive), are sent without an accompanying • Phase-noise: Defined by noise energy in a certain clock. The receiver generates a clock from an approxfrequency band (like 10 kHz offset from carrier). imate frequency reference, and then phase-aligns to the Highly dependent on VCO phase-noise, PLL band- transitions in the data stream with a PLL. This process is referred to as clock recovery. In order for this scheme to width, etc. work, the data stream must have a transition frequently • General parameters: Such as power consumption, enough to correct any drift in the PLL’s oscillator. Typsupply voltage range, output amplitude, etc. ically, some sort of line code, such as 8b/10b encoding, is used to put a hard upper bound on the maximum time between transitions.
5.3.4 Applications
Phase-locked loops are widely used for synchronization purposes; in space communications for coherent demodulation and threshold extension, bit synchronization, and symbol synchronization. Phase-locked loops can also be used to demodulate frequency-modulated signals. In radio transmitters, a PLL is used to synthesize new frequencies which are a multiple of a reference frequency, with the same stability as the reference frequency.
Deskewing
If a clock is sent in parallel with data, that clock can be used to sample the data. Because the clock must be received and amplified before it can drive the flip-flops which sample the data, there will be a finite, and process, temperature-, and voltage-dependent delay between the detected clock edge and the received data window. This delay limits the frequency at which data can be sent. One Other applications include: way of eliminating this delay is to include a deskew PLL on the receive side, so that the clock at each data flip-flop • Demodulation of both FM and AM signals is phase-matched to the received clock. In that type of ap• Recovery of small signals that otherwise would be plication, a special form of a PLL called a delay-locked lost in noise (lock-in amplifier to track the reference loop (DLL) is frequently used.[12] frequency) • Recovery of clock timing information from a data Clock generation stream such as from a disk drive • Clock multipliers in microprocessors that allow in- Many electronic systems include processors of various ternal processor elements to run faster than external sorts that operate at hundreds of megahertz. Typically, connections, while maintaining precise timing rela- the clocks supplied to these processors come from clock generator PLLs, which multiply a lower-frequency refertionships ence clock (usually 50 or 100 MHz) up to the operating • DTMF decoders, modems, and other tone decoders, frequency of the processor. The multiplication factor can for remote control and telecommunications be quite large in cases where the operating frequency is multiple gigahertz and the reference crystal is just tens or • DSP of video signals; Phase-locked loops are also hundreds of megahertz. used to synchronize phase and frequency to the input analog video signal so it can be sampled and digitally processed Spread spectrum • Atomic force microscopy in tapping mode, to detect All electronic systems emit some unwanted radio frechanges of the cantilever resonance frequency due to quency energy. Various regulatory agencies (such as the tip–surface interactions FCC in the United States) put limits on the emitted en• DC motor drive ergy and any interference caused by it. The emitted noise
5.3. PHASE-LOCKED LOOP generally appears at sharp spectral peaks (usually at the operating frequency of the device, and a few harmonics). A system designer can use a spread-spectrum PLL to reduce interference with high-Q receivers by spreading the energy over a larger portion of the spectrum. For example, by changing the operating frequency up and down by a small amount (about 1%), a device running at hundreds of megahertz can spread its interference evenly over a few megahertz of spectrum, which drastically reduces the amount of noise seen on broadcast FM radio channels, which have a bandwidth of several tens of kilohertz.
Clock distribution
131 Jitter and noise reduction One desirable property of all PLLs is that the reference and feedback clock edges be brought into very close alignment. The average difference in time between the phases of the two signals when the PLL has achieved lock is called the static phase offset (also called the steadystate phase error). The variance between these phases is called tracking jitter. Ideally, the static phase offset should be zero, and the tracking jitter should be as low as possible. Phase noise is another type of jitter observed in PLLs, and is caused by the oscillator itself and by elements used in the oscillator’s frequency control circuit. Some technologies are known to perform better than others in this regard. The best digital PLLs are constructed with emitter-coupled logic (ECL) elements, at the expense of high power consumption. To keep phase noise low in PLL circuits, it is best to avoid saturating logic families such as transistor-transistor logic (TTL) or CMOS. Another desirable property of all PLLs is that the phase and frequency of the generated clock be unaffected by rapid changes in the voltages of the power and ground supply lines, as well as the voltage of the substrate on which the PLL circuits are fabricated. This is called substrate and supply noise rejection. The higher the noise rejection, the better. To further improve the phase noise of the output, an injection locked oscillator can be employed following the VCO in the PLL.
Typically, the reference clock enters the chip and drives a phase locked loop (PLL), which then drives the system’s clock distribution. The clock distribution is usually balanced so that the clock arrives at every endpoint simultaneously. One of those endpoints is the PLL’s feedback input. The function of the PLL is to compare the distributed clock to the incoming reference clock, and vary the phase and frequency of its output until the reference and feedback clocks are phase and frequency matched. PLLs are ubiquitous—they tune clocks in systems several feet across, as well as clocks in small portions of individual chips. Sometimes the reference clock may not actually be a pure clock at all, but rather a data stream with enough transitions that the PLL is able to recover a regular clock from that stream. Sometimes the reference clock is the same frequency as the clock driven through the clock distribution, other times the distributed clock may be some rational multiple of the reference.
Frequency synthesis In digital wireless communication systems (GSM, CDMA etc.), PLLs are used to provide the local oscillator up-conversion during transmission and downconversion during reception. In most cellular handsets this function has been largely integrated into a single integrated circuit to reduce the cost and size of the handset. However, due to the high performance required of base station terminals, the transmission and reception circuits are built with discrete components to achieve the levels of performance required. GSM local oscillator modules are typically built with a frequency synthesizer integrated circuit and discrete resonator VCOs.
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5.3.5 Block diagram
Block diagram of a phase-locked loop
CHAPTER 5. COMMON INTEGRATED CIRCUITS Phase detector
Main article: phase detector
A phase detector compares two input signals and produces an error signal which is proportional to their phase difference. The error signal is then low-pass filtered and used to drive a VCO which creates an output phase. The output is fed through an optional divider back to the input of the system, producing a negative feedback loop. If the output phase drifts, the error signal will increase, driving the VCO phase in the opposite direction so as to reduce the error. Thus the output phase is locked to the phase at the other input. This input is called the reference.
A phase detector (PD) generates a voltage, which represents the phase difference between two signals. In a PLL, the two inputs of the phase detector are the reference input and the feedback from the VCO. The PD output voltage is used to control the VCO such that the phase difference between the two inputs is held constant, making it a negative feedback system. There are several types of phase detectors in the two main categories of analog and digital.
The oscillator generates a periodic output signal. Assume that initially the oscillator is at nearly the same frequency as the reference signal. If the phase from the oscillator falls behind that of the reference, the phase detector changes the control voltage of the oscillator so that it speeds up. Likewise, if the phase creeps ahead of the reference, the phase detector changes the control voltage to slow down the oscillator. Since initially the oscillator may be far from the reference frequency, practical phase detectors may also respond to frequency differences, so as to increase the lock-in range of allowable inputs.
The actual difference is determined by the DC loop gain.
Different types of phase detectors have different perforAnalog phase locked loops are generally built with an mance characteristics. analog phase detector, low pass filter and VCO placed in For instance, the frequency mixer produces harmonics a negative feedback configuration. A digital phase locked that adds complexity in applications where spectral purity loop uses a digital phase detector; it may also have a di- of the VCO signal is important. The resulting unwanted vider in the feedback path or in the reference path, or (spurious) sidebands, also called extquotedblreference both, in order to make the PLL’s output signal frequency spurs extquotedbl can dominate the filter requirements a rational multiple of the reference frequency. A non- and reduce the capture range and lock time well below integer multiple of the reference frequency can also be the requirements. In these applications the more complex created by replacing the simple divide-by-N counter in digital phase detectors are used which do not have as sethe feedback path with a programmable pulse swallow- vere a reference spur component on their output. Also, ing counter. This technique is usually referred to as a when in lock, the steady-state phase difference at the infractional-N synthesizer or fractional-N PLL. puts using this type of phase detector is near 90 degrees. A bang-bang charge pump phase detector must always have a dead band where the phases of inputs are close enough that the detector detects no phase error. For this reason, bang-bang phase detectors are associated with significant minimum peak-to-peak jitter, because of drift within the dead band. However these types, having outputs consisting of very narrow pulses at lock, are very useful for applications requiring very low VCO spurious outputs. The narrow pulses contain very little energy and are easy to filter out of the VCO control voltage. This Depending on the application, either the output of the results in low VCO control line ripple and therefore low controlled oscillator, or the control signal to the oscilla- FM sidebands on the VCO. tor, provides the useful output of the PLL system. In PLL applications it is frequently required to know
5.3.6 Elements
when the loop is out of lock. The more complex digital phase-frequency detectors usually have an output that allows a reliable indication of an out of lock condition.
5.3. PHASE-LOCKED LOOP Filter
133 Feedback path and optional divider
The block commonly called the PLL loop filter (usually a low pass filter) generally has two distinct functions. The primary function is to determine loop dynamics, also called stability. This is how the loop responds to disturbances, such as changes in the reference frequency, changes of the feedback divider, or at startup. Common considerations are the range over which the loop can achieve lock (pull-in range, lock range or capture range), how fast the loop achieves lock (lock time, lockup time or settling time) and damping behavior. Depending on the application, this may require one or more of the following: a simple proportion (gain or attenuation), an integral (low pass filter) and/or derivative (high pass filter). Loop parameters commonly examined for this are the loop’s gain margin and phase margin. Common concepts in control theory including the PID controller are used to design this function.
An Example Digital Divider (by 4) for use in the Feedback Path of a Multiplying PLL
PLLs may include a divider between the oscillator and the feedback input to the phase detector to produce a frequency synthesizer. A programmable divider is particularly useful in radio transmitter applications, since a The second common consideration is limiting the amount large number of transmit frequencies can be produced of reference frequency energy (ripple) appearing at the from a single stable, accurate, but expensive, quartz phase detector output that is then applied to the VCO crystal–controlled reference oscillator. control input. This frequency modulates the VCO and Some PLLs also include a divider between the reference produces FM sidebands commonly called “reference clock and the reference input to the phase detector. If spurs”. The low pass characteristic of this block can be the divider in the feedback path divides by N and the used to attenuate this energy, but at times a band reject reference input divider divides by M , it allows the PLL “notch” may also be useful. to multiply the reference frequency by N /M . It might The design of this block can be dominated by either of seem simpler to just feed the PLL a lower frequency, but these considerations, or can be a complex process jug- in some cases the reference frequency may be constrained gling the interactions of the two. Typical trade-offs are: by other issues, and then the reference divider is useful. increasing the bandwidth usually degrades the stability or too much damping for better stability will reduce the speed and increase settling time. Often also the phasenoise is affected.
Main article: Electronic oscillator
Frequency multiplication can also be attained by locking the VCO output to the Nth harmonic of the reference signal. Instead of a simple phase detector, the design uses a harmonic mixer (sampling mixer). The harmonic mixer turns the reference signal into an impulse train that is rich in harmonics.[13] The VCO output is coarse tuned to be close to one of those harmonics. Consequently, the desired harmonic mixer output (representing the difference between the N harmonic and the VCO output) falls within the loop filter passband.
All phase-locked loops employ an oscillator element with variable frequency capability. This can be an analog VCO either driven by analog circuitry in the case of an APLL or driven digitally through the use of a digital-toanalog converter as is the case for some DPLL designs. Pure digital oscillators such as a numerically controlled oscillator are used in ADPLLs.
It should also be noted that the feedback is not limited to a frequency divider. This element can be other elements such as a frequency multiplier, or a mixer. The multiplier will make the VCO output a sub-multiple (rather than a multiple) of the reference frequency. A mixer can translate the VCO frequency by a fixed offset. It may also be a combination of these. An example being a divider following a mixer; this allows the divider to operate at
Oscillator
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CHAPTER 5. COMMON INTEGRATED CIRCUITS
a much lower frequency than the VCO without a loss in xc (θ) there is a function φ(θ) such that the output G(t) loop gain. of Filter
5.3.7 Modeling
x˙ G(t)
Time domain model The equations governing a phase-locked loop with an analog multiplier as the phase detector and linear filter may be derived as follows. Let the input to the phase detector be xr (θr (t)) and the output of the VCO is xc (θc (t)) with phases θr (t) and θc (t) . Functions xc (θ) and xr (θ) describe waveforms of signals. Then the output of the phase detector xm (t) is given by
= Ax + bφ(θr (t) − θc (t)), = c∗ x,
in phase domain is asymptotically equal ( the difference G(t) − xf (t) is small with respect to the frequencies) to the output of the Filter in time domain model. [14] [15] Here function φ(θ) is a phase detector characteristic. Denote by θe (t) the phase difference θe = θr (t) − θc (t). Then the following dynamical system describes PLL behavior
xm (t) = xr (θr (t))xc (θc (t)) the VCO frequency is usually taken as a function of the VCO input g(t) as θ˙c (t) = ωc (t) = ωc + gv g(t) where gv is the sensitivity of the VCO and is expressed in Hz / V; ωc is a free-running frequency of VCO. The loop filter can be described by system of linear differential equations
x˙ ˙θe
= Ax + bφ(θe ), = ωe + gv (c∗ x).
x(0) = x0 ,
where xm (t) is an input of the filter, xf (t) is an output of the filter, A is n -by- n matrix, x ∈ Rn , b ∈ Rn , c ∈ Rn , . x0 ∈ Rn represents an initial state of the filter. The star symbol is a conjugate transpose. Hence the following system describes PLL
x(0) = x0 ,
θe (0) = φ0 .
Here ωe = ωr − ωc ; ωr is a frequency of reference oscillator (we assume that ωr is constant). Example Consider sinusoidal signals
xc (θ(t)) = Ac sin(θc (t)), x˙ = Ax + bxm (t), xf (t) = c∗ x,
x(0) = x0 ,
xr (θr (t)) = Ar cos(θr (t))
and simple one-pole RC circuit as a filter. The timedomain model takes the form
x˙ = −
1 1 x+ Ac Ar sin(θr (t)) cos(θc (t)), RC RC
θ˙c = ωc + gv (c∗ x) PD characteristics for this signals is equal[16] to
x˙ ˙θc
= Ax + bxr (θr (t))xc (θc (t)), = ωc + gv (c∗ x)
x(0) = x0 ,
where φ0 is an initial phase shift.
θc (0) = φ0 . φ(θr − θc ) =
Ac Ar sin(θr − θc ) 2
Hence the phase domain model takes form Phase domain model Consider the input of pll xr (θr (t)) and VCO output xc (θc (t)) are high frequency signals. Then for any piecewise differentiable 2π -periodic functions xr (θ) and
x˙ = −
1 1 Ac Ar x+ sin(θr − θc ), RC RC 2
θ˙c = ωc + gv (c∗ x).
5.3. PHASE-LOCKED LOOP This system of equations is equivalent to the equation of mathematical pendulum
x=
θ˙c − ωc ωr − θ˙e − ωc = , ∗ gv c gv c∗
x˙ =
θ¨c , gv c∗
θr = ωr t + Ψ, θe = θr − θc , θ˙e = θ˙r − θ˙c = ωr − θ˙c ,
135
θo = θi s2 +
Kp Kv RC Kp Kv s RC + RC
This is the form of a classic harmonic oscillator. The denominator can be related to that of a second order system:
s2 + 2sζωn + ωn2 Where • ζ is the damping factor
• ωn is the natural frequency of the loop 1 ¨ 1 A A ω − ω c r c r θe − θ˙e − sin θe = . gv c∗ gv c∗ RC 2RC gv c∗ RC For the one-pole RC filter, √
Linearized phase domain model ωn = Phase locked loops can also be analyzed as control systems by applying the Laplace transform. The loop response can be written as:
Kp Kv F (s) θo = θi s + Kp Kv F (s) Where • θo is the output phase in radians • θi is the input phase in radians • Kp is the phase detector gain in volts per radian • Kv is the VCO gain in radians per volt-second
Kp Kv RC
1 ζ= √ 2 Kp Kv RC The loop natural frequency is a measure of the response time of the loop, and the damping factor is a measure of the overshoot and ringing. Ideally, the natural frequency should be high and the damping factor should be near 0.707 (critical damping). With a single pole filter, it is not possible to control the loop frequency and damping factor independently. For the case of critical damping, 1 2Kp Kv √ ωc = Kp Kv 2 RC =
• F (s) is the loop filter transfer function (dimension- A slightly more effective filter, the lag-lead filter includes less) one pole and one zero. This can be realized with two resistors and one capacitor. The transfer function for this The loop characteristics can be controlled by inserting filter is different types of loop filters. The simplest filter is a onepole RC circuit. The loop transfer function in this case 1 + sCR2 is: F (s) = 1 + sC(R1 + R2 ) F (s) =
1 1 + sRC
The loop response becomes:
This filter has two time constants
τ1 = C(R1 + R2 )
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CHAPTER 5. COMMON INTEGRATED CIRCUITS
τ2 = CR2 Substituting above yields the following natural frequency and damping factor √ ωn = ζ=
Kp Kv τ1
1 ωn τ2 + 2ωn τ1 2
The loop filter components can be calculated independently for a given natural frequency and damping factor
τ1 =
Kp Kv ωn2
τ2 =
2ζ 1 − ωn Kp Kv
Real world loop filter design can be much more complex e.g. using higher order filters to reduce various types or source of phase noise. (See the D Banerjee ref below) Implementing a digital phase-locked loop in software
shifts prop = 1/128; deriv = 64; for it=1:numiterations % Simulate a local oscillator using a 16-bit counter phs = mod(phs + floor(freq/2^16), 2^16); ref = phs < 32768; % Get the next digital value (0 or 1) of the signal to track sig = tracksig(it); % Implement the phase-frequency detector rst = ~(qsig & qref); % Reset the “flip-flop” of the phase-frequency % detector when both signal and reference are high qsig = (qsig | (sig & ~lsig)) & rst; % Trigger signal flip-flop and leading edge of signal qref = (qref | (ref & ~lref)) & rst; % Trigger reference flip-flop on leading edge of reference lref = ref; lsig = sig; % Store these values for next iteration (for edge detection) ersig = qref - qsig; % Compute the error signal (whether frequency should increase or decrease) % Error signal is given by one or the other flip flop signal % Implement a pole-zero filter by proportional and derivative input to frequency filtered_ersig = ersig + (ersig - lersig) * deriv; % Keep error signal for proportional output lersig = ersig; % Integrate VCO frequency using the error signal freq = freq - 2^16 * filtered_ersig * prop; % Frequency is tracked as a fixed-point binary fraction % Store the current VCO frequency vcofreq(1, it) = freq / 2^16; % Store the error signal to show whether signal or reference is higher frequency ervec(1, it) = ersig; end In this example, an array tracksig is assumed to contain a reference signal to be tracked. The oscillator is implemented by a counter, with the most significant bit of the counter indicating the on/off status of the oscillator. This code simulates the two D-type flip-flops that comprise a phase-frequency comparator. When either the reference or signal has a positive edge, the corresponding flip-flop switches high. Once both reference and signal is high, both flip-flops are reset. Which flip-flop is high determines at that instant whether the reference or signal leads the other. The error signal is the difference between these two flip-flop values. The pole-zero filter is implemented by adding the error signal and its derivative to the filtered error signal. This in turn is integrated to find the oscillator frequency.
Digital phase locked loops can be implemented in hardware, using integrated circuits such as a CMOS 4046. However, with microcontrollers becoming faster, it may make sense to implement a phase locked loop in software for applications that do not require locking onto signals in the MHz range or faster, such as precisely controlling motor speeds. Software implementation has several advantages including easy customization of the feedback loop including changing the multiplication or division ratio between the signal being tracked and the output oscillator. Furthermore, a software implementation is useful to understand and experiment with. As an example of a phase-locked loop implemented using a phase frequency detector is presented in MATLAB, as this type of phase detector is robust and easy to implement. This example In practice, one would likely insert other operations into uses integer arithmetic rather than floating point, as such the feedback of this phase-locked loop. For example, an example is likely more useful in practice. if the phase locked loop were to implement a frequency % Initialize variables vcofreq = zeros(1, numiterations); multiplier, the oscillator signal could be divided in freervec = zeros(1, numiterations); % keep track of last quency before it is compared to the reference signal. states of reference, signal, and error signal qsig = 0; qref = 0; lref = 0; lsig = 0; lersig = 0; phs = 0; freq = 0; % Loop filter constants (proportional and derivative) % Currently powers of two to facilitate multiplication by
5.3. PHASE-LOCKED LOOP
5.3.8
See also
• Direct-digital synthesis • Costas loop • Kalman filter • Direct conversion receiver • Circle map - a simple mathematical model of the phase-locked loop showing both mode-locking and chaotic behavior. • Carrier recovery • Delay-locked loop (DLL) • PLL multibit • Shortt-Synchronome clock - slave pendulum phaselocked to master (ca 1921).
5.3.9
References
[1] If the frequency is constant and the initial phase is zero, then the phase of a sinusoid is proportional to time. [2] Christiaan Huygens, Horologium Oscillatorium … (Paris, France: F. Muguet, 1673), pages 18-19. From page 18: extquotedbl … illudque accidit memoratu dignum, … brevi tempore reduceret.” ( … and it is worth mentioning, since with two clocks constructed in this form and which we suspend in like manner, truly the cross beam is assigned two fulcrums [i.e., two pendulum clocks were suspended from the same wooden beam]; the motions of the pendulums thus share the opposite swings between the two [clocks], as the two clocks at no time move even a small distance, and the sound of both can be heard clearly together always: for if the innermost part [of one of the clocks] is disturbed with a little help, it will have been restored in a short time by the clocks themselves.) English translation provided by Ian Bruce’s translation of Horologium Oscillatorium … , pages 16-17. [3] See: • Lord Rayleigh, The Theory of Sound (London, England: Macmillan, 1896), vol. 2. The synchronization of organ pipes in opposed phase is mentioned in §322c, pages 221-222. • Lord Rayleigh (1907) “Acoustical notes — VII,” Philosophical Magazine, 6th series, 13 : 316-333. See “Tuning-forks with slight mutual influence,” pages 322-323.
137
[4] See: • Vincent (1919) “On some experiments in which two neighbouring maintained oscillatory circuits affect a resonating circuit,” Proceedings of the Physical Society of London, 32, pt. 2, 84-91. • W. H. Eccles and J. H. Vincent, British Patent Specifications, 163 : 462 (17 Feb. 1920). [5] E. V. Appleton (1923) “The automatic synchronization of triode oscillators,” Proceedings of the Cambridge Philosophical Society, 21 (Part III): 231-248. Available on-line at: Internet Archive. [6] Henri de Bellescize, “La réception synchrone,” L'Onde Électrique (later: Revue de l'Electricité et de l'Electronique), vol. 11, pages 230-240 (June 1932). [7] See also: French patent no. 635,451 (filed: 6 October 1931; issued: 29 September 1932); and U.S. patent “Synchronizing system,” no. 1,990,428 (filed: 29 September 1932; issued: 5 February 1935). [8] Notes for a University of Guelph course describing the PLL and early history, including an IC PLL tutorial [9] “National Television Systems Committee Video Display Signal IO”. Sxlist.com. Retrieved 2010-10-14. [10] A. B. Grebene, H. R. Camenzind, “Phase Locking As A New Approach For Tuned Integrated Circuits”, ISSCC Digest of Technical Papers, pp. 100-101, Feb. 1969. [11] Roland E. Best (2007). Phase-Locked Loops: Design, Simulation and Applications (6th ed.). McGraw Hill. ISBN 978-0-07-149375-8. [12] M Horowitz, C. Yang, S. Sidiropoulos (1998-01-01). “High-speed electrical signaling: overview and limitations”. IEEE Micro. [13] Typically, the reference sinewave drives a step recovery diode circuit to make this impulse train. The resulting impulse train drives a sample gate. [14] G. A. Leonov, N. V. Kuznetsov, M. V. Yuldashev, R. V. Yuldashev (2011). “Computation of Phase Detector Characteristics in Synchronization SysDoklady Mathematics 84 (1): 586–590. tems”. doi:10.1134/S1064562411040223. [15] N.V. Kuznetsov, G.A. Leonov, M.V. Yuldashev, R.V. Yuldashev (2011). “Analytical methods for computation of phase-detector characteristics and PLL design”. ISSCS 2011 – International Symposium on Signals, Circuits and Systems, Proceedings: 7–10. doi:10.1109/ISSCS.2011.5978639. [16] A. J. Viterbi, Principles of Coherent Communication, McGraw-Hill, New York, 1966
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5.3.10 Further reading
CHAPTER 5. COMMON INTEGRATED CIRCUITS
5.4 Voltage regulator
• Banerjee, Dean (2006), PLL Performance, Simulation and Design Handbook (4th ed.), National Semiconductor. • Best, R. E. (2003), Phase-locked Loops: Design, Simulation and Applications, McGraw-Hill, ISBN 007-141201-8 • de Bellescize, Henri (June 1932), “La réception Synchrone”, L'Onde Electrique 11: 230–240 • Dorf, Richard C. (1993), The Electrical Engineering Handbook, Boca Raton: CRC Press, ISBN 0-84930185-8
A popular three pin +12 V DC voltage regulator IC.
• Egan, William F. (1998), Phase-Lock Basics, John Wiley & Sons. (provides useful Matlab scripts for A voltage regulator is designed to automatically maintain a constant voltage level. A voltage regulator may be simulation) a simple extquotedblfeed-forward extquotedbl design or • Egan, William F. (2000), Frequency Synthesis by may include negative feedback control loops. It may use Phase Lock (2nd ed.), John Wiley and Sons. (pro- an electromechanical mechanism, or electronic components. Depending on the design, it may be used to reguvides useful Matlab scripts for simulation) late one or more AC or DC voltages. • Gardner, Floyd M. (2005), Phaselock Techniques (3rd ed.), Wiley-Interscience, ISBN 978-0-471- Electronic voltage regulators are found in devices such as computer power supplies where they stabilize the DC 43063-6 voltages used by the processor and other elements. In au• Klapper, J.; Frankle, J. T. (1972), Phase-Locked tomobile alternators and central power station generator and Frequency-Feedback Systems, Academic Press. plants, voltage regulators control the output of the plant. In an electric power distribution system, voltage regula(FM Demodulation) tors may be installed at a substation or along distribution • Kundert, Ken (August 2006), Predicting the Phase lines so that all customers receive steady voltage indepenNoise and Jitter of PLL-Based Frequency Synthesiz- dent of how much power is drawn from the line. ers (4g ed.), Designer’s Guide Consulting, Inc. • Liu, Mingliang (February 21, 2006), Build a 1.5-V 5.4.1 Measures of regulator quality 2.4-GHz CMOS PLL, Wireless Net Design Line. An article on designing a standard PLL IC for Bluetooth The output voltage can only be held roughly constant; the applications. regulation is specified by two measurements: • Wolaver, Dan H. (1991), Phase-Locked Loop Circuit Design, Prentice Hall, ISBN 0-13-662743-9 • Signal processing and system aspects of all-digital phase-locked loops (ADPLLs) • Phase-Locked Loop Tutorial, PLL • Temporal-code to rate-code conversion by neuronal phase-locked loops. Neural Comput 10:597-650., 1998
• load regulation is the change in output voltage for a given change in load current (for example: “typically 15 mV, maximum 100 mV for load currents between 5 mA and 1.4 A, at some specified temperature and input voltage”). • line regulation or input regulation is the degree to which output voltage changes with input (supply) voltage changes - as a ratio of output to input change (for example “typically 13 mV/V”), or the output
5.4. VOLTAGE REGULATOR voltage change over the entire specified input voltage range (for example “plus or minus 2% for input voltages between 90 V and 260 V, 50-60 Hz”). Other important parameters are: • Temperature coefficient of the output voltage is the change with temperature (perhaps averaged over a given temperature range). • Initial accuracy of a voltage regulator (or simply “the voltage accuracy”) reflects the error in output voltage for a fixed regulator without taking into account temperature or aging effects on output accuracy. • Dropout voltage is the minimum difference between input voltage and output voltage for which the regulator can still supply the specified current. A low drop-out (LDO) regulator is designed to work well even with an input supply only a volt or so above the output voltage. The input-output differential at which the voltage regulator will no longer maintain regulation is the dropout voltage. Further reduction in input voltage will result in reduced output voltage. This value is dependent on load current and junction temperature.
139 the load transient) or input voltage (called the line transient) occurs. Some regulators will tend to oscillate or have a slow response time which in some cases might lead to undesired results. This value is different from the regulation parameters, as that is the stable situation definition. The transient response shows the behaviour of the regulator on a change. This data is usually provided in the technical documentation of a regulator and is also dependent on output capacitance. • Mirror-image insertion protection means that a regulator is designed for use when a voltage, usually not higher than the maximum input voltage of the regulator, is applied to its output pin while its input terminal is at a low voltage, volt-free or grounded. Some regulators can continuously withstand this situation; others might only manage it for a limited time such as 60 seconds, as usually specified in the datasheet. This situation can occur when a three terminal regulator is incorrectly mounted for example on a PCB, with the output terminal connected to the unregulated DC input and the input connected to the load. Mirror-image insertion protection is also important when a regulator circuit is used in battery charging circuits, when external power fails or is not turned on and the output terminal remains at battery voltage.
• Absolute maximum ratings are defined for regulator components, specifying the continuous and peak output currents that may be used (sometimes inter- 5.4.2 Electronic voltage regulators nally limited), the maximum input voltage, maximum power dissipation at a given temperature, etc. A simple voltage regulator can be made from a resistor in series with a diode (or series of diodes). Due to the • Output noise (thermal white noise) and output logarithmic shape of diode V-I curves, the voltage across dynamic impedance may be specified as graphs the diode changes only slightly due to changes in curversus frequency, while output ripple noise (mains rent drawn or changes in the input. When precise voltage “hum” or switch-mode “hash” noise) may be given control and efficiency are not important, this design may as peak-to-peak or RMS voltages, or in terms of work fine. their spectra. Feedback voltage regulators operate by comparing the • Quiescent current in a regulator circuit is the cur- actual output voltage to some fixed reference voltage. rent drawn internally, not available to the load, nor- Any difference is amplified and used to control the regumally measured as the input current while no load is lation element in such a way as to reduce the voltage error. connected (and hence a source of inefficiency; some This forms a negative feedback control loop; increasing linear regulators are, surprisingly, more efficient at the open-loop gain tends to increase regulation accuracy very low current loads than switch-mode designs be- but reduce stability. (Stability is avoidance of oscillation, or ringing, during step changes.) There will also be a cause of this). trade-off between stability and the speed of the response • Transient response is the reaction of a regulator to changes. If the output voltage is too low (perhaps due when a (sudden) change of the load current (called to input voltage reducing or load current increasing), the
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CHAPTER 5. COMMON INTEGRATED CIRCUITS
regulation element is commanded, up to a point, to produce a higher output voltage–by dropping less of the input voltage (for linear series regulators and buck switching regulators), or to draw input current for longer periods (boost-type switching regulators); if the output voltage is too high, the regulation element will normally be commanded to produce a lower voltage. However, many regulators have over-current protection, so that they will entirely stop sourcing current (or limit the current in some way) if the output current is too high, and some regulators may also shut down if the input voltage is outside a given range (see also: crowbar circuits). Graph of voltage output on a time scale.
5.4.3 Electromechanical regulators electromagnet. The magnetic field produced by the current attracts a moving ferrous core held back under spring tension or gravitational pull. As voltage increases, so does the current, strengthening the magnetic field produced by the coil and pulling the core towards the field. The magnet is physically connected to a mechanical power switch, which opens as the magnet moves into the field. As voltage decreases, so does the current, releasing spring tension or the weight of the core and causing it to retract. This closes the switch and allows the power to flow once more.
Circuit design for a simple electromechanical voltage regulator.
If the mechanical regulator design is sensitive to small voltage fluctuations, the motion of the solenoid core can be used to move a selector switch across a range of resistances or transformer windings to gradually step the output voltage up or down, or to rotate the position of a moving-coil AC regulator. Early automobile generators and alternators had a mechanical voltage regulator using one, two, or three relays and various resistors to stabilize the generator’s output at slightly more than 6 or 12 V, independent of the engine's rpm or the varying load on the vehicle’s electrical system. Essentially, the relay(s) employed pulse width modulation to regulate the output of the generator, controlling the field current reaching the generator (or alternator) and in this way controlling the output voltage produced.
The regulators used for DC generators (but not alternators) also disconnect the generator when it was not producing electricity, thereby preventing the battery from A voltage stabilizer using electromechanical relays for switching. discharging back into the generator and attempting to run it as a motor. The rectifier diodes in an alternator autoIn electromechanical regulators, voltage regulation is eas- matically perform this function so that a specific relay is ily accomplished by coiling the sensing wire to make an not required; this appreciably simplified the regulator de-
5.4. VOLTAGE REGULATOR
141
sign.
voltage to a predetermined setpoint. When two or more More modern designs now use solid state technology generators are powering the same system (parallel opera(transistors) to perform the same function that the relays tion) the AVR receives information from more generators to match all output. perform in electromechanical regulators. Electromechanical regulators are used for mains voltage stabilisation — see AC voltage stabilizers below. 5.4.5
5.4.4
Automatic voltage regulator
AC voltage stabilizers
Coil-rotation AC voltage regulator
Basic design principle and circuit diagram for the rotating-coil AC voltage regulator.
This is an older type of regulator used in the 1920s that uses the principle of a fixed-position field coil and a second field coil that can be rotated on an axis in parallel with the fixed coil, similar to a variocoupler. Voltage regulator for generators.
To control the output of generators (as seen in ships and power stations, or on oil rigs, greenhouses and emergency power systems) automatic voltage regulators are used. This is an active system. While the basic principle is the same, the system itself is more complex. An automatic voltage regulator (or AVR for short) consist of several components such as diodes, capacitors, resistors and potentiometers or even microcontrollers, all placed on a circuit board. This is then mounted near the generator and connected with several wires to measure and adjust the generator. How an AVR works: In the first place the AVR monitors the output voltage and controls the input voltage for the exciter of the generator. By increasing or decreasing the generator control voltage, the output voltage of the generator increases or decreases accordingly. The AVR calculates how much voltage has to be sent to the exciter numerous times a second, therefore stabilizing the output
When the movable coil is positioned perpendicular to the fixed coil, the magnetic forces acting on the movable coil balance each other out and voltage output is unchanged. Rotating the coil in one direction or the other away from the center position will increase or decrease voltage in the secondary movable coil. This type of regulator can be automated via a servo control mechanism to advance the movable coil position in order to provide voltage increase or decrease. A braking mechanism or high ratio gearing is used to hold the rotating coil in place against the powerful magnetic forces acting on the moving coil. Electromechanical Electromechanical regulators called voltage stabilizers or tap-changers, have also been used to regulate the voltage on AC power distribution lines. These regulators operate by using a servomechanism to select the appropriate tap
142
CHAPTER 5. COMMON INTEGRATED CIRCUITS urating transformer used as a voltage regulator. These transformers use a tank circuit composed of a highvoltage resonant winding and a capacitor to produce a nearly constant average output voltage with a varying input current or varying load. The circuit has a primary on one side of a magnet shunt and the tuned circuit coil and secondary on the other side. The regulation is due to magnetic saturation in the section around the secondary. The ferroresonant approach is attractive due to its lack of active components, relying on the square loop saturation characteristics of the tank circuit to absorb variations in average input voltage. Saturating transformers provide a simple rugged method to stabilize an AC power supply.
Magnetic mains regulator
on an autotransformer with multiple taps, or by moving the wiper on a continuously variable auto transfomer. If the output voltage is not in the acceptable range, the servomechanism switches the tap, changing the turns ratio of the transformer, to move the secondary voltage into the acceptable region. The controls provide a dead band wherein the controller will not act, preventing the controller from constantly adjusting the voltage (“hunting”) as it varies by an acceptably small amount. PWM Static Voltage Regulator This is the latest technology of voltage regulation to provide real-time control of voltage fluctuation, sag, surge and also to control other power quality issues such as spikes & EMI/RFI electrical noises. This uses an IGBT regulator engine generating PWM AC voltage at high switching frequency. This AC PWM wave is superimposed on the main incoming wave through a buck-boost transformer, to provide precisely regulated AC voltage. The regulation in this technology is instantaneous, thus making it suitable for electronic machines which need precise regulated power. Constant-voltage transformer
Older designs of ferroresonant transformers had an output with high harmonic content, leading to a distorted output waveform. Modern devices are used to construct a perfect sine wave. The ferroresonant action is a flux limiter rather than a voltage regulator, but with a fixed supply frequency it can maintain an almost constant average output voltage even as the input voltage varies widely. The ferroresonant transformers, which are also known as Constant Voltage Transformers (CVTs) or ferros, are also good surge suppressors, as they provide high isolation and inherent short-circuit protection. A ferroresonant transformer can operate with an input voltage range ±40% or more of the nominal voltage. Output power factor remains in the range of 0.96 or higher from half to full load. Because it regenerates an output voltage waveform, output distortion, which is typically less than 4%, is independent of any input voltage distortion, including notching. Efficiency at full load is typically in the range of 89% to 93%. However, at low loads, efficiency can drop below 60%. The current-limiting capability also becomes a handicap when a CVT is used in an application with moderate to high inrush current like motors, transformers or magnets. In this case, the CVT has to be sized to accommodate the peak current, thus forcing it to run at low loads and poor efficiency. Minimum maintenance is required, as transformers and capacitors can be very reliable. Some units have included redundant capacitors to allow several capacitors to fail between inspections without any noticeable effect on the device’s performance.
The ferroresonant transformer, ferroresonant regu- Output voltage varies about 1.2% for every 1% change lator or constant-voltage transformer is a type of sat- in supply frequency. For example, a 2 Hz change in gen-
5.4. VOLTAGE REGULATOR
143
erator frequency, which is very large, results in an output to dissipate the excess energy. The power supply is devoltage change of only 4%, which has little effect for most signed to only supply a maximum amount of current that loads. is within the safe operating capability of the shunt reguIt accepts 100% single-phase switch-mode power supply lating device. loading without any requirement for derating, including If the stabilizer must provide more power, the shunt regall neutral components. ulator output is only used to provide the standard voltage Input current distortion remains less than 8% THD even reference for the electronic device, known as the voltage when supplying nonlinear loads with more than 100% stabilizer. The voltage stabilizer is the electronic device, able to deliver much larger currents on demand. current THD. Drawbacks of CVTs are their larger size, audible humming sound, and the high heat generation caused by sat- 5.4.7 Active regulators uration. Active regulators employ at least one active (amplifying) component such as a transistor or operational amplifier. Commercial use Shunt regulators are often (but not always) passive and simple, but always inefficient because they (essentially) Voltage regulators or stabilizers are used to compensate dump the excess current not needed by the load. When for voltage fluctuations in mains power. Large regula- more power must be supplied, more sophisticated circuits tors may be permanently installed on distribution lines. are used. In general, these active regulators can be diSmall portable regulators may be plugged in between sen- vided into several classes: sitive equipment and a wall outlet. Automatic voltage regulators are used on generator sets on ships, in emer• Linear series regulators gency power supplies, on oil rigs, etc. to stabilize fluctuations in power demand. For example, when a large • Switching regulators machine is turned on, the demand for power is suddenly a lot higher. The voltage regulator compensates for the • SCR regulators change in load. Commercial voltage regulators normally operate on a range of voltages, for example 150–240 V or 90–280 V. Servo stabilizers are also manufactured and Linear regulators used widely in spite of the fact that they are obsolete and Main article: Linear regulator use out-dated technology. Voltage regulators are used in devices like air conditioners, refrigerators, televisions etc. in order to protect them from fluctuating input voltage. The major problem faced is the use of relays in voltage regulators. Relays create sparks which result in faults in the product.
5.4.6
DC voltage stabilizers
Many simple DC power supplies regulate the voltage using either series or shunt regulators, but most apply a voltage reference using a shunt regulator such as a Zener diode, avalanche breakdown diode, or voltage regulator tube. Each of these devices begins conducting at a specified voltage and will conduct as much current as required to hold its terminal voltage to that specified voltage by diverting excess current from a non-ideal power source to ground, often through a relatively low-value resistor
Linear regulators are based on devices that operate in their linear region (in contrast, a switching regulator is based on a device forced to act as an on/off switch). In the past, one or more vacuum tubes were commonly used as the variable resistance. Modern designs use one or more transistors instead, perhaps within an Integrated Circuit. Linear designs have the advantage of very “clean” output with little noise introduced into their DC output, but are most often much less efficient and unable to step-up or invert the input voltage like switched supplies. All linear regulators require a higher input than the output. If the input voltage approaches the desired output voltage, the regulator will “drop out”. The input to output voltage differential at which this occurs is known as the regulator’s drop-out voltage. Special “low drop-out” regulators allow an input voltage that can be much lower, often approaching or equal to that of the desired output.
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CHAPTER 5. COMMON INTEGRATED CIRCUITS
Entire linear regulators are available as integrated circuits. These chips come in either fixed or adjustable voltage types.
• Switching regulators are required when the only power supply is a DC voltage, and a higher output voltage is required.
Switching regulators
• At high levels of power (above a few watts), switching regulators are cheaper (for example, the cost of removing heat generated is less).
Main article: Switched-mode power supply Switching regulators rapidly switch a series device on and off. The duty cycle of the switch sets how much charge is transferred to the load. This is controlled by a similar feedback mechanism as in a linear regulator. Because the series element is either fully conducting, or switched off, it dissipates almost no power; this is what gives the switching design its efficiency. Switching regulators are also able to generate output voltages which are higher than the input, or of opposite polarity — something not possible with a linear design.
SCR regulators Regulators powered from AC power circuits can use silicon controlled rectifiers (SCRs) as the series device. Whenever the output voltage is below the desired value, the SCR is triggered, allowing electricity to flow into the load until the AC mains voltage passes through zero (ending the half cycle). SCR regulators have the advantages of being both very efficient and very simple, but because they can not terminate an on-going half cycle of conduction, they are not capable of very accurate voltage regulation in response to rapidly changing loads. An alternative is the SCR shunt regulator which uses the regulator output as a trigger, both series and shunt designs are noisy, but powerful, as the device has a low on resistance.
Like linear regulators, nearly complete switching regulators are also available as integrated circuits. Unlike linear regulators, these usually require one external component: an inductor that acts as the energy storage element. (Large-valued inductors tend to be physically large relative to almost all other kinds of componentry, so they are rarely fabricated within integrated circuits and IC regula- Combination (hybrid) regulators tors — with some exceptions.[1][2] ) Many power supplies use more than one regulating method in series. For example, the output from a switchComparing linear vs. switching regulators ing regulator can be further regulated by a linear regulator. The switching regulator accepts a wide range of inThe two types of regulators have their different advan- put voltages and efficiently generates a (somewhat noisy) tages: voltage slightly above the ultimately desired output. That is followed by a linear regulator that generates exactly the • Linear regulators are best when low output noise desired voltage and eliminates nearly all the noise generated by the switching regulator. Other designs may use (and low RFI radiated noise) is required an SCR regulator as the “pre-regulator”, followed by an• Linear regulators are best when a fast response to other type of regulator. An efficient way of creating a input and output disturbances is required. variable-voltage, accurate output power supply is to com• At low levels of power, linear regulators are cheaper bine a multi-tapped transformer with an adjustable linear post-regulator. and occupy less printed circuit board space. • Switching regulators are best when power efficiency is critical (such as in portable computers), except that linear regulators are more efficient in a small number of cases (such as a 5 V microprocessor often in “sleep” mode fed from a 6 V battery, if the complexity of the switching circuit and the junction capacitance charging current means a high quiescent current in the switching regulator).
5.4.8
Example linear regulators
Transistor regulator In the simplest case a common collector transistor (emitter follower) is used with the base of the regulating transistor connected directly to the voltage reference:
5.4. VOLTAGE REGULATOR
145 Regulator with an operational amplifier
U
CE
+U Out
+U In
Rv
Q
The stability of the output voltage can be significantly increased by using an operational amplifier:
U
BE
U
Out
U
Z
R
L
U
CE
+U In
+U Out
Rv
Dz
+
_ U
Z
Dz
OA
R1
Q U
BE
R2
U
Out
R
L
R3
A simple transistor regulator will provide a relatively constant output voltage, Uout, for changes in the voltage of the power source, Uin, and for changes in load, RL, provided that Uin exceeds Uout by a sufficient margin, and that the power handling capacity of the transistor is not exceeded.
In this case, the operational amplifier drives the transistor with more current if the voltage at its inverting input drops below the output of the voltage reference at the non-inverting input. Using the voltage divider (R1, R2 and R3) allows choice of the arbitrary output voltage beThe output voltage of the stabilizer is equal to the zener tween U and Uᵢ . diode voltage less the base–emitter voltage of the transistor, UZ − UBE, where UBE is usually about 0.7 V for a silicon transistor, depending on the load current. If the 5.4.9 See also output voltage drops for any external reason, such as an increase in the current drawn by the load (causing a de• Constant current regulator crease in the Collector-Emitter junction voltage to ob• DC-to-DC converter serve KVL), the transistor’s base–emitter voltage (UBE) increases, turning the transistor on further and delivering • Third brush dynamo more current to increase the load voltage again. • Voltage regulator module Rv provides a bias current for both the zener diode and the transistor. The current in the diode is minimum when the load current is maximum. The circuit designer must choose a minimum voltage that can be tolerated 5.4.10 References across Rv, bearing in mind that the higher this voltage [1] Texas Instruments LM2825 Integrated Power Supply 1A requirement is, the higher the required input voltage, DC-DC Converter, retrieved 2010-09-19 Uin, and hence the lower the efficiency of the regulator. On the other hand, lower values of Rv lead to higher [2] Linear Technology μModule Regulators, retrieved 201103-08 power dissipation in the diode and to inferior regulator characteristics.[3] [3] Alley, Charles; Atwood, Kenneth (1973). Electronic EnRv =
VRmin IDmin +ILmax /(hF E +1)
gineering. New York and London: John Wiley & Sons. p. 534. ISBN 0-471-02450-3.
where VR min is the minimum voltage to be maintained across Rv ID min is the minimum current to be maintained through 5.4.11 Further reading the zener diode • Linear & Switching Voltage Regulator HandIL max is the maximum design load current book; ON Semiconductor; 118 pages; 2002; hFE is the forward current gain of the transistor, ICollecHB206/D.(Free PDF download) tor / IBase[3]
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CHAPTER 5. COMMON INTEGRATED CIRCUITS
5.5 Comparator For other uses, see Comparator (disambiguation).
5.5.2
V V
Op-amp voltage comparator
1 In electronics, a comparator is a device that compares two voltages or currents and outputs a digital signal indi2 cating which is larger. It has two analog input terminals V+ and V− and one binary digital output Vo . The output is ideally A simple op-amp comparator { 1, if V+ > V− Vo = 0, if V+ < V− A comparator consists of a specialized high-gain differential amplifier. They are commonly used in devices that measure and digitize analog signals, such as analog-to-digital converters (ADCs), as well as relaxation oscillators.
5.5.1 Differential Voltage The differential voltages must stay within the limits specified by the manufacturer. Early integrated comparators, like the LM111 family, and certain high-speed comparators like the LM119 family, require differential voltage ranges substantially lower than the power supply voltages (±15 V vs. 36 V).[1] Rail-to-rail comparators allow any differential voltages within the power supply range. When powered from a bipolar (dual rail) supply, VS− ≤ V+ , V− ≤ VS+ or, when powered from a unipolar TTL/CMOS power supply: 0 ≤ V+ , V− ≤ Vcc Specific rail-to-rail comparators with p-n-p input transistors, like the LM139 family, allow input potential to drop 0.3 volts below the negative supply rail, but do not allow it to rise above the positive rail.[2] Specific ultra-fast comparators, like the LMH7322, allow input signal to swing below the negative rail and above the positive rail, although by a narrow margin of only 0.2 V.[3] Differential input voltage (the voltage between two inputs) of a modern rail-to-rail comparator is usually limited only by the full swing of power supply.
Vout
An operational amplifier (op-amp) has a well balanced difference input and a very high gain. This parallels the characteristics of comparators and can be substituted in applications with low-performance requirements.[4] In theory, a standard op-amp operating in open-loop configuration (without negative feedback) may be used as a low-performance comparator. When the non-inverting input (V+) is at a higher voltage than the inverting input (V-), the high gain of the op-amp causes the output to saturate at the highest positive voltage it can output. When the non-inverting input (V+) drops below the inverting input (V-), the output saturates at the most negative voltage it can output. The op-amp’s output voltage is limited by the supply voltage. An op-amp operating in a linear mode with negative feedback, using a balanced, split-voltage power supply, (powered by ± VS) has its transfer function typically written as: Vout = Ao (V1 −V2 ) . However, this equation may not be applicable to a comparator circuit which is non-linear and operates open-loop (no negative feedback) In practice, using an operational amplifier as a comparator presents several disadvantages as compared to using a dedicated comparator:[5] 1. Op-amps are designed to operate in the linear mode with negative feedback. Hence, an op-amp typically has a lengthy recovery time from saturation. Almost all op-amps have an internal compensation capacitor which imposes slew rate limitations for high frequency signals. Consequently an op-amp makes a sloppy comparator with propagation delays that can be as long as tens of microseconds. 2. Since op-amps do not have any internal hysteresis, an external hysteresis network is always necessary for slow moving input signals. 3. The quiescent current specification of an op-amp is valid only when the feedback is active. Some op-
5.5. COMPARATOR
147
amps show an increased quiescent current when the analog to digital converter). If there is a fixed voltage inputs are not equal. source from, for example, a DC adjustable device in the signal path, a comparator is just the equivalent of a cas4. A comparator is designed to produce well lim- cade of amplifiers. When the voltages are nearly equal, ited output voltages that easily interface with digi- the output voltage will not fall into one of the logic levtal logic. Compatibility with digital logic must be els, thus analog signals will enter the digital domain with verified while using an op-amp as a comparator. unpredictable results. To make this range as small as possible, the amplifier cascade is high gain. The circuit con5. Some multiple-section op-amps may exhibit exsists of mainly Bipolar transistors. For very high frequentreme channel-channel interaction when used as cies, the input impedance of the stages is low. This recomparators. duces the saturation of the slow, large P-N junction bipo6. Many op-amps have back to back diodes between lar transistors that would otherwise lead to long recovery their inputs. Op-amp inputs usually follow each times. Fast small Schottky diodes, like those found in biother so this is fine. But comparator inputs are not nary logic designs, improve the performance significantly usually the same. The diodes can cause unexpected though the performance still lags that of circuits with amplifiers using analog signals. Slew rate has no meaning current through inputs. for these devices. For applications in flash ADCs the distributed signal across eight ports matches the voltage and current gain after each amplifier, and resistors then be5.5.3 Working have as level-shifters. The LM339 accomplishes this with an open collector output. When the inverting input is at a higher voltage than the non inverting input, the output of the comparator connects to the negative power supply. When the non inverting input is higher than the inverting input, the output is 'floating' (has a very high impedance to ground). The gain of op amp as comparator is given by this equation V(out)=V(in)*A With a pull-up resistor and a 0 to +5 V power supply, the output takes on the voltages 0 or +5 and can interface with TTL logic: Vout ≤ VCC when V+ ≥ V− else 0 .
5.5.4 Key specifications While it is easy to understand the basic task of a comparator, that is, comparing two voltages or currents, several A dedicated voltage comparator will generally be faster parameters must be considered while selecting a suitable than a general-purpose operational amplifier pressed into comparator: service as a comparator. A dedicated voltage comparator may also contain additional features such as an accurate, Speed and power internal voltage reference, an adjustable hysteresis and a clock gated input. While in general comparators are “fast,” their circuits Several voltage comparator ICs
A dedicated voltage comparator chip such as LM339 is designed to interface with a digital logic interface (to a TTL or a CMOS). The output is a binary state often used to interface real world signals to digital circuitry (see
are not immune to the classic speed-power tradeoff. High speed comparators use transistors with larger aspect ratios and hence also consume more power.[6] Depending on the application, select either a comparator
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CHAPTER 5. COMMON INTEGRATED CIRCUITS
with high speed or one that saves power. For exam- Output type ple, nano-powered comparators in space-saving chipscale packages (UCSP), DFN or SC70 packages such as MAX9027, LTC1540, LPV7215, MAX9060 and MCP6541 are ideal for ultra-low-power, portable applications. Likewise if a comparator is needed to implement a relaxation oscillator circuit to create a high speed clock signal then comparators having few nano seconds of propagation delay may be suitable. ADCMP572 (CML output), LMH7220 (LVDS Output), MAX999 (CMOS output / TTL output), LT1719 (CMOS output / TTL output), MAX9010 (TTL output), and MAX9601 (PECL output) are examples of some good high speed comparators.
Hysteresis A comparator normally changes its output state when the voltage between its inputs crosses through approximately zero volts. Small voltage fluctuations due to noise, always present on the inputs, can cause undesirable rapid changes between the two output states when the input voltage difference is near zero volts. To prevent this output oscillation, a small hysteresis of a few millivolts is integrated into many modern comparators.[7] For example, the LTC6702, MAX9021 and MAX9031 have internal hysteresis desensitizing them from input noise. In place of one switching point, hysteresis introduces two: one for rising voltages, and one for falling voltages. The difference between the higher-level trip value (VTRIP+) and the lower-level trip value (VTRIP-) equals the hysteresis voltage (VHYST). If the comparator does not have internal hysteresis or if the input noise is greater than the internal hysteresis then an external hysteresis network can be built using positive feedback from the output to the non-inverting input of the comparator. The resulting Schmitt trigger circuit gives additional noise immunity and a cleaner output signal. Some comparators such as LMP7300, LTC1540, MAX931, MAX971 and ADCMP341 also provide the hysteresis control through a separate hysteresis pin. These comparators make it possible to add a programmable hysteresis without feedback or complicated equations. Using a dedicated hysteresis pin is also convenient if the source impedance is high since the inputs are isolated from the hysteresis network.[8] When hysteresis is added then a comparator cannot resolve signals within the hysteresis band.
A Low Power CMOS Clocked Comparator
Because comparators have only two output states, their outputs are near zero or near the supply voltage. Bipolar rail-to-rail comparators have a common-emitter output that produces a small voltage drop between the output and each rail. That drop is equal to the collector-to-emitter voltage of a saturated transistor. When output currents are light, output voltages of CMOS rail-to-rail comparators, which rely on a saturated MOSFET, range closer to the rails than their bipolar counterparts.[9] On the basis of outputs, comparators can also be classified as open drain or push–pull. Comparators with an open-drain output stage use an external pull up resistor to a positive supply that defines the logic high level. Open drain comparators are more suitable for mixed-voltage system design. Since the output is high impedance for logic level high, open drain comparators can also be used to connect multiple comparators on to a single bus. Push pull output does not need a pull up resistor and can also source current unlike an open drain output. Internal reference The most frequent application for comparators is the comparison between a voltage and a stable reference. Most comparator manufacturers also offer comparators in which a reference voltage is integrated on to the chip. Combining the reference and comparator in one chip not only saves space, but also draws less supply current than a comparator with an external reference.[9]
5.5. COMPARATOR ICs with wide range of references are available such as MAX9062(200 mV reference), LT6700(400 mV reference), ADCMP350 (600 mV reference), MAX9025 (1.236 V reference), MAX9040 (2.048 V reference), TLV3012 (1.24 V reference) and TSM109 (2.5 V reference). Continuous versus clocked A continuous comparator will output either a “1” or a “0” any time a high or low signal is applied to its input and will change quickly when the inputs are updated. However, many applications only require comparator outputs at certain instances, such as in A/D converters and memory. By only strobing a comparator at certain intervals, higher accuracy and lower power can be achieved with a clocked (or dynamic) comparator structure, also called a latched comparator. Often latched comparators employ strong positive feedback for a “regeneration phase” when a clock is high, and have a “reset phase” when the clock is low.[10] This is in contrast to a continuous comparator, which can only employ weak positive feedback since there is no reset period.
5.5.5
Applications
Main article: Comparator applications
149 When using a comparator as a null detector, there are limits as to the accuracy of the zero value measurable. Zero output is given when the magnitude of the difference in the voltages multiplied by the gain of the amplifier is less than the voltage limits. For example, if the gain of the amplifier is 106 , and the voltage limits are ±6 V, then no output will be given if the difference in the voltages is less than 6 μV. One could refer to this as a sort of uncertainty in the measurement.[11] Zero-crossing detectors For this type of detector, a comparator detects each time an ac pulse changes polarity. The output of the comparator changes state each time the pulse changes its polarity, that is the output is HI (high) for a positive pulse and LO (low) for a negative pulse squares the input signal.[12] Relaxation oscillator A comparator can be used to build a relaxation oscillator. It uses both positive and negative feedback. The positive feedback is a Schmitt trigger configuration. Alone, the trigger is a bistable multivibrator. However, the slow negative feedback added to the trigger by the RC circuit causes the circuit to oscillate automatically. That is, the addition of the RC circuit turns the hysteretic bistable multivibrator into an astable multivibrator.[13]
Null detectors
Level shifter
A null detector is one that functions to identify when a given value is zero. Comparators can be a type of amplifier distinctively for null comparison measurements. It is the equivalent to a very high gain amplifier with wellbalanced inputs and controlled output limits. The circuit compares the two input voltages, determining the larger. The inputs are an unknown voltage and a reference voltage, usually referred to as vᵤ and vᵣ. A reference voltage is generally on the non-inverting input (+), while vᵤ is usually on the inverting input (−). (A circuit diagram would display the inputs according to their sign with respect to the output when a particular input is greater than the other.) The output is either positive or negative, for example ±12 V. In this case, the idea is to detect when there is no difference between in the input voltages. This gives the identity of the unknown voltage since the reference voltage is known.
This circuit requires only a single comparator with an open-drain output as in the LM393, TLV3011 or MAX9028. The circuit provides great flexibility in choosing the voltages to be translated by using a suitable pull up voltage. It also allows the translation of bipolar ±5 V logic to unipolar 3 V logic by using a comparator like the MAX972.[9] Analog-to-digital converters When a comparator performs the function of telling if an input voltage is above or below a given threshold, it is essentially performing a 1-bit quantization. This function is used in nearly all analog to digital converters (such as flash, pipeline, successive approximation, delta-sigma modulation, folding, interpolating, dual-slope and others)
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CHAPTER 5. COMMON INTEGRATED CIRCUITS
in combination with other devices to achieve a multi-bit quantization.[14]
[8] AN3616, Maxim Integrated Products, Adding Extra Hysteresis to Comparators.
Window detectors
[9] AN886, Maxim Integrated Products, Selecting the Right Comparator.
Comparators can also be used as window detectors. In a window detector, a comparator used to compare two voltages and determine whether a given input voltage is under voltage or over voltage.
5.5.6 See also • Zero crossing threshold detector • Digital comparator • Current comparator • Constant fraction discriminator • Flash ADC • Sorting network
[10] Pedro M. Figueiredo, João C. Vital (2009). Offset Reduction Techniques in High-Speed Analog-to-Digital Converters: Analysis, Design and Tradeoffs. Springer. pp. 54–62. ISBN 978-1-4020-9715-7. [11] Malmstadt, Howard V.; Enke, Christie G.; Crouch, Stanley R. (January 1981), Electronics and Instrumentation for Scientists, The Benjamin/Cummings Publishing Co, pp. 108–110, ISBN 0-8053-6917-1 [12] Electronics and Instrumentation for Scientists. Malmstadt, Enke, and Crouch, The Benjamin/Cummings Publishing Co., In., 1981, p.230. [13] Paul Horowitz and Winfield Hill: The Art of Electronics, Cambridge University Press, Second edition, Cambridge 1989, pp.284–285. [14] Phillip Allen and Douglas Holberg: CMOS Analog Circuit Design, Oxford University Press, Second edition, Oxford 2002.
This article incorporates public domain material from the General Services Administration document “Federal 5.5.8 External links Standard 1037C”. • IC Comparator reference page at home.cogeco.ca
5.5.7 References [1] LM111/LM211/LM311 datasheet. Texas Instruments. August 2003. Retrieved 2014-07-02. [2] LM139/LM239/LM339/LM2901/LM3302 datasheet. Texas Instruments. August 2012. Retrieved 2014-07-02. [3] LMH7322 datasheet. Texas Instruments. March 2013. Retrieved 2014-07-02. [4] Malmstadt, Enke and Crouch, Electronics and Instrumentation for Scientists, The Benjamin/Cummings Publishing Company, Inc., 1981, ISBN 0-8053-6917-1, Chapter 5. [5] Ron Mancini, extquotedblDesigning with comparators,” EDN, March 29, 2001. [6] Rogenmoser, R.; Kaeslin, H, “The impact of transistor sizing on power efficiency in submicron CMOS circuits,” Solid-State Circuits, IEEE Journal of Volume 32, Issue 7, Jul 1997 Page(s):1142–1145. [7] Ron Mancini, extquotedblAdding Hysteresis to comparators,” EDN, May 3, 2001.
• Comparator tutorial video with example circuits • A Java based resistor value search tool for analysing an inverting comparator circuit with hysteresis
Chapter 6
Sensors 6.1 Thermistor
called a positive temperature coefficient (PTC) thermistor, or posistor. If k is negative, the resistance decreases with increasing temperature, and the device is called a negative temperature coefficient (NTC) thermistor. Resistors that are not thermistors are designed to have a k as close to 0 as possible, so that their resistance remains nearly constant over a wide temperature range.
A thermistor is a type of resistor whose resistance varies significantly with temperature, more so than in standard resistors. The word is a portmanteau of thermal and resistor. Thermistors are widely used as inrush current limiters, temperature sensors, self-resetting overcurrent protectors, and self-regulating heating elements. Instead of the temperature coefficient k, sometimes the Thermistors differ from resistance temperature detectors temperature coefficient of resistance αT (alpha sub T) is [2] (RTDs) in that the material used in a thermistor is gen- used. It is defined as erally a ceramic or polymer, while RTDs use pure metals. The temperature response is also different; RTDs 1 dR αT = . are useful over larger temperature ranges, while thermisR(T ) dT tors typically achieve a higher precision within a limited This αT coefficient should not be confused with the a temperature range, typically −90 °C to 130 °C.[1] parameter below.
6.1.1
Basic operation
6.1.2 Steinhart–Hart equation
Assuming, as a first-order approximation, that the relationship between resistance and temperature is linear, In practice, the linear approximation (above) works only over a small temperature range. For accurate temperature then: measurements, the resistance/temperature curve of the device must be described in more detail. The Steinhart– Hart equation is a widely used third-order approximation: ∆R = k∆T where
1 = a + b ln(R) + c (ln(R))3 T where a, b and c are called the Steinhart–Hart parameters, and must be specified for each device. T is the temperature in kelvin and R is the resistance in ohms. To give resistance as a function of temperature, the above can be rearranged into:
∆R ∆T k Thermistors can be classified into two types, depending on the classification of k . If k is positive, the resistance increases with increasing temperature, and the device is
151
y
R = e(x− 2 )
1 3
1
−(x+ y2 ) 3
152
CHAPTER 6. SENSORS
6.1.4
where y=
a− T1 c
and x =
√( ) b 3 3c
+
y2 4
The error in the Steinhart–Hart equation is generally less than 0.02 °C in the measurement of temperature over a 200 °C range.[3] As an example, typical values for a thermistor with a resistance of 3000 Ω at room temperature (25 °C = 298.15 K) are: a = 1.40 × 10−3 b = 2.37 × 10−4 c = 9.90 × 10−8
6.1.3 B or β parameter equation
Conduction model
NTC Many NTC thermistors are made from a pressed disc, rod, plate, bead or cast chip of a semiconductor such as a sintered metal oxide. They work because raising the temperature of a semiconductor increases the number of active charge carriers - it promotes them into the conduction band. The more charge carriers that are available, the more current a material can conduct. In certain materials like ferric oxide (Fe2 O3 ) with titanium (Ti) doping a n-type semiconductor is formed and the charge carriers are electrons. In materials such as nickel oxide (NiO) with lithium (Li) doping a p-type semiconductor is created where holes are the charge carriers.[4] This is described in the formula:
NTC thermistors can also be characterised with the B (or I =n·A·v·e β) parameter equation, which is essentially the Steinhart– Hart equation with a = (1/T0 ) − (1/B) ln(R0 ) , b = I = electric current (amperes) 1/B and c = 0 , n = density of charge carriers (count/m³) A = cross-sectional area of the material (m²) ( ) v = velocity of charge carriers (m/s) 1 1 1 R = + ln e = charge of an electron ( e = 1.602 × 10−19 coulomb) T T0 B R0 Where the temperatures are in kelvin and R0 is the resis- Over large changes in temperature, calibration is nectance at temperature T 0 (25 °C = 298.15 K). Solving for essary. Over small changes in temperature, if the right semiconductor is used, the resistance of the material is R yields: linearly proportional to the temperature. There are many different semiconducting thermistors with a range from −B( T1 − T1 ) about 0.01 kelvin to 2,000 kelvins (−273.14 °C to 1,700 0 R = R0 e °C). or, alternatively, PTC R = r∞ eB/T where r∞ = R0 e−B/T0 . This can be solved for the temperature:
T =
B ln (R/r∞ )
The B-parameter equation can also be written as ln R = B/T + ln r∞ . This can be used to convert the function of resistance vs. temperature of a thermistor into a linear function of ln R vs. 1/T . The average slope of this function will then yield an estimate of the value of the B parameter.
Most PTC thermistors are of the “switching” type, which means that their resistance rises suddenly at a certain critical temperature. The devices are made of a doped polycrystalline ceramic containing barium titanate (BaTiO3 ) and other compounds. The dielectric constant of this ferroelectric material varies with temperature. Below the Curie point temperature, the high dielectric constant prevents the formation of potential barriers between the crystal grains, leading to a low resistance. In this region the device has a small negative temperature coefficient. At the Curie point temperature, the dielectric constant drops sufficiently to allow the formation of potential barriers at the grain boundaries, and the resistance increases
6.1. THERMISTOR
153
sharply. At even higher temperatures, the material reverts heat energy is transferred to the surrounding environto NTC behaviour. ment. The rate of transfer is well described by Newton’s Another type of thermistor is a silistor, a thermally sen- law of cooling: sitive silicon resistor. Silistors employ silicon as the semiconductive component material. In contrary to the “switching” type thermistor, silistors have an almost linear resistance-temperature characteristic.[5]
PT = K(T (R) − T0 )
The degaussing coils in many CRT monitors were controlled by thermistors bonded to a small heating element. The thermistor would be connected in series with the coil across the AC input, with the heater also directly connected to the AC input. When cold the thermistor would allow a large current to flow through but would be quickly heated by the heating element and the current would trail to zero. This would degauss the screen every time the power is removed for long enough for the device to cool.
where T(R) is the temperature of the thermistor as a function of its resistance R, T0 is the temperature of the surroundings, and K is the dissipation constant, usually expressed in units of milliwatts per degree Celsius. At equilibrium, the two rates must be equal.
Another device similar in function to PTC thermistor is the polymer PTC, which is sold under brand names such as extquotedblPolyswitch extquotedbl “Semifuse”, and “Multifuse”. This consists of a slice of plastic with carbon grains embedded in it. When the plastic is cool, the carbon grains are all in contact with each other, forming a conductive path through the device. When the plastic heats up, it expands, forcing the carbon grains apart, and causing the resistance of the device to rise rapidly. Like the BaTiO3 thermistor, this device has a highly nonlinear resistance/temperature response and is used for switching, not for proportional temperature measurement.
The current and voltage across the thermistor will depend on the particular circuit configuration. As a simple example, if the voltage across the thermistor is held fixed, then by Ohm’s Law we have I = V /R and the equilibrium equation can be solved for the ambient temperature as a function of the measured resistance of the thermistor:
6.1.5
Self-heating effects
PE = PT
T0 = T (R) −
V2 KR
The dissipation constant is a measure of the thermal connection of the thermistor to its surroundings. It is generally given for the thermistor in still air, and in well-stirred oil. Typical values for a small glass bead thermistor are 1.5 mW/°C in still air and 6.0 mW/°C in stirred oil. If the temperature of the environment is known beforehand, then a thermistor may be used to measure the value of the dissipation constant. For example, the thermistor may be used as a flow rate sensor, since the dissipation constant increases with the rate of flow of a fluid past the thermistor.
When a current flows through a thermistor, it will generate heat which will raise the temperature of the thermistor above that of its environment. If the thermistor is being used to measure the temperature of the environment, this electrical heating may introduce a significant error if a correction is not made. Alternatively, this effect itself can be exploited. It can, for example, make a sensitive air-flow device employed in a sailplane rate-of-climb The power dissipated in a thermistor is typically maininstrument, the electronic variometer, or serve as a timer tained at a very low level to ensure insignificant temfor a relay as was formerly done in telephone exchanges. perature measurement error due to self heating. However, some thermistor applications depend upon signifiThe electrical power input to the thermistor is just: cant “self heating” to raise the body temperature of the thermistor well above the ambient temperature so the sensor then detects even subtle changes in the thermal PE = IV conductivity of the environment. Some of these applicawhere I is current and V is the voltage drop across the tions include liquid level detection, liquid flow measurethermistor. This power is converted to heat, and this ment and air flow measurement.[2]
154
6.1.6 Applications • PTC thermistors can be used as current-limiting devices for circuit protection, as replacements for fuses. Current through the device causes a small amount of resistive heating. If the current is large enough to generate more heat than the device can lose to its surroundings, the device heats up, causing its resistance to increase. This creates a selfreinforcing effect that drives the resistance upwards, therefore limiting the current. • PTC thermistors were used as timers in the degaussing coil circuit of most CRT displays. When the display unit is initially switched on, current flows through the thermistor and degaussing coil. The coil and thermistor are intentionally sized so that the current flow will heat the thermistor to the point that the degaussing coil shuts off in under a second. For effective degaussing, it is necessary that the magnitude of the alternating magnetic field produced by the degaussing coil decreases smoothly and continuously, rather than sharply switching off or decreasing in steps; the PTC thermistor accomplishes this naturally as it heats up. A degaussing circuit using a PTC thermistor is simple, reliable (for its simplicity), and inexpensive.
CHAPTER 6. SENSORS coolant temperature and/or oil temperature inside the engine and provide data to the ECU and, indirectly, to the dashboard. • NTC thermistors can be also used to monitor the temperature of an incubator. • Thermistors are also commonly used in modern digital thermostats and to monitor the temperature of battery packs while charging. • Thermistors are often used in the hot ends of 3D printers; they monitor the heat produced and allow the printer’s control circuitry to keep a constant temperature for melting the plastic filament. • NTC thermistors are used in the Food Handling and Processing industry, especially for food storage systems and food preparation. Maintaining the correct temperature is critical to prevent food borne illness. • NTC thermistors are used throughout the Consumer Appliance industry for measuring temperature. Toasters, coffee makers, refrigerators, freezers, hair dryers, etc. all rely on thermistors for proper temperature control. • NTC thermistors come in bare and lugged forms, the former is for point sensing to achieve high accuracy for specific points, such as laser diode die, etc.[8]
• PTC thermistors were used as heater in automotive industry to provide additional heat inside cabin with diesel engine or to heat diesel in cold climatic conditions before engine injection. 6.1.7
History
• PTC thermistors are used in temperature compen- The first NTC thermistor was discovered in 1833 by sated synthesizer voltage controlled oscillators.[6] Michael Faraday, who reported on the semiconducting • NTC thermistors are used as resistance thermome- behavior of silver sulfide. Faraday noticed that the reters in low-temperature measurements of the order sistance of silver sulfide decreased dramatically as temperature increased. (This was also the first documented of 10 K. observation of a semiconducting material.) [9] • NTC thermistors can be used as inrush-current limBecause early thermistors were difficult to produce and iting devices in power supply circuits. They present applications for the technology were limited, commera higher resistance initially which prevents large curcial production of thermistors did not begin until the rents from flowing at turn-on, and then heat up and 1930s.[10] A commercially viable thermistor was inbecome much lower resistance to allow higher curvented by Samuel Ruben in 1930.[11] rent flow during normal operation. These thermistors are usually much larger than measuring type thermistors, and are purposely designed for this 6.1.8 See also application.[7] • Iron-hydrogen resistor • NTC thermistors are regularly used in automotive • Thermocouple applications. For example, they monitor things like
6.2. PHOTODIODE
6.1.9
155
References
[1] “NTC Thermistors”. Micro-chip Technologies. 2010. [2] Thermistor Terminology. U.S. Sensor [3] “Practical Temperature Measurements”. Agilent Application Note. Agilent Semiconductor. [4] L. W Turner, ed. (1976). Electronics Engineer’s Reference Book (4 ed.). Butterworths. pp. 6–29 to 6–41. ISBN 0408001682. [5] “PTC Thermistors and Silistors” The Resistor Guide [6] Temperature Compensated VCO [7] Inrush Current Limiting Power Thermistors. U.S. Sensor [8] “PTC Thermistors Guide- “Publish By Analog Electronic Technologies”. extquotedbl. [9] “1833 - First Semiconductor Effect is Recorded”. Computer History Museum. Retrieved 24 June 2014. [10] McGee, Thomas (1988). “Chapter 9”. Principles and Methods of Temperature Measurement. John Wiley & Sons. p. 203.
Three Si and one Ge (bottom) photodiodes
Anode
Cathode
[11] Jones, Deric P., ed. (2009). Biomedical Sensors. Momentum Press. p. 12.
6.1.10
External links
Symbol for photodiode.
• The thermistor at bucknell.edu
Photodiodes are similar to regular semiconductor diodes except that they may be either exposed (to detect vacuum UV or X-rays) or packaged with a window or optical fiber • “Thermistors & Thermocouples:Matching the Tool connection to allow light to reach the sensitive part of the to the Task in Thermal Validation” - Journal of Valdevice. Many diodes designed for use specifically as a idation Technology photodiode use a PIN junction rather than a p-n junction, to increase the speed of response. A photodiode is designed to operate in reverse bias.[1] • Software for thermistor calculation at Sourceforge
6.2 Photodiode
A photodiode is a semiconductor device that converts light into current. The current is generated when photons are absorbed in the photodiode. A small amount of current is also produced when no light is present. Photodiodes may contain optical filters, built-in lenses, and may have large or small surface areas. Photodiodes usually have a slower response time as its surface area increases. The common, traditional solar cell used to generate electric solar power is a large area photodiode.
6.2.1 Principle of operation A photodiode is a p-n junction or PIN structure. When a photon of sufficient energy strikes the diode, it creates an electron-hole pair. This mechanism is also known as the inner photoelectric effect. If the absorption occurs in the junction’s depletion region, or one diffusion length away from it, these carriers are swept from the junction by the built-in electric field of the depletion region. Thus holes
156
CHAPTER 6. SENSORS rent of a good PIN diode is so low (<1 nA) that the Johnson–Nyquist noise of the load resistance in a typical circuit often dominates. Other modes of operation Avalanche photodiodes have a similar structure to regular photodiodes, but they are operated with much higher reverse bias. This allows each photo-generated carrier to be multiplied by avalanche breakdown, resulting in internal gain within the photodiode, which increases the effective responsivity of the device.
I-V characteristic of a photodiode. The linear load lines represent the response of the external circuit: I=(Applied bias voltageDiode voltage)/Total resistance. The points of intersection with the curves represent the actual current and voltage for a given bias, resistance and illumination.
move toward the anode, and electrons toward the cathode, and a photocurrent is produced. The total current through the photodiode is the sum of the dark current (current that is generated in the absence of light) and the photocurrent, so the dark current must be minimized to maximize the sensitivity of the device.[2] Photovoltaic mode When used in zero bias or photovoltaic mode, the flow of photocurrent out of the device is restricted and a voltage builds up. This mode exploits the photovoltaic effect, which is the basis for solar cells – a traditional solar cell is just a large area photodiode. Photoconductive mode In this mode the diode is often reverse biased (with the cathode driven positive with respect to the anode). This reduces the response time because the additional reverse bias increases the width of the depletion layer, which decreases the junction’s capacitance. The reverse bias also increases the dark current without much change in the photocurrent. For a given spectral distribution, the photocurrent is linearly proportional to the illuminance (and to the irradiance).[3]
Electronic symbol for a phototransistor
A phototransistor is a light-sensitive transistor. A common type of phototransistor, called a photobipolar transistor, is in essence a bipolar transistor encased in a transparent case so that light can reach the base-collector junction. It was invented by Dr. John N. Shive (more famous for his wave machine) at Bell Labs in 1948,[4]:205 but it wasn't announced until 1950.[5] The electrons that are generated by photons in the base-collector junction are injected into the base, and this photodiode current Although this mode is faster, the photoconductive mode is amplified by the transistor’s current gain β (or h ₑ). tends to exhibit more electronic noise. The leakage cur- If the emitter is left unconnected, the phototransistor
becomes a photodiode. While phototransistors have a higher responsivity for light they are not able to detect low levels of light any better than photodiodes. Phototransistors also have significantly longer response times. Field-effect phototransistors, also known as photoFETs, are light-sensitive field-effect transistors. Unlike photobipolar transistors, photoFETs control drain-source current by creating a gate voltage.
6.2.2
Materials
The material used to make a photodiode is critical to defining its properties, because only photons with sufficient energy to excite electrons across the material’s bandgap will produce significant photocurrents.
157
response [A/W]
6.2. PHOTODIODE
0.6 0.5 0.4 0.3 0.2 0.1 0
400
600
800
1000
wavelength [nm]
Materials commonly used to produce photodiodes Response of a silicon photo diode vs wavelength of the incident include:[6] light Because of their greater bandgap, silicon-based photodiodes generate less noise than germanium-based photodi- Dark current The current through the photodiode in odes. the absence of light, when it is operated in photoconductive mode. The dark current includes photocurrent generated by background radiation and the Unwanted photodiode effects saturation current of the semiconductor junction. Dark current must be accounted for by calibration Any p-n junction, if illuminated, is potentially a photoif a photodiode is used to make an accurate optical diode. Semiconductor devices such as transistors and power measurement, and it is also a source of noise ICs contain p-n junctions, and will not function corwhen a photodiode is used in an optical communirectly if they are illuminated by unwanted electromagcation system. netic radiation (light) of wavelength suitable to produce a photocurrent;[7][8] this is avoided by encapsulating devices in opaque housings. If these housings are not com- Response time A photon absorbed by the semiconducting material will generate an electron-hole pair pletely opaque to high-energy radiation (ultraviolet, X[9] which will in turn start moving in the material unrays, gamma rays), transistors and ICs can malfunction der the effect of the electric field and thus generate a due to induced photo-currents. Background radiation [10] current. The finite duration of this current is known from the packaging is also significant. Radiation hardas the transit-time spread and can be evaluated by ening mitigates these effects. using Ramo’s theorem. One can also show with this theorem that the total charge generated in the exter6.2.3 Features nal circuit is well e and not 2e as might seem by the presence of the two carriers. Indeed the integral of Critical performance parameters of a photodiode include: the current due to both electron and hole over time must be equal to e. The resistance and capacitance Responsivity The Spectral responsivity is a ratio of of the photodiode and the external circuitry give rise the generated photocurrent to incident light power, to another response time known as RC time constant expressed in A/W when used in photoconductive τ = RC . This combination of R and C integrates mode. The wavelength-dependence may also be exthe photoresponse over time and thus lengthens the impulse response of the photodiode. When used in pressed as a Quantum efficiency, or the ratio of the number of photogenerated carriers to incident phoan optical communication system, the response time tons, a unitless quantity. determines the bandwidth available for signal mod-
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CHAPTER 6. SENSORS ulation and thus data transmission.
of a mechanical obstruction to the beam (slotted optical switch), or to couple two digital or analog circuits while Noise-equivalent power (NEP) The minimum input maintaining extremely high electrical isolation between optical power to generate photocurrent, equal to the them, often for safety (optocoupler). rms noise current in a 1 hertz bandwidth. NEP is Photodiodes are often used for accurate measurement of essentially the minimum detectable power. The re- light intensity in science and industry. They generally lated characteristic detectivity ( D ) is the inverse have a more linear response than photoconductors. of NEP, 1/NEP. There is also the specific detectivity ( D⋆ ) which is the detectivity multiplied by the They are also widely used in various medical applications, such as detectors for computed tomography (cousquare root √ of the area ( A ) of the photodetector, ( pled with scintillators), instruments to analyze samples ⋆ D = D A ) for a 1 Hz bandwidth. The specific detectivity allows different systems to be compared (immunoassay), and pulse oximeters. independent of sensor area and system bandwidth; PIN diodes are much faster and more sensitive than pa higher detectivity value indicates a low-noise de- n junction diodes, and hence are often used for optical vice or system.[11] Although it is traditional to give ( communications and in lighting regulation. D⋆ ) in many catalogues as a measure of the diode’s P-N photodiodes are not used to measure extremely low quality, in practice, it is hardly ever the key paramlight intensities. Instead, if high sensitivity is needed, eter. avalanche photodiodes, intensified charge-coupled devices or photomultiplier tubes are used for applications When a photodiode is used in an optical communication such as astronomy, spectroscopy, night vision equipment system, all these parameters contribute to the sensitivity and laser rangefinding. of the optical receiver, which is the minimum input power required for the receiver to achieve a specified bit error Pinned photodiode is not a PIN photodiode, it has p+/n/p regions in it. It has a shallow P+ implant in N type difrate. fusion layer over a P-type epitaxial substrate layer. It is used in CMOS Active pixel sensor.[12]
6.2.4 Applications P-N photodiodes are used in similar applications to other Comparison with photomultipliers photodetectors, such as photoconductors, charge-coupled [13] devices, and photomultiplier tubes. They may be used Advantages compared to photomultipliers: to generate an output which is dependent upon the illu1. Excellent linearity of output current as a function of mination (analog; for measurement and the like), or to incident light change the state of circuitry (digital; either for control and switching, or digital signal processing). 2. Spectral response from 190 nm to 1100 Photodiodes are used in consumer electronics devices nm (silicon), longer wavelengths with other such as compact disc players, smoke detectors, and the semiconductor materials receivers for infrared remote control devices used to con3. Low noise trol equipment from televisions to air conditioners. For many applications either photodiodes or photoconductors 4. Ruggedized to mechanical stress may be used. Either type of photosensor may be used for light measurement, as in camera light meters, or to 5. Low cost respond to light levels, as in switching on street lighting after dark. 6. Compact and light weight Photosensors of all types may be used to respond to in7. Long lifetime cident light, or to a source of light which is part of the same circuit or system. A photodiode is often combined 8. High quantum efficiency, typically 60-80% [14] into a single component with an emitter of light, usually a light-emitting diode (LED), either to detect the presence 9. No high voltage required
6.2. PHOTODIODE Disadvantages compared to photomultipliers: 1. Small area 2. No internal gain (except avalanche photodiodes, but their gain is typically 102 –103 compared to up to 108 for the photomultiplier) 3. Much lower overall sensitivity 4. Photon counting only possible with specially designed, usually cooled photodiodes, with special electronic circuits
159
6.2.6 See also • Electronics • Band gap • Infrared • Optoelectronics • Optical interconnect • Light Peak • Interconnect bottleneck • Optical fiber cable
5. Response time for many designs is slower
• Optical communication
6. latent effect
• Parallel optical interface • Opto-isolator
6.2.5
Photodiode array
• Semiconductor device • Solar cell • Avalanche photodiode • Transducer • LEDs as Photodiode Light Sensors • Light meter • Image sensor • Transimpedance amplifier
6.2.7 References This article incorporates public domain material from the General Services Administration document “Federal Standard 1037C”.
A 2 x 2 cm photodiode array chip with more than 200 diodes
A one-dimensional array of hundreds or thousands of photodiodes can be used as a position sensor, for example as part of an angle sensor.[15] One advantage of photodiode arrays (PDAs) is that they allow for high speed parallel read out since the driving electronics may not be built in like a traditional CMOS or CCD sensor.
[1] James F. Cox (26 June 2001). Fundamentals of linear electronics: integrated and discrete. Cengage Learning. pp. 91–. ISBN 978-0-7668-3018-9. Retrieved 20 August 2011. [2] Filip Tavernier, Michiel Steyaert High-Speed Optical Receivers with Integrated Photodiode in Nanoscale CMOS Springer, 2011 ISBN 1-4419-9924-8, Chapter 3 From Light to Electric Current - The Photodiode [3] “Photodiode slide”.
160
[4] Michael Riordan and Lillian Hoddeson. Crystal Fire: The Invention of the Transistor and the Birth of the Information Age. ISBN 9780393318517. [5] “The phototransistor”. Bell Laboratories RECORD. May 1950. [6] Held. G, Introduction to Light Emitting Diode Technology and Applications, CRC Press, (Worldwide, 2008). Ch. 5 p. 116. ISBN 1-4200-7662-0 [7] Z. Shanfield et al, 1988, Investigation of radiation effects on semiconductor devices and integrated circuits, DNA-TR-88-221, www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA210165
CHAPTER 6. SENSORS
6.2.8
External links
• Technical Information Hamamatsu Photonics • Using the Photodiode to convert the PC to a Light Intensity Logger • Design Fundamentals for Phototransistor Circuits • Working principles of photodiodes
6.3 Photoresistor
[8] Krzysztof Iniewski, ed, 2010, Radiation Effects in Semiconductors, CRC Press, ISBN 978-1-4398-2694-2 [9] H.R. Zeller, 1995, Cosmic ray induced failures in high power semiconductor devices, www.sciencedirect.com/ science/article/pii/0038110195000825 [10] T. May and M. Woods, Alpha-particle-induced soft errors in dynamic memories”, IEEE Trans. Elec. Dev., vol. 26, No. 1, pp 2, Jan 1979, cited in R. C. Baumann 2004, Soft errors in commercial integrated circuits, Int. J. High Speed Electronics and Systems, Vol. 14, No 2 (2004) 299-309: “alpha particles emitted from the natural radioactive decay of uranium, thorium, and aughter isotopes present as impurities in packaging materials were found to be the dominant cause of [soft error rate] in [dynamic random-access memories].”
The symbol for a photoresistor[1]
A photoresistor or light-dependent resistor (LDR) or photocell is a light-controlled variable resistor. The resistance of a photoresistor decreases with increasing incident light intensity; in other words, it exhibits photoconductivity. A photoresistor can be applied in [12] http://electronics.stackexchange.com/questions/83018/ difference-between-buried-photodiode-and-pinned-photodiode light-sensitive detector circuits, and light- and darkactivated switching circuits. [11] Graham Brooker, Introduction to Sensors for Ranging and Imaging, ScitTech Publishing, 2009 ISBN 9781891121746 page 87
[13] Photodiode Technical Guide on Hamamatsu website
A photoresistor is made of a high resistance semiconductor. In the dark, a photoresistor can have a resistance as high as a few megaohms (MΩ), while in the light, a photoresistor can have a resistance as low as a few hundred ohms. If incident light on [15] Wei Gao (2010). Precision Nanometrology: Sensors and a photoresistor exceeds a certain frequency, photons Measuring Systems for Nanomanufacturing. Springer. pp. absorbed by the semiconductor give bound electrons 15–16. ISBN 978-1-84996-253-7. enough energy to jump into the conduction band. The resulting free electrons (and their hole partners) conduct • Gowar, John, Optical Communication Systems, 2 ed., electricity, thereby lowering resistance. The resistance Prentice-Hall, Hempstead UK, 1993 (ISBN 0-13- range and sensitivity of a photoresistor can substantially 638727-6) differ among dissimilar devices. Moreover, unique [14] Knoll, F.G. (2010). Radiation detection and measurement −4th ed. p. 298. Wiley, Hoboken, NJ. ISBN 978-0-47013148-0
6.3. PHOTORESISTOR
161
photoresistors may react substantially differently to Photoresistors also exhibit a certain degree of latency bephotons within certain wavelength bands. tween the moment they are hit by light and the subseA photoelectric device can be either intrinsic or extrin- quent moment that their resistance actually drops. This sic. An intrinsic semiconductor has its own charge car- drop is usually about 10 milliseconds. Also, they exhibit a riers and is not an efficient semiconductor, for example, much longer latency when going from lighted to dark ensilicon. In intrinsic devices the only available electrons vironments, often of as long as one second. This property are in the valence band, and hence the photon must have makes them unsuitable for sensing rapidly flashing lights diode cannot enough energy to excite the electron across the entire (unless the flashing is so frequent that the [3] detect the drop in light between flashes). bandgap. Extrinsic devices have impurities, also called dopants, added whose ground state energy is closer to the conduction band; since the electrons do not have as far to jump, lower energy photons (that is, longer wavelengths and lower frequencies) are sufficient to trigger the device. If a sample of silicon has some of its atoms replaced by phosphorus atoms (impurities), there will be extra electrons available for conduction. This is an example of an extrinsic semiconductor.[2]
6.3.2 Applications Photoresistors come in many types. Inexpensive cadmium sulphide cells can be found in many consumer items such as camera light meters, street lights, clock radios, alarm devices, night lights, outdoor clocks, solar street lamps and solar road studs, etc. They are also used in some dynamic compressors together with a small incandescent or neon lamp, or lightemitting diode to control gain reduction. A common usage of this application can be found in many guitar amplifiers that incorporate an onboard tremolo effect, as the oscillating light patterns control the level of signal running through the amp circuit. The use of CdS and CdSe[4] photoresistors is severely restricted in Europe due to the RoHS ban on cadmium. Lead sulphide (PbS) and indium antimonide (InSb) LDRs (light-dependent resistors) are used for the midinfrared spectral region. Ge:Cu photoconductors are among the best far-infrared detectors available, and are used for infrared astronomy and infrared spectroscopy.
The internal components of a photoelectric control for a typical American streetlight. The photoresistor is facing rightwards, and controls whether current flows through the heater which opens the main power contacts. At night, the heater cools, closing the power contacts, energizing the street light.
6.3.1
Design considerations
6.3.3 References [1] British Standard 3939 [2] Diffenderfes, Robert (2005). Electronic Devices: System and Applications. New Delhi: Delimar. p. 480. ISBN 978-1401835149.
Photoresistors are less light-sensitive devices than photo- [3] http://www.resistorguide.com/photoresistor/ diodes or phototransistors: the two latter components are [4] “Silonex: TO-18 photocells on ceramic substrate extquottrue semiconductor devices, while a photoresistor is pasedbl (PDF). Retrieved 17 October 2013. sive component and does not have a PN-junction. The photoresistivity of any photoresistor may vary widely depending on ambient temperature, making them unsuit- 6.3.4 See also able for applications requiring precise measurement of • Optoelectronics or sensitivity to light.
162 • Photodiode • Phototransistor
6.3.5 External links • Using a photoresistor to measure nocturnal light levels - The Moonlight Sensor • Using a photoresistor to track light • Connecting a photoresistor to a circuit • Photoresistor overview - detailing operation, structure and circuit information
CHAPTER 6. SENSORS • off-resistance: the resistance when switched off. This is typically a number of megohms or gigaohms. • signal range: the minimum and maximum voltages allowed for the signal to be passed through. If these are exceeded, the switch may be destroyed by excessive currents. Older types of switches can even latch up, which means that they continue to conduct excessive currents even after the faulty signal is removed. • charge injection. This effect causes the switch to inject a small electric charge into the signal when it switches on, causing a small spike or glitch. The charge injection is specified in coulombs.
6.4.1
6.4 Analogue switch The analogue (or analog) switch, also called the bilateral switch, is an electronic component that behaves in a similar way to a relay, but has no moving parts. The switching element is normally a pair MOSFET transistors, one an N-channel device, the other a Pchannel device. The device can conduct analog or digital signals in either direction when on and isolates the switched terminals when off. Analogue switches are usually manufactured as integrated circuits in packages containing multiple switches (typically two, four or eight). These include the 4016 and 4066 from the 4000 series. The control input to the device may be a signal that switches between the positive and negative supply voltages, with the more positive voltage switching the device on and the more negative switching the device off. Other circuits are designed to communicate through a serial port with a host controller in order to set switches on or off. The signal being switched must remain within the bounds of the positive and negative supply rails which are connected to the P-MOS and N-MOS body terminals. The switch generally provides good isolation between the control signal and the input/output signals. They are not used for high voltage switching. Important parameters of an analogue switch are: • on-resistance: the resistance when switched on. This commonly ranges from 5 ohms to a few hundred ohms.
See also
• Analog-to-digital converter • Telecommunications equipment
Chapter 7
The Decibel 7.1 Decibel
The decibel symbol is often qualified with a suffix that indicates which reference quantity has been used or some other property of the quantity being measured. For exThis article is about the unit of level. For other uses, see ample, dBm indicates a reference level of one milliwatt, Decibel (disambiguation). while dBu is referenced to approximately 0.775 volts RMS.[2] The decibel (dB) is a logarithmic unit used to express the ratio between two values of a physical quantity, often power or intensity. One of these quantities is often a reference value, and in this case the decibel can be used to express the absolute level of the physical quantity, as in the case of sound pressure. The number of decibels is ten times the logarithm to base 10 of the ratio of two power quantities,[1] or of the ratio of the squares of two field amplitude quantities. One decibel is one tenth of one bel, named in honor of Alexander Graham Bell. The bel is seldom used without the deci- prefix. The definition of the decibel is based on the measurement practices in telephony of the early 20th century in the Bell System in the United States. Today, the unit is used for a wide variety of measurements in science and engineering, most prominently in acoustics, electronics, and control theory. In electronics, the gains of amplifiers, attenuation of signals, and signal-to-noise ratios are often expressed in decibels. The decibel confers a number of advantages, such as the ability to conveniently represent very large or small numbers, and the ability to carry out multiplication of ratios by simple addition and subtraction. A change in power by a factor of 10 corresponds to a 10 dB change in level. A change in power by a factor of two approximately corresponds to a 3 dB change. A change in voltage by a factor of 10 results in a change in power by a factor of 100 and corresponds to a 20 dB change. A change in voltage ratio by a factor of two approximately corresponds to a 6 dB change.
In the International System of Quantities, the decibel is defined as a unit of level or level difference, equal to onetenth of a bel. The bel is then defined in terms of the neper, an alternative unit of level of root-power quantities, applicable when the natural logarithm (base e) is used to define the level.[3]
7.1.1 History The decibel originates from methods used to quantify signal losses in telephone circuits. These losses were originally measured in units of Miles of Standard Cable (MSC), where 1 MSC corresponded to the loss of power over a 1 mile (approximately 1.6 km) length of standard telephone cable at a frequency of 5000 radians per second (795.8 Hz), and roughly matched the smallest attenuation detectable to the average listener. Standard telephone cable was defined as “a cable having uniformly distributed resistance of 88 ohms per loop mile and uniformly distributed shunt capacitance of .054 microfarad per mile” (approximately 19 gauge).[4] The transmission unit (TU) was devised by engineers of the Bell Telephone Laboratories in the 1920s to replace the MSC. 1 TU was defined as ten times the base-10 logarithm of the ratio of measured power to a reference power level.[5] The definitions were conveniently chosen such that 1 TU approximately equaled 1 MSC (specifically, 1.056 TU = 1 MSC).The threshold of hearing is 25 dB[6] In 1928, the Bell system renamed the TU the decibel,[7]
163
164
CHAPTER 7. THE DECIBEL
being one tenth of a newly defined unit for the base-10 logarithm of the power ratio. It was named the bel, in honor of their founder and telecommunications pioneer Alexander Graham Bell.[8] The bel is seldom used, as the decibel was the proposed working unit.[9]
is deprecated by ISO, which favors root-power. Neither IEC nor ISO permit the use of modifiers such as dBA or dBV; such units, though widely used, are not defined by international standards.
The naming and early definition of the decibel is de- 7.1.2 scribed in the NBS Standard’s Yearbook of 1931:[10] Since the earliest days of the telephone, the need for a unit in which to measure the transmission efficiency of telephone facilities has been recognized. The introduction of cable in 1896 afforded a stable basis for a convenient unit and the “mile of standard” cable came into general use shortly thereafter. This unit was employed up to 1923 when a new unit was adopted as being more suitable for modern telephone work. The new transmission unit is widely used among the foreign telephone organizations and recently it was termed the “decibel” at the suggestion of the International Advisory Committee on Long Distance Telephony. The decibel may be defined by the statement that two amounts of power differ by 1 decibel when they are in the ratio of 100.1 and any two amounts of power differ by N decibels when they are in the ratio of 10N(0.1) . The number of transmission units expressing the ratio of any two powers is therefore ten times the common logarithm of that ratio. This method of designating the gain or loss of power in telephone circuits permits direct addition or subtraction of the units expressing the efficiency of different parts of the circuit... Standards In April 2003, the International Committee for Weights and Measures (CIPM) considered a recommendation for the decibel’s inclusion in the International System of Units (SI), but decided not to adopt the decibel as an SI unit.[11] However, the decibel is recognized by other international bodies such as the International Electrotechnical Commission (IEC) and International Organization for Standardization (ISO).[12] The IEC permits the use of the decibel with field quantities as well as power and this recommendation is followed by many national standards bodies, such as NIST, which justifies the use of the decibel for voltage ratios.[13] The term field quantity
Definition
The decibel (dB) is one tenth of the bel (B): 1B = 10dB. The bel is (1/2) ln(10) nepers. The bel represents a ratio between two power quantities of 10:1, and a ratio between two field quantities of √10:1.[14] A field quantity is a quantity such as voltage, current, pressure, electric field strength, velocity, or charge density, the square of which in linear systems is proportional to power.[15] A power quantity is a power or a quantity directly proportional to power, e.g., energy density, acoustic intensity and luminous intensity. The method of calculation of a ratio in decibels depends on whether the measured property is a power quantity or a field quantity. Two signals that differ by one decibel have a power ratio 1 of 10 10 which is approximately 1.25892, and an ampli√ 1 tude (field) ratio of 10 10 (1.12202).[16][17] Although permissible, the bel is rarely used with other SI unit prefixes than deci. It is preferred to use hundredths of a decibel rather than millibels.[18] Conversions The bel is defined by ISO Standard 80000-3:2006 as (1/2) ln(10) nepers (Np), where ln denotes the natural logarithm. Because the decibel is one tenth of a bel, it follows that 1 dB = (1/20) ln(10) Np. The same standard defines 1 Np as equal to 1 (thereby relating all of the units as nondimensional natural log of field-quantity ratios, 1 dB = 0.11513..., 1 B = 1.1513...). Since logarithm differences measured in these units are used to represent power ratios and field ratios, the values of the ratios represented by each unit are also included in the table. Power quantities When referring to measurements of power or intensity, a ratio can be expressed in decibels by evaluating ten times the base-10 logarithm of the ratio of the measured quantity to the reference level. Thus, the ratio of a power value
7.1. DECIBEL
165
P 1 to another power value P 0 is represented by L B, that where V 1 is the voltage being measured, V 0 is a specified ratio expressed in decibels,[19] which is calculated using reference voltage, and G B is the power gain expressed in the formula: decibels. A similar formula holds for current. ( LdB = 10 log10
P1 P0
The term root-power quantity is introduced by ISO Standard 80000-1:2009 as a substitute of field quantity. The term field quantity is deprecated by that standard.
)
The base-10 logarithm of the ratio of the two power levels is the number of bels. The number of decibels is ten times the number of bels (equivalently, a decibel is one-tenth of a bel). P 1 and P 0 must measure the same type of quantity, and have the same units before calculating the ratio. If P 1 = P 0 in the above equation, then L B = 0. If P 1 is greater than P 0 then L B is positive; if P 1 is less than P 0 then L B is negative. Rearranging the above equation gives the following formula for P 1 in terms of P 0 and L B:
Examples All of these examples yield dimensionless answers in dB because they are relative ratios expressed in decibels. The unit dBW is often used to denote a ratio for which the reference is 1 W, and similarly dBm for a 1 mW reference point. • Calculating the ratio of 1 kW (one kilowatt, or 1000 watts) to 1 W in decibels yields: (
P1 = 10
LdB 10
GdB = 10 log10
P0
• The ratio of is
Field quantities When referring to measurements of field amplitude, it is usual to consider the ratio of the squares of A1 (measured amplitude) and A0 (reference amplitude). This is because in most applications power is proportional to the square of amplitude, and it is desirable for the two decibel formulations to give the same result in such typical cases. Thus, the following definition is used: ( LdB = 10 log10
A21 A20
)
( = 20 log10
) A1 . A0
The formula may be rearranged to give
√
A1 = 10
) ≡ 30 dB
1000 V ≈ 31.62 V to 1 V in decibels (
GdB = 20 log10
31.62 V 1V
) ≡ 30 dB
(31.62 V/1 V)2 ≈ 1 kW/1 W , illustrating the consequence from the definitions above that GdB has the same value, 30 dB , regardless of whether it is obtained from powers or from amplitudes, provided that in the specific system being considered power ratios are equal to amplitude ratios squared. • The ratio of 1 mW (one milliwatt) to 10 W in decibels is obtained with the formula ( GdB = 10 log10
LdB 20
1000 W 1W
0.001 W 10 W
) ≡ −40 dB
A0
Similarly, in electrical circuits, dissipated power is typically proportional to the square of voltage or current when the impedance is held constant. Taking voltage as an example, this leads to the equation: ( GdB = 20 log10
V1 V0
)
• The power ratio corresponding to a 3 dB change in level is given by 3
G = 10 10 × 1 = 1.99526... ≈ 2 A change in power ratio by a factor of 10 is a change of 10 dB. A change in power ratio by a factor of two is approximately a change of 3 dB. More precisely, the factor is 103/10 , or 1.9953, about 0.24% different from exactly
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2. Similarly, an increase of 3 dB implies an increase in √ voltage by a factor of approximately 2 , or about 1.41, an increase of 6 dB corresponds to approximately four times the power and twice the voltage, and so on. In exact terms the power ratio is 106/10 , or about 3.9811, a relative error of about 0.5%.
Calculated exactly, the output is 1 W x 1025/10 = 316.2 W. The approximate value has an error of only +0.4% with respect to the actual value which is negligible given the precision of the values supplied and the accuracy of most measurement instrumentation.
7.1.3 Properties The decibel has the following properties: • The logarithmic nature of the decibel means that a very large range of ratios can be represented by a convenient number, in a similar manner to scientific notation. This allows one to clearly visualize huge changes of some quantity. See Bode plot and semilog plot. For example, 120 dB SPL may be clearer than a “a trillion times more intense than the threshold of hearing”, or easier to interpret than “20 pascals of sound pressure”. • The unit is an additive function, which means that the overall gain of a multi-component system, such as a series of amplifier stages, can be calculated by summing the gains in decibels of the individual components, rather than multiply the amplification factors; that is, log(A × B × C) = log(A) + log(B) + log(C). Practically, this means that, armed only with the knowledge that 1 dB is approximately 26% power gain, 3 dB is approximately 2× power gain, and 10 dB is 10× power gain, it is possible to determine the power ratio of a system from the gain in dB with only simple addition and multiplication. For example:
7.1.4
Advantages and disadvantages
Advantages • According to Mitschke,[20] “The advantage of using a logarithmic measure is that in a transmission chain, there are many elements concatenated, and each has its own gain or attenuation. To obtain the total, addition of decibel values is much more convenient than multiplication of the individual factors.” • The human perception of the intensity of, for example, sound or light, is more nearly linearly related to the logarithm of intensity than to the intensity itself, per the Weber–Fechner law, so the dB scale can be useful to describe perceptual levels or level differences. Disadvantages According to several articles published in Electrical Engineering[21] and the Journal of the Acoustical Society of America,[22][23][24] the decibel suffers from the following disadvantages: • The decibel creates confusion.
A system consists of 3 amplifiers in series, with gains (ratio of power out to in) of 10 dB, 8 dB, and 7 dB respectively, for a total gain of 25 dB. Broken into combinations of 10, 3, and 1 dB, this is: 25 dB = 10 dB + 10 dB + 3 dB + 1 dB + 1 dB With an input of 1 watt, the output is approximately 1 W x 10 x 10 x 2 x 1.26 x 1.26 = ~317.5 W
• The logarithmic form obscures reasoning. • Decibels are more related to the era of slide rules than that of modern digital processing. • Decibels are cumbersome and difficult to interpret. Hickling concludes “Decibels are a useless affectation, which is impeding the development of noise control as an engineering discipline”.[23] Another disadvantage is that quantities in decibels are not necessarily additive,[25][26] thus being “of unacceptable form for use in dimensional analysis extquotedbl.[27]
7.1. DECIBEL
167
For the same reason that decibels excel at multiplicative operations (e.g., antenna gain), they are awkward when dealing with additive operations. Peters (2013, p. 13)[28] provides several examples:
that the ear can hear is greater than or equal to 1 trillion (1012 ).[30] Such large measurement ranges are conveniently expressed in logarithmic units: the base-10 logarithm of 1012 is 12, which is expressed as a sound pressure level of 120 dB re 20 micropascals. Since the hu• “if two machines each individually produce a [sound man ear is not equally sensitive to all sound frequencies, pressure] level of, say, 90 dB at a certain point, then noise levels at maximum human sensitivity, somewhere when both are operating together we should expect between 2 and 4 kHz, are factored more heavily into the combined sound pressure level to increase to 93 some measurements using frequency weighting. (See also Stevens’ power law.) dB, but certaintly not to 180 dB! extquotedbl • “supposed that the noise from a machine is measured (including the contribution of background noise) and found to be 87 dBA but when the machine is switched off the background noise alone is measured as 83 dBA. ... the machine noise [level (alone)] may be obtained by 'subtracting' the 83 dBA background noise from the combined level of 87 dBA; i.e., 84.8 dBA.” • “in order to find a representative value of the sound level in a room a number of measurements are taken at different positions within the room, and an average value is calculated. (...) Compare the logarithmic and arithmetic averages of ... 70 dB and 90 dB: logarithmic average = 87 dB; arithmetic average = 80 dB.”
Further information: Examples of sound pressure and sound pressure levels
Electronics In electronics, the decibel is often used to express power or amplitude ratios (gains), in preference to arithmetic ratios or percentages. One advantage is that the total decibel gain of a series of components (such as amplifiers and attenuators) can be calculated simply by summing the decibel gains of the individual components. Similarly, in telecommunications, decibels denote signal gain or loss from a transmitter to a receiver through some medium (free space, waveguide, coaxial cable, fiber optics, etc.) using a link budget.
The decibel unit can also be combined with a suffix to create an absolute unit of electric power. For example, it can be combined with “m” for “milliwatt” to produce Acoustics the extquotedbldBm extquotedbl. Zero dBm is the level corresponding to one milliwatt, and 1 dBm is one decibel The decibel is commonly used in acoustics as a unit greater (about 1.259 mW). of sound pressure level, for a reference pressure of 20 micropascals in air[29] and 1 micropascal in water. The In professional audio specifications, a popular unit is the reference pressure in air is set at the typical threshold of dBu. The suffix u stands for unloaded, and was probably perception of an average human and there are common chosen to be similar to lowercase v, as dBv was the older comparisons used to illustrate different levels of sound name for the same unit. It was changed to avoid conpressure. Sound pressure is a field quantity, therefore the fusion with dBV. The dBu is a root mean square (RMS) measurement of voltage that uses as its reference approxfield version of the unit definition is used: imately 0.775 VRMS. Chosen for historical reasons, the ( ) prms reference value is the voltage level which delivers 1 mW Lp = 20 log10 pref dB of power in a 600 ohm resistor, which used to be the stanwhere pᵣₑ is equal to the standard reference dard reference impedance in telephone circuits. sound pressure level of 20 micropascals in air or 1 micropascal in water. Optics The human ear has a large dynamic range in audio reception. The ratio of the sound intensity that causes perma- In an optical link, if a known amount of optical power, in nent damage during short exposure to the quietest sound dBm (referenced to 1 mW), is launched into a fiber, and
7.1.5
Uses
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the losses, in dB (decibels), of each electronic component (e.g., connectors, splices, and lengths of fiber) are known, the overall link loss may be quickly calculated by addition and subtraction of decibel quantities.[31]
In cases such as this, where the numerical value of the reference is explicitly and exactly stated, the decibel measurement is called an “absolute” measurement, in the sense that the exact value of the measured quantity can In spectrometry and optics, the blocking unit used to be recovered using the formula given earlier. If the numerical value of the reference is not explicitly stated, as measure optical density is equivalent to −1 B. in the dB gain of an amplifier, then the decibel measurement is purely relative. Video and digital imaging The SI does not permit attaching qualifiers to units, whether as suffix or prefix, other than standard SI preIn connection with video and digital image sensors, deci- fixes. Therefore, even though the decibel is accepted for bels generally represent ratios of video voltages or dig- use alongside SI units, the practice of attaching a suffix to itized light levels, using 20 log of the ratio, even when the basic dB unit, forming compound units such as dBm, the represented optical power is directly proportional to dBu, dBA, etc., is not.[13] The proper way, according to the voltage or level, not to its square, as in a CCD imager the IEC 60027-3,[12] is either as Lx (re xᵣₑ ) or as Lx/xᵣₑ , where response voltage is linear in intensity.[32] Thus, a where x is the quantity symbol and xᵣₑ is the value of the camera signal-to-noise ratio or dynamic range of 40 dB reference quantity, e.g., LE (re 1 μV/m) = LE/₍₁ μV/ ₎ for represents a power ratio of 100:1 between signal power the electric field strength E relative to 1 μV/m reference and noise power, not 10,000:1.[33] Sometimes the 20 log value. ratio definition is applied to electron counts or photon counts directly, which are proportional to intensity with- Outside of documents adhering to SI units, the practice out the need to consider whether the voltage response is is very common as illustrated by the following examples. There is no general rule, with various discipline-specific linear.[34] practices. Sometimes the suffix is a unit symbol (“W”, However, as mentioned above, the 10 log intensity con- extquotedblK”, extquotedblm”), sometimes it’s a translitvention prevails more generally in physical optics, includ- eration of a unit symbol (“uV” instead of μV for micro ing fiber optics, so the terminology can become murky volt), sometimes it’s an acronym for the units name (“sm” between the conventions of digital photographic technol- for m2 , “m” for mW), other times it’s a mnemonic for ogy and physics. Most commonly, quantities called “dy- the type of quantity being calculated (“i” for antenna gain namic range” or “signal-to-noise” (of the camera) would w.r.t. an isotropic antenna, extquotedblλ extquotedbl for be specified in 20 log dBs, but in related contexts (e.g. anything normalized by the EM wavelength), or otherattenuation, gain, intensifier SNR, or rejection ratio) the wise a general attribute or identifier about the nature of term should be interpreted cautiously, as confusion of the the quantity (“A” for A-weighted sound pressure level). two units can result in very large misunderstandings of the The suffix is often connected with a dash (dB-Hz), with value. a space (dB HL), with no intervening character (dBm), Photographers also often use an alternative base-2 log or enclosed in parentheses, dB(sm). unit, the f-stop, and in software contexts these image level ratios, particularly dynamic range, are often loosely re- Voltage ferred to by the number of bits needed to represent the quantity, such that 60 dB (digital photographic) is roughly Since the decibel is defined with respect to power, not equal to 10 f-stops or 10 bits, since 103 is nearly equal to amplitude, conversions of voltage ratios to decibels must 210 . square the amplitude, or use the factor of 20 instead of 10, as discussed above.
7.1.6 Suffixes and reference values
dBV
dB(VRMS) – voltage relative to 1 volt, regardSuffixes are commonly attached to the basic dB unit in less of impedance.[2] order to indicate the reference value against which the decibel measurement is taken. For example, dBm indidBu or dBv cates power measurement relative to 1 milliwatt.
7.1. DECIBEL
169 Acoustics
Probably the most common usage of “decibels” in reference to sound level is dB SPL, sound pressure level referenced to the nominal threshold of human hearing:[38] The measures of pressure (a field quantity) use the factor A schematic showing the relationship between dBu (the voltage of 20, and the measures of power (e.g. dB SIL and dB source) and dBm (the power dissipated as heat by the 600 Ω SWL) use the factor of 10. resistor)
√ RMS voltage relative to 0.6 V ≈ 0.7746 V ≈ −2.218 dBV .[2] Originally dBv, it was changed to dBu to avoid confusion with dBV.[35] The “v” comes from “volt”, while “u” comes from “unloaded”. dBu can be used regardless of impedance, but is derived from a 600 Ω load dissipating 0 dBm (1 mW). The reference √ voltage comes from the computation V = 600 Ω · 0.001 W . In professional audio, equipment may be calibrated to indicate a “0” on the VU meters some finite time after a signal has been applied at an amplitude of +4 dBu. Consumer equipment will more often use a much lower “nominal” signal level of −10 dBV.[36] Therefore, many devices offer dual voltage operation (with different gain or “trim” settings) for interoperability reasons. A switch or adjustment that covers at least the range between +4 dBu and −10 dBV is common in professional equipment.
dB SPL dB SPL (sound pressure level) – for sound in air and other gases, relative to 20 micropascals (μPa) = 2×10−5 Pa, approximately the quietest sound a human can hear. For sound in water and other liquids, a reference pressure of 1 μPa is used.[39] An RMS sound pressure of one pascal corresponds to a level of 94 dB SPL. dB SIL dB sound intensity level – relative to 10−12 W/m2 , which is roughly the threshold of human hearing in air. dB SWL dB sound power level – relative to 10−12 W. dB(A), dB(B), and dB(C)
dBmV dB(mVRMS) – voltage relative to 1 millivolt across 75 Ω.[37] Widely used in cable television networks, where the nominal strength of a single TV signal at the receiver terminals is about 0 dBmV. Cable TV uses 75 Ω coaxial cable, so 0 dBmV corresponds to −78.75 dBW (−48.75 dBm) or ~13 nW. dBμV or dBuV dB(μVRMS) – voltage relative to 1 microvolt. Widely used in television and aerial amplifier specifications. 60 dBμV = 0 dBmV.
These symbols are often used to denote the use of different weighting filters, used to approximate the human ear’s response to sound, although the measurement is still in dB (SPL). These measurements usually refer to noise and noisome effects on humans and animals, and are in widespread use in the industry with regard to noise control issues, regulations and environmental standards. Other variations that may be seen are dBA or dBA. According to ANSI standards, the preferred usage is to write LA = x dB. Nevertheless, the units dBA and dB(A) are still commonly used as a shorthand for A-weighted measurements. Compare dBc, used in telecommunications.
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dB HL or dB hearing level is used in audiograms as a measure of hearing loss. The reference level varies with frequency according to a minimum audibility curve as defined in ANSI and other standards, such that the resulting audiogram shows deviation from what is regarded as 'normal' hearing.
dB(Z) – decibel relative to Z = 1 mm6 m−3 :[43] energy of reflectivity (weather radar), related to the amount of transmitted power returned to the radar receiver. Values above 15–20 dBZ usually indicate falling precipitation.[44]
dB Q is sometimes used to denote weighted noise level, dBsm commonly using the ITU-R 468 noise weighting dB(m2 ) – decibel relative to one square meter: measure of the radar cross section (RCS) of a target. The power reflected by the target is Audio electronics proportional to its RCS. “Stealth” aircraft and insects have negative RCS measured in dBsm, dBm large flat plates or non-stealthy aircraft have positive values.[45] dB(mW) – power relative to 1 milliwatt. In audio and telephony, dBm is typically referenced Radio power, energy, and field strength relative to a 600 ohm impedance,[40] while in radio frequency work dBm is typically referdBc dBc – relative to carrier—in telecommunications, enced relative to a 50 ohm impedance.[41] this indicates the relative levels of noise or sideband power, compared with the carrier power. Compare dBFS dBC, used in acoustics. dB(full scale) – the amplitude of a signal compared with the maximum which a device can handle before clipping occurs. Full-scale may be defined as the power level of a full-scale sinusoid or alternatively a full-scale square wave. A signal measured with reference to a full-scale sine-wave will appear 3dB weaker when referenced to a full-scale square wave, thus: 0 dBFS(ref=fullscale sine wave) = −3 dBFS(ref=fullscale square wave). dBTP dB(true peak) - peak amplitude of a signal compared with the maximum which a device can handle before clipping occurs.[42] In digital systems, 0 dBTP would equal the highest level (number) the processor is capable of representing. Measured values are always negative or zero, since they are less than or equal to full-scale.
dBJ dB(J) – energy relative to 1 joule. 1 joule = 1 watt second = 1 watt per hertz, so power spectral density can be expressed in dBJ. dBm dB(mW) – power relative to 1 milliwatt. Traditionally associated with the telephone and broadcasting industry to express audio-power levels referenced to one milliwatt of power, normally with a 600 ohm load, which is a voltage level of 0.775 volts or 775 millivolts. This is still commonly used to express audio levels with professional audio equipment. In the radio field, dBm is usually referenced to a 50 ohm load, with the resultant voltage being 0.224 volts. dBμV/m or dBuV/m dB(μV/m) – electric field strength relative to 1 microvolt per meter. Often used to specify the signal strength from a television broadcast at a receiving site (the signal measured at the antenna output will be in dBμV). dBf dB(fW) – power relative to 1 femtowatt.
Radar
dBW dB(W) – power relative to 1 watt.
dBZ
dBk dB(kW) – power relative to 1 kilowatt.
7.1. DECIBEL
171
Antenna measurements
Hz. Commonly used in link budget calculations. Also used in carrier-to-noise-density ratio (not to be confused with carrier-to-noise ratio, in dB).
dBi dB(isotropic) – the forward gain of an antenna compared with the hypothetical isotropic antenna, which uniformly distributes energy in all directions. Linear polarization of the EM field is assumed unless noted otherwise.
dBov or dBO dB(overload) – the amplitude of a signal (usually audio) compared with the maximum which a device can handle before clipping occurs. Similar to dBFS, but also applicable to analog systems.
dBd dB(dipole) – the forward gain of an antenna compared with a half-wave dipole antenna. 0 dBd = 2.15 dBi
dBr dB(relative) – simply a relative difference from something else, which is made apparent in context. The difference of a filter’s response to nominal levels, for instance.
dBiC dB(isotropic circular) – the forward gain of an antenna compared to a circularly polarized isotropic antenna. There is no fixed conversion rule between dBiC and dBi, as it depends on the receiving antenna and the field polarization.
dBrn dB above reference noise. See also dBrnC dBrnC dBrnC represents an audio level measurement, typically in a telephone circuit, relative to the circuit noise level, with the measurement of this level frequency-weighted by a standard C-message weighting filter. The Cmessage weighting filter was chiefly used in North America. The Psophometric filter is used for this purpose on international circuits. See Psophometric weighting to see a comparison of frequency response curves for the Cmessage weighting and Psophometric weighting filters.[47]
dBq dB(quarterwave) – the forward gain of an antenna compared to a quarter wavelength whip. Rarely used, except in some marketing material. 0 dBq = −0.85 dBi dBsm dB(m2 ) – decibel relative to one square meter: measure of the antenna effective area.[46] dBm−1 dB(m−1 ) – decibel relative to reciprocal of meter: measure of the antenna factor.
dBK dB(K) – decibels relative to kelvin: Used to express noise temperature.[48] dB/K
Other measurements dB-Hz dB(Hz) – bandwidth relative to one hertz. E.g., 20 dB-Hz corresponds to a bandwidth of 100
dB(K−1 ) – decibels relative to reciprocal of kelvin [49] -- not decibels per kelvin: Used for the G/T factor, a figure of merit utilized in satellite communications, relating the antenna gain G to the receiver system noise equivalent temperature T.[50][51]
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7.1.7 Related units mBm mB(mW) – power relative to 1 milliwatt, in millibels (one hundredth of a decibel). 100 mBm = 1dBm. This unit is in the Wi-Fi drivers of the Linux kernel[52] and the regulatory domain sections.[53] Np or cNp Another closely related unit is the neper (Np) or centineper (cNp). Like the decibel, the neper is a unit of level.[54] The linear approximation 1cNp =~ 1% for small percentage differences is widely used finance. 1 Np = 20 log10 e dB ≈ 8.685889638 dB
7.1.8 Fractions Attenuation constants, in fields such as optical fiber communication and radio propagation path loss, are often expressed as a fraction or ratio to distance of transmission. dB/m means decibels per meter, dB/mi is decibels per mile, for example. These quantities are to be manipulated obeying the rules of dimensional analysis, e.g., a 100-meter run with a 3.5 dB/km fiber yields a loss of 0.35 dB = 3.5 dB/km × 0.1 km.
7.1.9 See also • Apparent magnitude • Cent in music • dB drag racing • Equal-loudness contour • Noise (environmental) • Phon • Richter magnitude scale • Signal noise • Sone
7.1.10
Notes and references
[1] IEEE Standard 100 Dictionary of IEEE Standards Terms, Seventh Edition, The Institute of Electrical and Electronics Engineering, New York, 2000; ISBN 0-7381-2601-2; page 288 [2] Analog Devices : Virtual Design Center : Interactive Design Tools : Utilities : VRMS / dBm / dBu / dBV calculator [3] “ISO 80000-3:2006”. International Organization for Standardization. Retrieved 20 July 2013. [4] Johnson, Kenneth Simonds (1944). Transmission Circuits for Telephonic Communication: Methods of Analysis and Design. New York: D. Van Nostrand Co. p. 10. [5] Don Davis and Carolyn Davis (1997). Sound system engineering (2nd ed.). Focal Press. p. 35. ISBN 978-0-24080305-0. [6] Bell Labs (1925). Transmission Circuits for Telephonic Communication. [7] R. V. L. Hartley (Dec 1928). extquotedbl'TU' becomes 'Decibel' extquotedbl. Bell Laboratories Record (AT&T) 7 (4): 137–139. [8] Martin, W. H. (January 1929). “DeciBel—The New Name for the Transmission Unit”. Bell System Technical Journal 8 (1). [9] 100 Years of Telephone Switching, p. 276, Robert J. Chapuis, Amos E. Joel, 2003 [10] William H. Harrison (1931). “Standards for Transmission of Speech”. Standards Yearbook (National Bureau of Standards, U. S. Govt. Printing Office) 119 [11] Consultative Committee for Units, Meeting minutes, Section 3 [12] “Letter symbols to be used in electrical technology – Part 3: Logarithmic and related quantities, and their units”, IEC 60027-3 Ed. 3.0, International Electrotechnical Commission, 19 July 2002. [13] Thompson, A. and Taylor, B. N. sec 8.7, “Logarithmic quantities and units: level, neper, bel”, Guide for the Use of the International System of Units (SI) 2008 Edition, NIST Special Publication 811, 2nd printing (November 2008), SP811 PDF [14] “International Standard CEI-IEC 27-3 Letter symbols to be used in electrical technology Part 3: Logarithmic quantities and units”. International Electrotechnical Commission.
7.1. DECIBEL
[15] Brian C.J. Moore (1995). Hearing. Academic Press. p. 11. ISBN 9780080533865. [16] Mark, James E., Physical properties of polymers handbook, Springer, 2007, p 1025: extquotedbl… the decibel represents a reduction in power of 1.258 times.” [17] Yost, William, Fundamentals of hearing: an introduction, Holt, Rinehart and Winston, 1985, p 206: extquotedbl… a pressure ratio of 1.122 equals +1.0 dB”
173
[33] Francis T. S. Yu and Xiangyang Yang (1997). Introduction to optical engineering. Cambridge University Press. pp. 102–103. ISBN 978-0-521-57493-8. [34] Junichi Nakamura (2006). “Basics of Image Sensors”. In Junichi Nakamura. Image sensors and signal processing for digital still cameras. CRC Press. pp. 79–83. ISBN 978-0-8493-3545-7.
[18] Fedor Mitschke, Fiber Optics: Physics and Technology, Springer, 2010 ISBN 3642037038.
[35] What is the difference between dBv, dBu, dBV, dBm, dB SPL, and plain old dB? Why not just use regular voltage and power measurements? – rec.audio.pro Audio Professional FAQ
[19] David M. Pozar (2005). Microwave Engineering (3rd ed.). Wiley. p. 63. ISBN 978-0-471-44878-5.
[36] deltamedia.com. “DB or Not DB”. Deltamedia.com. Retrieved 2013-09-16.
[20] Fiber Optics (Springer, 2010)
[37] The IEEE Standard Dictionary of Electrical and Electronics terms (6th ed.). IEEE. 1996 [1941]. ISBN 1-55937833-6.
[21] C W Horton, “The bewildering decibel”, Elec. Eng., 73, 550-555 (1954). [22] C S Clay (1999), Underwater sound transmission and SI units, J Acoust Soc Am 106, 3047 [23] R Hickling (1999), Noise Control and SI Units, J Acoust Soc Am 106, 3048 [24] D M F Chapman (2000), Decibels, SI units, and standards, J Acoust Soc Am 108, 480 [25] Nicholas P. Cheremisinoff (1996) Noise Control in Industry: A Practical Guide, Elsevier, 203 pp, p. [26] Andrew Clennel Palmer (2008), Dimensional Analysis and Intelligent Experimentation, World Scientific, 154 pp, p.13
[38] Jay Rose (2002). Audio postproduction for digital video. Focal Press,. p. 25. ISBN 978-1-57820-116-7. [39] Morfey, C. L. (2001). Dictionary of Acoustics. Academic Press, San Diego. [40] Bigelow, Stephen. Understanding Telephone Electronics. Newnes. p. 16. ISBN 978-0750671750. [41] Carr, Joseph (2002). RF Components and Circuits. Newnes. pp. 45–46. ISBN 978-0750648448. [42] ITU-R BS.1770 [43] “Glossary: D’s”. National Weather Service. Retrieved 2013-04-25.
[27] J.C. Gibbings, Dimensional Analysis, p.37, Springer, 2011 ISBN 1849963177.
[44] “Radar FAQ from WSI”. Archived from the original on 2008-05-18. Retrieved 2008-03-18.
[28] R J Peters, Acoustics and Noise Control, Routledge, Nov 12, 2013, 400 pages
[45] “Definition at Everything2”. Retrieved 2008-08-06.
[29] “Electronic Engineer’s Handbook” by Donald G. Fink, Editor-in-Chief ISBN 0-07-020980-4 Published by McGraw Hill, page 19-3
[46] EW 102: A Second Course in Electronic Warfare - David Adamy - Google Livros. Books.google.com.br. Retrieved 2013-09-16.
[30] National Institute on Deafness and Other Communications Disorders, Noise-Induced Hearing Loss (National Institutes of Health, 2008).
[47] dBrnC is defined on page 230 in “Engineering and Operations in the Bell System,” (2ed), R.F. Rey (technical editor), copyright 1983, AT&T Bell Laboratories, Murray Hill, NJ, ISBN 0-932764-04-5
[31] Bob Chomycz (2000). Fiber optic installer’s field manual. McGraw-Hill Professional. pp. 123–126. ISBN 978-007-135604-6.
[48] Satellite Communication: Concepts And Applications K. N. Raja Rao - Google Livros. Books.google.com.br. 2013-01-31. Retrieved 2013-09-16.
[32] Stephen J. Sangwine and Robin E. N. Horne (1998). The Colour Image Processing Handbook. Springer. pp. 127– 130. ISBN 978-0-412-80620-9.
[49] Comprehensive Glossary of Telecom Abbreviations and Acronyms - Ali Akbar Arabi - Google Livros. Books.google.com.br. Retrieved 2013-09-16.
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[50] The Digital Satellite TV Handbook - Mark E. Long - Google Livros. Books.google.com.br. Retrieved 2013-09-16. [51] Reference Data for Engineers: Radio, Electronics, Computers and Communications - Mac E. Van Valkenburg Google Livros. Books.google.com.br. 2001-10-19. Retrieved 2013-09-16. [52] setting the TX power for a Wi-Fi device in Linux showing units in mBm [53] kernel notification of change in regulatory domain showing units in mBm [54] “ISO 80000-3:2006”. International Organization for Standardization. Retrieved 20 July 2013.
7.1.11 External links • What is a decibel? With sound files and animations • Conversion of sound level units: dBSPL or dBA to sound pressure p and sound intensity J • OSHA Regulations on Occupational Noise Exposure
7.2 Noise (electronics)
CHAPTER 7. THE DECIBEL trical signal, a characteristic of all electronic circuits.[1] Noise generated by electronic devices varies greatly, as it can be produced by several different effects. Thermal noise is unavoidable at non-zero temperature (see fluctuation-dissipation theorem), while other types depend mostly on device type (such as shot noise,[1][2] which needs steep potential barrier) or manufacturing quality and semiconductor defects, such as conductance fluctuations, including 1/f noise. In communication systems, noise is an error or undesired random disturbance of a useful information signal in a communication channel. The noise is a summation of unwanted or disturbing energy from natural and sometimes man-made sources. Noise is, however, typically distinguished from interference, (e.g. cross-talk, deliberate jamming or other unwanted electromagnetic interference from specific transmitters), for example in the signal-to-noise ratio (SNR), signal-to-interference ratio (SIR) and signal-to-noise plus interference ratio (SNIR) measures. Noise is also typically distinguished from distortion, which is an unwanted systematic alteration of the signal waveform by the communication equipment, for example in the signal-to-noise and distortion ratio (SINAD). In a carrier-modulated passband analog communication system, a certain carrier-to-noise ratio (CNR) at the radio receiver input would result in a certain signalto-noise ratio in the detected message signal. In a digital communications system, a certain E /N 0 (normalized signal-to-noise ratio) would result in a certain bit error rate (BER).
This article is about fundamental noise processes. For noise arising from outside sources, see electromagnetic While noise is generally unwanted, it can serve a useful compatibility and electromagnetic interference. In electronics, noise is a random fluctuation in an elec- purpose in some applications, such as random number generation or dithering.
7.2.1
Noise types
Thermal noise Main article: Johnson–Nyquist noise Johnson–Nyquist noise[1] (sometimes thermal, Johnson or Nyquist noise) is unavoidable, and generated by the random thermal motion of charge carriers (usually electrons), inside an electrical conductor, which happens regardless of any applied voltage. Analog display of random fluctuations in voltage: e.g., pink noise.
Thermal noise is approximately white, meaning that its power spectral density is nearly equal throughout the
7.2. NOISE (ELECTRONICS) frequency spectrum. The amplitude of the signal has very nearly a Gaussian probability density function. A communication system affected by thermal noise is often modeled as an additive white Gaussian noise (AWGN) channel.
175 sively within the material; the electrons do not have discrete arrivial times. Shot noise has been demonstrated in mesoscopic resistors when the size of the resistive element becomes shorter than the electron-phonon scattering length.[3]
The root mean square (RMS) voltage due to thermal noise vn , generated in a resistance R (ohms) over bandwidth Flicker noise Δf (hertz), is given by Main article: Flicker noise vn =
√
4kB T R∆f
Flicker noise, also known as 1/f noise, is a signal or prowhere kB is Boltzmann’s constant (joules per kelvin) and cess with a frequency spectrum that falls off steadily into the higher frequencies, with a pink spectrum. It occurs T is the resistor’s absolute temperature (kelvin). in almost all electronic devices, and results from a variety As the amount of thermal noise generated depends upon of effects, though always related to a direct current. the temperature of the circuit, very sensitive circuits such as preamplifiers in radio telescopes are sometimes cooled in liquid nitrogen to reduce the noise level. Intermodulation noise Shot noise
This type of noise is caused when signals of different frequencies share the same medium.
Main article: Shot noise Crosstalk Shot noise in electronic devices results from unavoidable random statistical fluctuations of the electric current when the charge carriers (such as electrons) traverse a gap. The current is a flow of discrete charges, and the fluctuation in the arrivals of those charges creates shot noise. Shot noise is similar to the noise created by rain falling on a tin roof. The flow of rain may be relatively constant, but the raindrops arrive discretely. The root-mean-square value of the shot noise current in is given by the Schottky formula √ in = 2Iq∆B where I is the DC current, q is the charge of an electron, and ΔB is the bandwidth in hertz. The shot noise assumes independent arrivals. Vacuum tubes have shot noise because the electrons randomly leave the cathode and arrive at the anode (plate). A tube may not exhibit the full shot noise effect: the presence of a space charge tends to smooth out the arrival times (and thus reduce the randomness of the current).
This is unwanted coupling of signals. Impulse noise short peak of noise example Lightning, electrical disturbances,flaws in communication system Interference Contamination by various signals from human sources example Power lines transmitters It does not disappear when signal is switched off. Burst noise Main article: Burst noise
Burst noise consists of sudden step-like transitions between two or more levels (non-Gaussian), as high as several hundred microvolts, at random and unpredictable Conductors and resistors typically do not exhibit shot times. Each shift in offset voltage or current lasts for sevnoise because the electrons thermalize and move diffu- eral milliseconds, and the intervals between pulses tend
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CHAPTER 7. THE DECIBEL
to be in the audio range (less than 100 Hz), leading to the fluorescent lamps cause industrial noise. These noises are term popcorn noise for the popping or crackling sounds it produced by the discharge present in all these operations. produces in audio circuits. Transit-time noise If the time taken by the electrons from traveling from emitter to collector becomes comparable to the period of the signal being amplified, that is, at frequencies above VHF and beyond, so-called transit-time effect takes place and noise input admittance of the transistor increases. From the frequency at which this effect becomes significant it goes on increasing with frequency and quickly dominates over other terms. Avalanche noise Avalanche noise is the noise produced when a junction diode is operated at the onset of avalanche breakdown, a semiconductor junction phenomenon in which carriers in a high voltage gradient develop sufficient energy to dislodge additional carriers through physical impact, creating ragged current flows.
Extraterrestrial noise Noise from outside the Earth includes: Solar noise Noise that originates from the Sun is called solar noise. Under normal conditions there is constant radiation from the Sun due to its high temperature. Electrical disturbances such as corona discharges, as well as sunspots can produce additional noise. Cosmic noise Main article: Cosmic noise Distant stars generate noise called cosmic noise. While these stars are too far away to individually affect terrestrial communications systems, their large number leads to appreciable collective effects. Cosmic noise has been observed in a range from 8 MHz to 1.43 GHz. Reduction of noise coupling
7.2.2 Coupled noise
In many cases noise found on a signal in a circuit is unwanted. When creating a circuit, one usually wants a See also: Electromagnetic compatibility true output of what the circuit has accomplished. There are many different noise reduction techniques that can Energy external of the receiver can couple noise, also by change a noisy altered output signal to a more theoretical energy conversion. Generally this is done by fundamental output signal. interaction, in electronics mainly by Inductive coupling and/or capacitive coupling. 1. Faraday cage – A Faraday cage is a good way to reduce the overall noise in a complete circuit. The Atmospheric noise (static noise) Faraday cage can be thought of as an enclosure that separates the complete circuit from outside power Main article: Atmospheric noise lines and any other signal that may alter the true signal. A Faraday cage will usually block out most electromagnetic and electrostatic noise. This noise is also called static noise and it is the natural source of disturbance caused by lightning discharge of 2. Capacitive coupling – A current through two resisin thunderstorm and the natural(electrical) disturbances tors, or any other type of conductor, close to each occurring in the nature. other in a circuit can create unwanted capacitive coupling. If this happens an AC signal from one part of the circuit can be accidentally picked up in Industrial noise another part. The two resistors (conductors) act like Sources such as automobiles, aircraft, ignition eleca capacitor thus transferring AC signals. There may tric motors and switching gear, High voltage wires and be other reasons for which capacitive coupling is
7.2. NOISE (ELECTRONICS)
177
wanted but then it would not be thought of as elec- 7.2.3 tronic noise. 3. Ground loops – When grounding a circuit, it is important to avoid ground loops. Ground loops occur when there is a voltage drop between the two ground potentials. Since ground is thought of as 0V, the presence of a voltage is undesirable at any point of a ground bus. If this is the case, it would not be a true ground. A good way to fix this is to bring all the ground wires to the same potential in a ground bus. 4. Shielding cables – In general, using shielded cables to protect the wires from unwanted noise frequencies in a sensitive circuit is good practice. A shielded wire can be thought of as a small Faraday cage for a specific wire as it uses a plastic or rubber enclosing the true wire. Just outside of the rubber/plastic covering is a conductive metal that intercepts any noise signal. Because the conductive metal is grounded, the noise signal runs straight to ground before ever getting to the true wire. It is important to ground the shield at only one end to avoid a ground loop on the shield.
Quantification
The noise level in an electronic system is typically measured as an electrical power N in watts or dBm, a root mean square (RMS) voltage (identical to the noise standard deviation) in volts, dBμV or a mean squared error (MSE) in volts squared. Noise may also be characterized by its probability distribution and noise spectral density N 0 (f) in watts per hertz. A noise signal is typically considered as a linear addition to a useful information signal. Typical signal quality measures involving noise are signal-to-noise ratio (SNR or S/N), signal-to-quantization noise ratio (SQNR) in analog-to-digital conversion and compression, peak signal-to-noise ratio (PSNR) in image and video coding, E /N 0 in digital transmission, carrier to noise ratio (CNR) before the detector in carrier-modulated systems, and noise figure in cascaded amplifiers. Noise is a random process, characterized by stochastic properties such as its variance, distribution, and spectral density. The spectral distribution of noise can vary with frequency, so its power density is measured in watts per hertz (W/Hz). Since the power in a resistive element is proportional to the square of the voltage across it, noise voltage (density) can be described by taking the square root of the noise power density, resulting in volts per √ root hertz ( V/ Hz ). Integrated circuit devices, such as operational amplifiers commonly quote equivalent input noise level in these terms (at room temperature).
5. Twisted pair wiring – Twisting wires very tightly together in a circuit will dramatically reduce electromagnetic noise. Twisting the wires decreases the loop size in which a magnetic field can run through to produce a current between the wires. Even if the wires are twisted very tightly, there may still be small loops somewhere between them, but because they are twisted the magnetic field going through the Noise power is measured in watts or decibels (dB) relative smaller loops induces a current flowing in opposite to a standard power, usually indicated by adding a suffix ways in each wire and thus cancelling them out. after dB. Examples of electrical noise-level measurement units are dBu, dBm0, dBrn, dBrnC, and dBrn(f 1 − f 2 ), 6. Notch filters – Notch filters or band-rejection filters dBrn(144-line). are essential when eliminating a specific noise frequency. For example, in most cases the power lines within a building run at 60 Hz. Sometimes a sensitive circuit will pick up this 60 Hz noise through some unwanted antenna (could be as simple as a wire in the circuit). Running the output through a notch filter at 60 Hz will amplify the desired signal without amplifying the 60 Hz noise. So in a sense the noise will be lost at the output of the filter.
Noise levels are usually viewed in opposition to signal levels and so are often seen as part of a signal-to-noise ratio (SNR). Telecommunication systems strive to increase the ratio of signal level to noise level in order to effectively transmit data. In practice, if the transmitted signal falls below the level of the noise (often designated as the noise floor) in the system, data can no longer be decoded at the receiver. Noise in telecommunication systems is a product of both internal and external sources to the system.
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7.2.4 Dither
• Scherz, Paul. (2006, Nov 14) Practical Electronics for Inventors. ed. McGraw-Hill.
If the noise source is correlated with the signal, such as in the case of quantisation error, the intentional introduction of additional noise, called dither, can reduce overall 7.2.8 Further reading noise in the bandwidth of interest. This technique allows • Sh. Kogan (1996). Electronic Noise and Fluctuaretrieval of signals below the nominal detection threshtions in Solids. Cambridge University Press. ISBN old of an instrument. This is an example of stochastic 0-521-46034-4. resonance.
7.2.5 See also • Discovery of cosmic microwave background radiation • Generation–recombination noise
7.2.9
External links
• Active Filter (Sallen & Key) Noise Study
7.3 Switched capacitor
• Matched filter for noise reduction in modems A switched capacitor is an electronic circuit element • Noise reduction and noise cancellation for audio and used for discrete time signal processing. It works by movimages ing charges into and out of capacitors when switches are • Error correction for digital signals subject to noise. opened and closed. Usually, non-overlapping signals are used to control the switches, so that not all switches are • Phonon noise closed simultaneously. Filters implemented with these elements are termed “switched-capacitor filters,” and depend only on the ratios between capacitances. This 7.2.6 Notes makes them much more suitable for use within integrated circuits, where accurately specified resistors and capaci[1] Motchenbacher, C. D.; Connelly, J. A. (1993). Low-noise tors are not economical to construct.[1] electronic system design. Wiley Interscience. [2] Kish, L. B.; Granqvist, C. G. (November 2000). “Noise in nanotechnology”. Microelectronics Reliability (Elsevier) 40 (11): 1833–1837. doi:10.1016/S00262714(00)00063-9.
7.3.1
The switched capacitor resistor
[3] Steinbach, Andrew; Martinis, John; Devoret, Michel (1996-05-13). “Observation of Hot-Electron Shot Noise in a Metallic Resistor”. Phys. Rev. Lett. 76 (20): 38.6–38.9. Bibcode:1996PhRvL..76...38M. doi:10.1103/PhysRevLett.76.38.
7.2.7 References • White noise calculator, thermal noise - Voltage in microvolts, conversion to noise level in dBu and dBV and vice versa •
This article incorporates public domain mate- Switched-capacitor resistor rial from the General Services Administration document “Federal Standard 1037C” (in support of MIL- The simplest switched capacitor (SC) circuit is the STD-188). switched capacitor resistor, made of one capacitor C and
7.3. SWITCHED CAPACITOR
179
two switches S1 and S2 which connect the capacitor with So the equivalent resistance R (i.e., the voltage–current a given frequency alternately to the input and output of relationship) is: the SC. Each switching cycle transfers a charge q from the input to the output at the switching frequency f . ReV 1 call that the charge q on a capacitor C with a voltage V R= = . I CS f between the plates is given by: Thus, the SC behaves like a resistor whose value depends on capacitance CS and switching frequency f. q = CV where V is the voltage across the capacitor. Therefore, when S1 is closed while S2 is open, the charge stored in the capacitor CS is:
qIN = CS VIN . When S2 is closed, some of that charge is transferred out of the capacitor, after which the charge that remains in capacitor CS is:
qOUT = CS VOUT .
The SC resistor is used as a replacement for simple resistors in integrated circuits because it is easier to fabricate reliably with a wide range of values. It also has the benefit that its value can be adjusted by changing the switching frequency (i.e., it is a programmable resistance). See also: operational amplifier applications. q = CV This same circuit can be used in discrete time systems (such as analog to digital converters) as a track and hold circuit. During the appropriate clock phase, the capacitor samples the analog voltage through switch one and in the second phase presents this held sampled value to an electronic circuit for processing.
7.3.2 The Parasitic Sensitive Integrator
Thus, the charge moved out of the capacitor to the output is:
q = qIN − qOUT = CS (VIN − VOUT ) Because this charge q is transferred at a rate f, the rate of transfer of charge per unit time is:
I = qf.
A Simple Switched Capacitor Parasitic-Sensitive Integrator
Often switched capacitor circuits are used to provide acNote that we use I, the symbol for electric current, for curate voltage gain and integration by switching a samthis quantity. This is to demonstrate that a continuous pled capacitor onto an op-amp with a capacitor Cf b in transfer of charge from one node to another is equivalent feedback. One of the earliest of these circuits is the to a current. Substituting for q in the above, we have: parasitic-Sensitive integrator developed by the Czech engineer Bedrich Hosticka.[2] Let us analyze what happens in this case. Denote by T = 1/f the switching period. I = CS (VIN − VOUT )f Recall that in capacitors Let V be the voltage across the SC from input to output. So:
V = VIN − VOUT .
charge = capacitance × voltage Then, at the instant when S1 opens and S2 closes, we have the following:
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CHAPTER 7. THE DECIBEL
1) Because Cs has just charged:
Use In Discrete-Time Systems
The delaying parasitic insensitive integrator has a wide use in discrete time electronic circuits such as biquad filQs (t) = Cs · Vs (t) ters, anti-alias structures, and delta sigma data converters. 2) Because the feedback cap, Cf b , is suddenly charged This circuit implements the following z-domain function: with that much charge (by the opamp, which seeks a virtual short circuit between its inputs): 1 H(z) = z−1 Qf b (t) = Qs (t − T ) + Qf b (t − T )
7.3.4
Now dividing 2) by Cf b :
Vf b (t) =
The Multiplying Digital to Analog Converter
Qs (t − T ) + Vf b (t − T ) Cf b
And inserting 1):
Vf b (t) =
Cs · Vs (t − T ) + Vf b (t − T ) Cf b
This last equation represents what is going on in Cf b - it increases (or decreases) its voltage each cycle according to the charge that is being “pumped” from Cs (due to the A 1.5 bit Multiplying Digital to Analog Converter op-amp). However, there is a more elegant way to formulate this fact if T is very short. Let us introduce dt ← T and dVf b ← Vf b (t)−Vf b (t−dt) and rewrite the last equation divided by dt:
dVf b (t) Cs =f · Vs (t) dt Cf b
One useful characteristic of switched capacitor circuits is that they can be used to perform many circuit tasks at the same time, which is difficult with non-discrete time components. The multiplying digital to analog converter (MDAC) is an example as it can take an analog input, add a digital value to it, and multiply this by some factor based on the capacitor ratios. The output of the MDAC is given by the following:
Therefore, the op-amp output voltage takes the form:
VOU T (t) = −Vf b (t) = −
1 1 f Cs Cf b
VOut =
∫
Vi · (C1 + C2 ) − (d − 1) · Vr · C2 + Vos · (C1 + C2 + Cp ) C1 +
Vs (t)dt
(C1 +C2 +Cp ) A
The MDAC is a common component in modern pipeline Note that this is an integrator with an “equivalent resis- analog to digital converters as well as other precision ana1 tance” Req = f C . This allows its on-line or runtime log electronics and was first created in the form[3]above by s adjustment (if we manage to make the switches oscillate Stephen Lewis and others at Bell Laboratories. according to some signal given by e.g. a microcontroller).
7.3.5 7.3.3 The Parasitic Insensitive Integrator
See also
• Nyquist–Shannon sampling theorem
7.4. H BRIDGE • Aliasing • Switched-mode power supply • Charge pump
181
7.4.1 General H bridges are available as integrated circuits, or can be built from discrete components.[1]
The term H bridge is derived from the typical graphical representation of such a circuit. An H bridge is built 7.3.6 References with four switches (solid-state or mechanical). When the switches S1 and S4 (according to the first figure) are [1] Switched Capacitor Circuits, Swarthmore College course closed (and S2 and S3 are open) a positive voltage will be notes, accessed 2009-05-02 applied across the motor. By opening S1 and S4 switches [2] B. Hosticka, R. Brodersen, P. Gray, “MOS Sampled Data and closing S2 and S3 switches, this voltage is reversed, Recursive Filters. ng Switched Capacitor Integrators,” allowing reverse operation of the motor. IEEE Journal of Solid State Circuits, Vol SC-12, No.6, December 1977. [3] Stephen H. Lewis et al., “A 10-bit, 20Msample/s Analog to Digital Converter, IEEE Journal of Solid State Circuits, March 1992
Using the nomenclature above, the switches S1 and S2 should never be closed at the same time, as this would cause a short circuit on the input voltage source. The same applies to the switches S3 and S4. This condition is known as shoot-through.
• Mingliang Liu, Demystifying Switched-Capacitor 7.4.2 Circuits, ISBN 0-7506-7907-7
Operation
7.4 H bridge
The two basic states of an H bridge
The H-bridge arrangement is generally used to reverse the polarity of the motor, but can also be used to 'brake' the motor, where the motor comes to a sudden stop, as the motor’s terminals are shorted, or to let the motor 'free run' to a stop, as the motor is effectively disconnected from the circuit. The following table summarises operation, with S1-S4 corresponding to the diagram above. Structure of an H bridge (highlighted in red)
An H bridge is an electronic circuit that enables a volt- 7.4.3 Construction age to be applied across a load in either direction. These circuits are often used in robotics and other applications Relays to allow DC motors to run forwards and backwards.[1] Most DC-to-AC converters (power inverters), most A way to build[2]an H bridge is use an array of relays from AC/AC converters, the DC-to-DC push–pull converter, a relay board. most motor controllers, and many other kinds of power electronics use H bridges. In particular, a bipolar stepper motor is almost invariably driven by a motor controller containing two H bridges.
A “double pole double throw” relay can generally achieve the same electrical functionality as an H bridge (considering the usual function of the device). However a semiconductor-based H bridge would be preferable to the
182
CHAPTER 7. THE DECIBEL channel MOSFETs. This requires a more complex design since the gates of the high side MOSFETs must be driven positive with respect to the DC supply rail. Many integrated circuit MOSFET gate drivers include a charge pump within the device to achieve this. Alternatively, a switched-mode DC–DC converter can be used to provide isolated ('floating') supplies to the gate drive circuitry. A multiple-output flyback converter is well-suited to this application.
Structure of an H bridge (highlighted in red)
Another method for driving MOSFET-bridges is the use of a specialised transformer known as a GDT (Gate Drive Transformer), which gives the isolated outputs for driving the upper FETs gates. The transformer core is usually a ferrite toroid, with 1:1 or 4:9 winding ratio. However, this method can only be used with high frequency signals. The design of the transformer is also very important, as the leakage inductance should be minimized, or cross conduction may occur. The outputs of the transformer also need to be usually clamped by Zener diodes, because high voltage spikes could destroy the MOSFET gates. Variants
A common variation of this circuit uses just the two transistors on one side of the load, similar to a class AB amplifier. Such a configuration is called a “half bridge”.[3] L298 dual H bridge motor driver The half bridge is used in some switched-mode power supplies that use synchronous rectifiers and in switching relay where a smaller physical size, high speed switching, amplifiers. The half-H bridge type is commonly abbrevior low driving voltage (or low driving power) is needed, ated to “Half-H” to distinguish it from full (“Full-H”) H or where the wearing out of mechanical parts is undesir- bridges. Another common variation, adding a third 'leg' able. to the bridge, creates a three-phase inverter. The threephase inverter is the core of any AC motor drive.
A solid-state H bridge is typically constructed using opposite polarity devices, such as PNP BJTs or P-channel MOSFETs connected to the high voltage bus and NPN BJTs or N-channel MOSFETs connected to the low voltage bus.
A further variation is the half-controlled bridge, where the low-side switching device on one side of the bridge, and the high-side switching device on the opposite side of the bridge, are each replaced with diodes. This eliminates the shoot-through failure mode, and is commonly used to drive variable or switched reluctance machines and actuators where bi-directional current flow is not required.
N channel-only semiconductors
Commercially available
N and P channel semiconductors
The most efficient MOSFET designs use N-channel There are many commercially available inexpensive sinMOSFETs on both the high side and low side because gle and dual H-bridge packages, and L293x series are the they typically have a third of the ON resistance of P- most common ones. Few packages, like L9110,[4] have
7.5. HALL EFFECT SENSOR built-in flyback diodes for back EMF protection.
7.4.4
Operation as an inverter
A common use of the H bridge is an inverter. The arrangement is sometimes known as a single-phase bridge inverter. The H bridge with a DC supply will generate a square wave voltage waveform across the load. For a purely inductive load, the current waveform would be a triangle wave, with its peak depending on the inductance, switching frequency, and input voltage.
7.4.5
See also
183 Projects • Tutorial: Build a 5A H-Bridge motor controller • Building an H-bridge-controlled motor with photocells to track light • H-bridge motor control with 4017 (in Turkish) • Using the HIP4081A for H-bridge control • Using the L293D H bridge for DC motor control • A simple circuit designed around L293D motor driver IC
7.5 Hall effect sensor
• Active rectification • Commutator (electric)
7.4.6
References
[1] Al Williams (2002). Microcontroller projects using the Basic Stamp (2nd ed.). Focal Press. p. 344. ISBN 978-157820-101-3. [2] wordpress.com [3] “The Half-bridge Circuit Revealed” Tom Ribarich (2012) [4] wordpress.com A wheel containing two magnets passing by a Hall effect sensor
7.4.7
External links
• H-Bridge Theory and Practice • Brief H-Bridge Theory of Operation
A Hall effect sensor is a transducer that varies its output voltage in response to a magnetic field. Hall effect sensors are used for proximity switching, positioning, speed detection, and current sensing applications.[1]
• H-bridge tutorial discussing various driving modes In its simplest form, the sensor operates as an analog transducer, directly returning a voltage. With a known and using back-EMF magnetic field, its distance from the Hall plate can be de• PWM DC Motor Controller Using MOSFETs and termined. Using groups of sensors, the relative position IR2110 H-Bridge Driver of the magnet can be deduced. Frequently, a Hall sensor is combined with circuitry that allows the device to act in a digital (on/off) mode, and • Derivation of formulas to estimate H-bridge con- may be called a switch in this configuration. Comtroller current (Vex, JAGUAR,Victor). Discusses monly seen in industrial applications such as the pictured why some H-bridges used in robotics have non- pneumatic cylinder, they are also used in consumer equipment; for example some computer printers use them to linear current and speed responses. • H-Bridges on the BEAM Robotics Wiki
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CHAPTER 7. THE DECIBEL
Engine fan with Hall effect sensor
The magnetic piston (1) in this pneumatic cylinder will cause the Hall effect sensors (2 and 3) mounted on its outer wall to activate when it is fully retracted or extended.
Commonly used circuit symbol
7.5.1
Hall probe
A Hall probe contains an indium compound semiconductor crystal such as indium antimonide, mounted on an aluminum backing plate, and encapsulated in the probe head. The plane of the crystal is detect missing paper and open covers. When high relia- perpendicular to the probe handle. Connecting leads bility is required, they are used in keyboards. from the crystal are brought down through the handle to Hall sensors are commonly used to time the speed of the circuit box. wheels and shafts, such as for internal combustion engine When the Hall probe is held so that the magnetic field ignition timing, tachometers and anti-lock braking sys- lines are passing at right angles through the sensor of tems. They are used in brushless DC electric motors to the probe, the meter gives a reading of the value of detect the position of the permanent magnet. In the pic- magnetic flux density (B). A current is passed through tured wheel with two equally spaced magnets, the voltage the crystal which, when placed in a magnetic field has from the sensor will peak twice for each revolution. This a extquotedblHall effect extquotedbl voltage developed arrangement is commonly used to regulate the speed of across it. The Hall effect is seen when a conductor disk drives. is passed through a uniform magnetic field. The natu-
7.5. HALL EFFECT SENSOR ral electron drift of the charge carriers causes the magnetic field to apply a Lorentz force (the force exerted on a charged particle in an electromagnetic field) to these charge carriers. The result is what is seen as a charge separation, with a buildup of either positive or negative charges on the bottom or on the top of the plate. The crystal measures 5 mm square. The probe handle, being made of a non-ferrous material, has no disturbing effect on the field. A Hall probe should be calibrated against a known value of magnetic field strength. For a solenoid the Hall probe is placed in the center.
7.5.2
Working principle
When a beam of charged particles passes through a magnetic field, forces act on the particles and the beam is deflected from its straight line path. The beam of charged particles refers to the electrons flowing through a conductor. When a current carrying conductor is placed in a magnetic field perpendicular to the path of the electrons, the electrons are deflected from its straight line path. Therefore, one side of the conductor becomes negative portion and the other side becomes positive one. The transverse voltage is measured and is known as Hall Voltage.[2]
185 • indium antimonide (InSb) • graphene [3]
7.5.4 Signal processing and interface Hall effect sensors are linear transducers. As a result such sensors require linear circuit for processing of the sensor’s output signal. Such a linear circuit: • provides constant driving current to the sensors • amplifies the output signal In some cases linear circuit may cancel the offset voltage of Hall effect sensors. Moreover, AC modulation of driving current may reduce the influence of offset voltage on characteristics of Hall effect sensor. Hall effect sensors with linear transducers are commonly integrated with digital electronics. This enables advanced corrections of the sensor’s characteristics (e.g. temperature coefficient corrections) and digital interfacing to microprocessor systems. In some solutions of IC Hall effect sensors DSP is implemented. The simplest digital processing circuit is an electronic comparator enabling switch on/off operation, which is useful in industrial automation applications. The Hall effect sensors interfaces may include input diagnostics, fault protection for transient conditions, and short/open circuit detection. It may also provide and monitor the current to the Hall effect sensor itself. There are precision IC products available to handle these features.
The charge separation continues until the force on the charged particles from the electric field balances the force produced by magnetic field. If the current is constant, then the Hall voltage is a measure of the magnetic flux density. There are two forms of Hall Effect Sensors. One is linear where the output voltage linearly varies with the magnetic flux density. The other is known as threshold where there is a sharp drop of output voltage at a partic- 7.5.5 Advantages ular magnetic flux density. A Hall effect sensor may operate as an electronic switch.
7.5.3
Materials for Hall effect sensors
The key factor deciding on sensitivity of Hall effect sensors is high electron mobility. As a result following materials are especially suitable for Hall effect sensors: • gallium arsenide (GaAs) • indium arsenide (InAs) • indium phosphide (InP)
• Such a switch costs less than a mechanical switch and is much more reliable. • It can be operated up to 100 kHz. • It does not suffer from contact bounce because a solid state switch with hysteresis is used rather than a mechanical contact. • It will not be affected by environmental contaminants since the sensor is in a sealed package. Therefore it can be used under severe conditions.
186 In the case of linear sensor (for the magnetic field strength measurements), a Hall effect sensor: • can measure a wide range of magnetic fields • is available that can measure either North or South pole magnetic fields • can be flat
7.5.6 Disadvantages Hall effect sensors provide much lower measuring accuracy than fluxgate magnetometers or magnetoresistance based sensors. Moreover, Hall effect sensors drift significantly, requiring compensation.
7.5.7 Applications Position sensing Sensing the presence of magnetic object (connected with the position sensing) is the most common industrial application of Hall effect sensors, especially these operating in the switch mode (on/off mode). The Hall effect sensors are also used in the brushless DC motor to sense the position of the rotor and to switch the transistor in the right sequence. DC current transformers Hall effect sensors may be utilized for contactless measurements of DC current in current transformers. In such a case the Hall effect sensor is mounted in the gap in magnetic core around the current conductor.[4] As a result, the DC magnetic flux can be measured, and the DC current in the conductor can be calculated. Automotive fuel level indicator The Hall sensor is used in some automotive fuel level Indicators. The main principle of operation of such indicator is position sensing of floating element.[5] This can either be done by using a vertical float magnet or a rotating lever sensor. • In a vertical float system a permanent magnet is mounted on the surface of a floating object. The
CHAPTER 7. THE DECIBEL current carrying conductor is fixed on the top of the tank lining up with the magnet. When the level of fuel rises, an increasing magnetic field is applied on the current resulting in higher Hall voltage. As the fuel level decreases, the Hall voltage will also decrease. The fuel level is indicated and displayed by proper signal condition of Hall voltage. • In a rotating lever sensor a diametrically magnetized ring magnet rotates about a linear hall sensor. The sensor only measures the perpendicular (vertical) component of the field. The strength of the field measured correlates directly to the angle of the lever and thus the level of the fuel tank.
7.5.8
References
[1] Ed Ramsden (2006). Hall-effect sensors: theory and applications (2, illustrated ed.). Elsevier. ISBN 0-7506-79344. [2] R. S. Popović (2004). Hall effect devices (2, illustrated ed.). CRC Press. ISBN 0-7503-0855-9. [3] Petruk, O.; Szewczyk, R.; Ciuk, T. et al. (2014). “Sensitivity and Offset Voltage Testing in the HallEffect Sensors Made of Graphene”. Advances in Intelligent Systems and Computing (Springer) 267: 631. doi:10.1007/978-3-319-05353-0_60. [4] Petruk, O.; Szewczyk, R.; Salach, J.; Nowicki, M. (2014). “Digitally Controlled Current Transformer with Hall Sensor”. Advances in Intelligent Systems and Computing (Springer) 267: 641. doi:10.1007/978-3-319-053530_61. [5] https://www.infineon.com/dgdl/AppNote_ Liquid_Level_Sensing_Rev.1.0.pdf?folderId= db3a30431ce5fb52011d4cae1f582dad&fileId= db3a30432313ff5e0123a385f3b2262d
7.5.9
Further reading
• A. Baumgartner et al., “Classical Hall effect in scanning gate experiments”, Phys. Rev. B, 74, 165426 (2006), doi:10.1103/PhysRevB.74.165426
Chapter 8
Filters 8.1 Low-pass filter
Electronics
A low-pass filter is a filter that passes signals with a frequency lower than a certain cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The amount of attenuation for each frequency depends on the filter design. The filter is sometimes called a high-cut filter, or treble cut filter in audio applications. A low-pass filter is the opposite of a high-pass filter. A band-pass filter is a combination of a low-pass and a high-pass filter. Low-pass filters exist in many different forms, including electronic circuits (such as a hiss filter used in audio), anti-aliasing filters for conditioning signals prior to analog-to-digital conversion, digital filters for smoothing sets of data, acoustic barriers, blurring of images, and so on. The moving average operation used in fields such as finance is a particular kind of low-pass filter, and can be analyzed with the same signal processing techniques as are used for other low-pass filters. Low-pass filters provide a smoother form of a signal, removing the short-term fluctuations, and leaving the longer-term trend.
In an electronic low-pass RC filter for voltage signals, high frequencies in the input signal are attenuated, but the filter has little attenuation below the cutoff frequency determined by its RC time constant. For current signals, a similar circuit, using a resistor and capacitor in parallel, works in a similar manner. (See current divider discussed in more detail below.) Electronic low-pass filters are used on inputs to subwoofers and other types of loudspeakers, to block high pitches that they can't efficiently reproduce. Radio transmitters use low-pass filters to block harmonic emissions that might interfere with other communications. The tone knob on many electric guitars is a low-pass filter used to reduce the amount of treble in the sound. An integrator is another time constant low-pass filter.[1] Telephone lines fitted with DSL splitters use low-pass and high-pass filters to separate DSL and POTS signals sharing the same pair of wires.[2][3]
Low-pass filters also play a significant role in the sculpting of sound created by analogue and virtual analogue An optical filter can correctly be called a low-pass fil- synthesisers. See subtractive synthesis. ter, but conventionally is called a longpass filter (low frequency is long wavelength), to avoid confusion.
8.1.2 Ideal and real filters
8.1.1
Examples
Acoustics A stiff physical barrier tends to reflect higher sound frequencies, and so acts as a low-pass filter for transmitting sound. When music is playing in another room, the low notes are easily heard, while the high notes are attenuated.
An ideal low-pass filter completely eliminates all frequencies above the cutoff frequency while passing those below unchanged; its frequency response is a rectangular function and is a brick-wall filter. The transition region present in practical filters does not exist in an ideal filter. An ideal low-pass filter can be realized mathematically (theoretically) by multiplying a signal by the rectangular function in the frequency domain or, equivalently, convolution with its impulse response, a sinc function, in
187
188
CHAPTER 8. FILTERS digital-to-analog converters use real filter approximations.
sin(πx) πx
1.0 0.8
8.1.3
0.6 0.4
Continuous-time low-pass filters
10 Cutoff frequency
0.2
0
x
-6
-4
-2
2
4
−3.01 dB
6
−10
The sinc function, the impulse response of an ideal low-pass filter.
Gain (dB)
-0.2
Slope: −20 dB/decade
−20
−30
−40
−50 Passband
the time domain. However, the ideal filter is impossible to realize without also having signals of infinite extent in time, and so generally needs to be approximated for real ongoing signals, because the sinc function’s support region extends to all past and future times. The filter would therefore need to have infinite delay, or knowledge of the infinite future and past, in order to perform the convolution. It is effectively realizable for pre-recorded digital signals by assuming extensions of zero into the past and future, or more typically by making the signal repetitive and using Fourier analysis. Real filters for real-time applications approximate the ideal filter by truncating and windowing the infinite impulse response to make a finite impulse response; applying that filter requires delaying the signal for a moderate period of time, allowing the computation to “see” a little bit into the future. This delay is manifested as phase shift. Greater accuracy in approximation requires a longer delay. An ideal low-pass filter results in ringing artifacts via the Gibbs phenomenon. These can be reduced or worsened by choice of windowing function, and the design and choice of real filters involves understanding and minimizing these artifacts. For example, “simple truncation [of sinc] causes severe ringing artifacts,” in signal reconstruction, and to reduce these artifacts one uses window functions “which drop off more smoothly at the edges.”[4] The Whittaker–Shannon interpolation formula describes how to use a perfect low-pass filter to reconstruct a continuous signal from a sampled digital signal. Real
−60 0.001
0.01
Stopband
0.1
1
10
100
1000
Angular frequency (rad/s)
The gain-magnitude frequency response of a first-order (onepole) low-pass filter. Power gain is shown in decibels (i.e., a 3 dB decline reflects an additional half-power attenuation). Angular frequency is shown on a logarithmic scale in units of radians per second.
There are many different types of filter circuits, with different responses to changing frequency. The frequency response of a filter is generally represented using a Bode plot, and the filter is characterized by its cutoff frequency and rate of frequency rolloff. In all cases, at the cutoff frequency, the filter attenuates the input power by half or 3 dB. So the order of the filter determines the amount of additional attenuation for frequencies higher than the cutoff frequency. • A first-order filter, for example, reduces the signal amplitude by half (so power reduces by a factor of 4), or 6 dB, every time the frequency doubles (goes up one octave); more precisely, the power rolloff approaches 20 dB per decade in the limit of high frequency. The magnitude Bode plot for a first-order filter looks like a horizontal line below the cutoff frequency, and a diagonal line above the cutoff frequency. There is also a “knee curve” at the boundary between the two, which smoothly transitions between the two straight line regions. If the transfer function of a first-order low-pass filter has a zero as well as a pole, the Bode plot flattens out again, at some maximum attenuation of high frequencies;
8.1. LOW-PASS FILTER
189
such an effect is caused for example by a little bit of Laplace notation the input leaking around the one-pole filter; this onepole–one-zero filter is still a first-order low-pass. See Continuous-time filters can also be described in terms of the Laplace transform of their impulse response, in Pole–zero plot and RC circuit. a way that lets all characteristics of the filter be easily analyzed by considering the pattern of poles and zeros of • A second-order filter attenuates higher frequencies the Laplace transform in the complex plane. (In discrete more steeply. The Bode plot for this type of filter time, one can similarly consider the Z-transform of the resembles that of a first-order filter, except that it impulse response.) falls off more quickly. For example, a second-order Butterworth filter reduces the signal amplitude to For example, a first-order low-pass filter can be described one fourth its original level every time the frequency in Laplace notation as: doubles (so power decreases by 12 dB per octave, or 40 dB per decade). Other all-pole second-order filOutput 1 ters may roll off at different rates initially depending =K Input 1 + sτ on their Q factor, but approach the same final rate of 12 dB per octave; as with the first-order filters, where s is the Laplace transform variable, τ is the filter zeroes in the transfer function can change the high- time constant, and K is the filter passband gain. frequency asymptote. See RLC circuit.
8.1.4 Electronic low-pass filters
• Third- and higher-order filters are defined similarly. In general, the final rate of power rolloff for an Passive electronic realization order- n all-pole filter is 6n dB per octave (i.e., 20n dB per decade).
Vin
On any Butterworth filter, if one extends the horizontal line to the right and the diagonal line to the upper-left (the asymptotes of the function), they intersect at exactly the cutoff frequency. The frequency response at the cutoff frequency in a first-order filter is 3 dB below the horizontal line. The various types of filters (Butterworth filter, Chebyshev filter, Bessel filter, etc.) all have differentlooking knee curves. Many second-order filters have “peaking” or resonance that puts their frequency response at the cutoff frequency above the horizontal line. Furthermore, the actual frequency where this peaking occurs can be predicted without calculus, as shown by Cartwright[5] et al. For third-order filters, the peaking and its frequency of occurrence can too be predicted without calculus as recently shown by Cartwright[6] et al. See electronic filter for other types. Passive, first order low-pass RC filter The meanings of 'low' and 'high'—that is, the cutoff frequency—depend on the characteristics of the filter. The One simple low-pass filter circuit consists of a resistor term “low-pass filter” merely refers to the shape of the fil- in series with a load, and a capacitor in parallel with the ter’s response; a high-pass filter could be built that cuts off load. The capacitor exhibits reactance, and blocks lowat a lower frequency than any low-pass filter—it is their frequency signals, forcing them through the load instead. responses that set them apart. Electronic circuits can be At higher frequencies the reactance drops, and the capacdevised for any desired frequency range, right up through itor effectively functions as a short circuit. The combinamicrowave frequencies (above 1 GHz) and higher. tion of resistance and capacitance gives the time constant
R
Vout
C
190
CHAPTER 8. FILTERS
C
of the filter τ = RC (represented by the Greek letter tau). The break frequency, also called the turnover frequency or cutoff frequency (in hertz), is determined by the time constant:
fc =
1 1 = 2πτ 2πRC
R2 vin
R1
vout
or equivalently (in radians per second):
ωc =
1 1 = τ RC
An active low-pass filter
This circuit may be understood by considering the time the capacitor needs to charge or discharge through the Active electronic realization resistor: Another type of electrical circuit is an active low-pass filter. • At low frequencies, there is plenty of time for the capacitor to charge up to practically the same voltage In the operational amplifier circuit shown in the figure, the cutoff frequency (in hertz) is defined as: as the input voltage. • At high frequencies, the capacitor only has time to 1 charge up a small amount before the input switches fc = 2πR 2C direction. The output goes up and down only a small fraction of the amount the input goes up and down. or equivalently (in radians per second): At double the frequency, there’s only time for it to charge up half the amount. 1 ωc = R 2C Another way to understand this circuit is through the concept of reactance at a particular frequency: The gain in the passband is −R2 /R1 , and the stopband drops off at −6 dB per octave (that is −20 dB per decade) • Since direct current (DC) cannot flow through the as it is a first-order filter. capacitor, DC input must flow out the path marked Vout (analogous to removing the capacitor). Discrete-time realization • Since alternating current (AC) flows very well through the capacitor, almost as well as it flows through solid wire, AC input flows out through the capacitor, effectively short circuiting to ground (analogous to replacing the capacitor with just a wire).
For another method of conversion from continuous- to discrete-time, see Bilinear transform. Many digital filters are designed to give low-pass characteristics. Both infinite impulse response and finite impulse response low pass filters as well as filters using fourier transforms are widely used.
The capacitor is not an “on/off” object (like the block or pass fluidic explanation above). The capacitor variably acts between these two extremes. It is the Bode plot and Simple infinite impulse response filter The effect of frequency response that show this variability. an infinite impulse response low-pass filter can be simu-
8.1. LOW-PASS FILTER
191
lated on a computer by analyzing an RC filter’s behavior That is, this discrete-time implementation of a simple RC in the time domain, and then discretizing the model. low-pass filter is the exponentially-weighted moving average
R
where
yi = αxi +(1−α)yi−1
vin
C
vout
∆T RC + ∆T
By definition, the smoothing factor 0 ≤ α ≤ 1 . The expression for α yields the equivalent time constant RC in terms of the sampling period ∆T and smoothing factor α : (
A simple low-pass RC filter
α≜
RC = ∆T
1−α α
)
From the circuit diagram to the right, according to If α = 0.5 , then the RC time constant is equal to the samKirchhoff’s Laws and the definition of capacitance: pling period. If α ≪ 0.5 , then RC is significantly larger than the sampling interval, and ∆T ≈ αRC . The filter recurrence relation provides a way to determine the output samples in terms of the input samples and the preceding output. The following pseudocode algorithm simulates the effect of a low-pass filter on a series of digital samples: where Qc (t) is the charge stored in the capacitor at time // Return RC low-pass filter output samples, given input t . Substituting equation Q into equation I gives i(t) = samples, // time interval dt, and time constant RC funcout tion lowpass(real[0..n] x, real dt, real RC) var real[0..n] C dv d t , which can be substituted into equation V so that: y var real α := dt / (RC + dt) y[0] := x[0] for i from 1 to n y[i] := α * x[i] + (1-α) * y[i-1] return y d vout The loop that calculates each of the n outputs can be vin (t) − vout (t) = RC dt refactored into the equivalent: This equation can be discretized. For simplicity, assume that samples of the input and output are taken at evenlyspaced points in time separated by ∆T time. Let the samples of vin be represented by the sequence (x1 , x2 , ..., xn ) , and let vout be represented by the sequence (y1 , y2 , ..., yn ) , which correspond to the same points in time. Making these substitutions:
xi − yi = RC
yi − yi−1 ∆T
And rearranging terms gives the recurrence relation contribution Input
z ( yi = xi
output previous from Inertia
}| ){ z ( }| ){ ∆T RC + yi−1 . RC + ∆T RC + ∆T
for i from 1 to n y[i] := y[i-1] + α * (x[i] - y[i-1]) That is, the change from one filter output to the next is proportional to the difference between the previous output and the next input. This exponential smoothing property matches the exponential decay seen in the continuous-time system. As expected, as the time constant RC increases, the discrete-time smoothing parameter α decreases, and the output samples (y1 , y2 , ..., yn ) respond more slowly to a change in the input samples (x1 , x2 , ..., xn ) ; the system has more inertia. This filter is an infinite-impulse-response (IIR) single-pole low-pass filter. Finite impulse response Finite-impulse-response filters can be built that approximate to the sinc function time-domain response of an ideal sharp-cutoff low-pass
192
CHAPTER 8. FILTERS
filter. In practice, the time-domain response must be time 8.2 High-pass filter truncated and is often of a simplified shape; in the simplest case, a running average can be used, giving a square This article is about an electronic component. For the time response.[7] Australian band, see High Pass Filter (band).
8.1.5 See also
A high-pass filter (HPF) is an electronic filter that passes high-frequency signals but attenuates (reduces the amplitude of) signals with frequencies lower than the • Baseband cutoff frequency. The actual amount of attenuation for • DSL filter each frequency varies from filter to filter. A high-pass filter is usually modeled as a linear time-invariant system. It is sometimes called a low-cut filter or bass-cut fil8.1.6 References ter.[1] High-pass filters have many uses, such as blocking DC from circuitry sensitive to non-zero average voltages [1] Sedra, Adel; Smith, Kenneth C. (1991). Microelectronic or RF devices. They can also be used in conjunction with Circuits, 3 ed. Saunders College Publishing. p. 60. ISBN a low-pass filter to make a bandpass filter. 0-03-051648-X. [2] “ADSL filters explained”. Epanorama.net. Retrieved 2013-09-24.
8.2.1
[3] “Home Networking – Local Area Network”. Pcweenie.com. 2009-04-12. Retrieved 2013-09-24.
C
[4] Mastering Windows: Improving Reconstruction [5] K. V. Cartwright, P. Russell and E. J. Kaminsky,”Finding the maximum magnitude response (gain) of second-order filters without calculus,” Lat. Am. J. Phys. Educ. Vol. 6, No. 4, pp. 559-565, 2012.
First-order continuous-time implementation
Vin
Vout R
[6] Cartwright, K. V.; P. Russell and E. J. Kaminsky (2013). “Finding the maximum and minimum magnitude responses (gains) of third-order filters without calculus”. Lat. Am. J. Phys. Educ. 7 (4): 582–587. [7] Signal recovery from noise in electronic instrumentation – T H Whilmshurst
The simple first-order electronic high-pass filter shown in Figure 1 is implemented by placing an input voltage across the series combination of a capacitor and a resistor Low-pass filter and using the voltage across the resistor as an output. The product of the resistance and capacitance (R×C) is the Low Pass Filter java simulator time constant (τ); it is inversely proportional to the cutoff ECE 209: Review of Circuits as LTI Systems, a frequency fc, that is, short primer on the mathematical analysis of (electrical) LTI systems. 1 1 fc = = , ECE 209: Sources of Phase Shift, an intuitive expla2πτ 2πRC nation of the source of phase shift in a low-pass filter. Also verifies simple passive LPF transfer func- where fc is in hertz, τ is in seconds, R is in ohms, and C tion by means of trigonometric identity. is in farads.
8.1.7 External links • • •
•
Figure 1: A passive, analog, first-order high-pass filter, realized by an RC circuit
8.2. HIGH-PASS FILTER
193
I(t)
z ( }| ){ ( ) d Vin d Vout d Vin d Vout Vout (t) = C − R = RC − dt dt dt dt This equation can be discretized. For simplicity, assume that samples of the input and output are taken at evenly-spaced points in time separated by ∆T time. Let the samples of Vin be represented by the sequence (x1 , x2 , . . . , xn ) , and let Vout be represented by the sequence (y1 , y2 , . . . , yn ) which correspond to the same points in time. Making these substitutions:
Figure 2: An active high-pass filter
Figure 2 shows an active electronic implementation of a first-order high-pass filter using an operational amplifier. In this case, the filter has a passband gain of -R2 /R1 and has a corner frequency of
( yi = RC
xi − xi−1 yi − yi−1 − ∆T ∆T
)
And rearranging terms gives the recurrence relation fc =
1 1 = , 2πτ 2πR1 C
inputs prior from contribution Decaying
z
}| { RC yi−1 RC + ∆T
input in change from Contribution
}| { Because this filter is active, it may have non-unity passRC + (xi − xi−1 ) band gain. That is, high-frequency signals are inverted yi = RC + ∆T and amplified by R2 /R1 . That is, this discrete-time implementation of a simple continuous-time RC high-pass filter is
8.2.2
z
Discrete-time realization
RC For another method of conversion from continuous- to yi = αyi−1 +α(xi −xi−1 ) where α≜ RC + ∆T discrete-time, see Bilinear transform. By definition, 0 ≤ α ≤ 1 . The expression for parameter α yields the equivalent time constant RC in terms of the Discrete-time high-pass filters can also be designed. sampling period ∆T and α : Discrete-time filter design is beyond the scope of this article; however, a simple example comes from the conversion of the continuous-time high-pass filter above to ( ) α a discrete-time realization. That is, the continuous-time RC = ∆T 1−α behavior can be discretized. From the circuit in Figure 1 above, according to If α = 0.5 , then the RC time constant equal to the Kirchhoff’s Laws and the definition of capacitance: sampling period. If α ≪ 0.5 , then RC is significantly smaller than the sampling interval, and RC ≈ α∆T . Vout (t) = I(t) R Qc (t) = C (Vin (t) − Vout (t)) I(t) = ddQtc
(V) (Q) (I)
Algorithmic implementation
The filter recurrence relation provides a way to determine the output samples in terms of the input samples and the where Qc (t) is the charge stored in the capacitor at time preceding output. The following pseudocode algorithm t . Substituting Equation (Q) into Equation (I) and then will simulate the effect of a high-pass filter on a series of Equation (I) into Equation (V) gives: digital samples:
194 // Return RC high-pass filter output samples, given input samples, // time interval dt, and time constant RC function highpass(real[0..n] x, real dt, real RC) var real[0..n] y var real α := RC / (RC + dt) y[0] := x[0] for i from 1 to n y[i] := α * y[i-1] + α * (x[i] - x[i-1]) return y The loop which calculates each of the n outputs can be refactored into the equivalent: for i from 1 to n y[i] := α * (y[i-1] + x[i] - x[i-1])
CHAPTER 8. FILTERS is built into a loudspeaker cabinet it is normally a passive filter that also includes a low-pass filter for the woofer and so often employs both a capacitor and inductor (although very simple high-pass filters for tweeters can consist of a series capacitor and nothing else). As an example, the formula above, applied to a tweeter with R=10 Ohm, will determine the capacitor value for a cut-off frequency of 1 5 kHz. C = 2πf1 R = 6.28×5000×10 = 3.18 × 10−6 , or approx 3.2 μF.
An alternative, which provides good quality sound withHowever, the earlier form shows how the parameter α out inductors (which are prone to parasitic coupling, are changes the impact of the prior output y[i-1] and current expensive, and may have significant internal resistance) change in input (x[i] - x[i-1]). In particular, is to employ bi-amplification with active RC filters or active digital filters with separate power amplifiers for each • A large α implies that the output will decay very loudspeaker. Such low-current and low-voltage line level slowly but will also be strongly influenced by even crossovers are called active crossovers.[1] small changes in input. By the relationship between Rumble filters are high-pass filters applied to the removal parameter α and time constant RC above, a large of unwanted sounds near to the lower end of the audible α corresponds to a large RC and therefore a low range or below. For example, noises (e.g., footsteps, or corner frequency of the filter. Hence, this case cor- motor noises from record players and tape decks) may be responds to a high-pass filter with a very narrow stop removed because they are undesired or may overload the band. Because it is excited by small changes and RIAA equalization circuit of the preamp.[1] tends to hold its prior output values for a long time, it can pass relatively low frequencies. However, a High-pass filters are also used for AC coupling at the inconstant input (i.e., an input with (x[i] - x[i-1])=0) puts of many audio power amplifiers, for preventing the will always decay to zero, as would be expected with amplification of DC currents which may harm the amplifier, rob the amplifier of headroom, and generate waste a high-pass filter with a large RC . heat at the loudspeakers voice coil. One amplifier, the • A small α implies that the output will decay quickly professional audio model DC300 made by Crown Interand will require large changes in the input (i.e., (x[i] national beginning in the 1960s, did not have high-pass - x[i-1]) is large) to cause the output to change much. filtering at all, and could be used to amplify the DC sigBy the relationship between parameter α and time nal of a common 9-volt battery at the input to supply 18 constant RC above, a small α corresponds to a small volts DC in an emergency for mixing console power.[2] RC and therefore a high corner frequency of the fil- However, that model’s basic design has been superseded ter. Hence, this case corresponds to a high-pass fil- by newer designs such as the Crown Macro-Tech series ter with a very wide stop band. Because it requires developed in the late 1980s which included 10 Hz highlarge (i.e., fast) changes and tends to quickly forget pass filtering on the inputs and switchable 35 Hz highits prior output values, it can only pass relatively high pass filtering on the outputs.[3] Another example is the frequencies, as would be expected with a high-pass QSC Audio PLX amplifier series which includes an infilter with a small RC . ternal 5 Hz high-pass filter which is applied to the inputs whenever the optional 50 and 30 Hz high-pass filters are turned off.[4]
8.2.3 Applications Audio
High-pass filters have many applications. They are used as part of an audio crossover to direct high frequencies to a tweeter while attenuating bass signals which could interfere with, or damage, the speaker. When such a filter
Mixing consoles often include high-pass filtering at each channel strip. Some models have fixed-slope, fixedfrequency high-pass filters at 80 or 100 Hz that can be engaged; other models have 'sweepable HPF'—a highpass filter of fixed slope that can be set within a specified frequency range, such as from 20 to 400 Hz on the Midas Heritage 3000, or 20 to 20,000 Hz on the Yamaha M7CL
8.2. HIGH-PASS FILTER
A 75 Hz “low cut” filter from an input channel of a Mackie 1402 mixing console as measured by Smaart software. This high-pass filter has a slope of 18 dB per octave.
195
Example of high-pass filter applied to the right half of a photograph. Left side is unmodified, Right side is with a high-pass filter applied (in this case, with a radius of 4.9)
digital mixing console. Veteran systems engineer and live sound mixer Bruce Main recommends that high-pass fil- 8.2.4 See also ters be engaged for most mixer input sources, except for • DSL filter those such as kick drum, bass guitar and piano, sources which will have useful low frequency sounds. Main writes • Band-stop filter that DI unit inputs (as opposed to microphone inputs) do not need high-pass filtering as they are not subject to • Band-pass filter modulation by low-frequency stage wash—low frequency sounds coming from the subwoofers or the public ad• Bias tee dress system and wrapping around to the stage. Main • Low-pass filter indicates that high-pass filters are commonly used for directional microphones which have a proximity effect—a • Differentiator low-frequency boost for very close sources. This low frequency boost commonly causes problems up to 200 or 300 Hz, but Main notes that he has seen microphones 8.2.5 References that benefit from a 500 Hz HPF setting on the console.[5]
Image High-pass and low-pass filters are also used in digital image processing to perform image modifications, enhancements, noise reduction, etc., using designs done in either the spatial domain or the frequency domain.[6] A high-pass filter, if the imaging software does not have one, can be done by duplicating the layer, putting a gaussian blur, inverting, and then blending with the original layer using an opacity (say 50%) with the original layer.[7] The unsharp masking, or sharpening, operation used in image editing software is a high-boost filter, a generalization of high-pass.
[1] Watkinson, John (1998). The Art of Sound Reproduction. Focal Press. pp. 268, 479. ISBN 0-240-51512-9. Retrieved March 9, 2010. [2] Andrews, Keith; posting as ssltech (January 11, 2010). “Re: Running the board for a show this big? extquotedbl. Recording, Engineering & Production. ProSoundWeb. Retrieved 9 March 2010. [3] “Operation Manual: MA-5002VZ”. Macro-Tech Series. Crown Audio. 2007. Retrieved March 9, 2010. [4] “User Manual: PLX Series Amplifiers”. QSC Audio. 1999. Retrieved March 9, 2010. [5] Main, Bruce (February 16, 2010). “Cut 'Em Off At The Pass: Effective Uses Of High-Pass Filtering”. Live Sound International (Framingham, Massachusetts: ProSoundWeb, EH Publishing).
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[6] Paul M. Mather (2004). Computer processing of remotely sensed images: an introduction (3rd ed.). John Wiley and Sons. p. 181. ISBN 978-0-470-84919-4. [7] “Gimp tutorial with high-pass filter operation”.
L Vi
C
C L
L
C
Vo
8.2.6 External links • Common Impulse Responses • ECE 209: Review of Circuits as LTI Systems, a A medium-complexity example of a band-pass filter. short primer on the mathematical analysis of (electrical) LTI systems. • ECE 209: Sources of Phase Shift, an intuitive explanation of the source of phase shift in a high-pass fil- Bandpass is an adjective that describes a type of filter or ter. Also verifies simple passive LPF transfer func- filtering process; it is to be distinguished from passband, tion by means of trigonometric identity. which refers to the actual portion of affected spectrum. Hence, one might say “A dual bandpass filter has two passbands.” A bandpass signal is a signal containing a band of frequencies not adjacent to zero frequency, such 8.3 Band-pass filter as a signal that comes out of a bandpass filter.[2] An ideal bandpass filter would have a completely flat passband (e.g. with no gain/attenuation throughout) and would completely attenuate all frequencies outside the passband. Additionally, the transition out of the pass−3 dB band would be instantaneous in frequency. In practice, no bandpass filter is ideal. The filter does not attenuate all frequencies outside the desired frequency range completely; in particular, there is a region just outside the intended passband where frequencies are attenuated, but B not rejected. This is known as the filter roll-off, and it f is usually expressed in dB of attenuation per octave or decade of frequency. Generally, the design of a filter fL f0 fH seeks to make the roll-off as narrow as possible, thus alBandwidth measured at half-power points (gain −3 dB, √2/2, or lowing the filter to perform as close as possible to its inabout 0.707 relative to peak) on a diagram showing magnitude tended design. Often, this is achieved at the expense of pass-band or stop-band ripple. transfer function versus frequency for a band-pass filter. 0 dB
The bandwidth of the filter is simply the difference beA band-pass filter is a device that passes frequencies tween the upper and lower cutoff frequencies. The shape within a certain range and rejects (attenuates) frequen- factor is the ratio of bandwidths measured using two cies outside that range. different attenuation values to determine the cutoff frequency, e.g., a shape factor of 2:1 at 30/3 dB means the bandwidth measured between frequencies at 30 dB atten8.3.1 Description uation is twice that measured between frequencies at 3 dB An example of an analogue electronic band-pass filter attenuation. is an RLC circuit (a resistor–inductor–capacitor circuit). Optical band-pass filters are common in photography and These filters can also be created by combining a low-pass theatre lighting work. These filters take the form of a filter with a high-pass filter.[1] transparent coloured film or sheet.
8.3. BAND-PASS FILTER
8.3.2
Q-factor
A band-pass filter can be characterised by its Q-factor. The Q-factor is the inverse of the fractional bandwidth. A high-Q filter will have a narrow passband and a low-Q filter will have a wide passband. These are respectively referred to as narrow-band and wide-band filters.
8.3.3
Applications
197
8.3.5 References [1] E. R. Kanasewich (1981). Time Sequence Analysis in Geophysics. University of Alberta. p. 260. ISBN 0-88864074-9. [2] Belle A. Shenoi (2006). Introduction to digital signal processing and filter design. John Wiley and Sons. p. 120. ISBN 978-0-471-46482-2. [3] Norman Stuart Sutherland (1979). Tutorial Essays in Psychology. Lawrence Erlbaum Associates. p. 68. ISBN 0-470-26652-X.
Bandpass filters are widely used in wireless transmitters and receivers. The main function of such a filter in a 8.3.6 transmitter is to limit the bandwidth of the output signal to the band allocated for the transmission. This prevents the transmitter from interfering with other stations. In a receiver, a bandpass filter allows signals within a selected range of frequencies to be heard or decoded, while preventing signals at unwanted frequencies from getting through. A bandpass filter also optimizes the signal-tonoise ratio and sensitivity of a receiver. In both transmitting and receiving applications, welldesigned bandpass filters, having the optimum bandwidth for the mode and speed of communication being used, maximize the number of signal transmitters that can exist in a system, while minimizing the interference or competition among signals. Outside of electronics and signal processing, one example of the use of band-pass filters is in the atmospheric sciences. It is common to band-pass filter recent meteorological data with a period range of, for example, 3 to 10 days, so that only cyclones remain as fluctuations in the data fields. In neuroscience, visual cortical simple cells were first shown by David Hubel and Torsten Wiesel to have response properties that resemble Gabor filters, which are band-pass.[3]
8.3.4
See also
• Atomic line filter • Audio crossover • Band-stop filter
External links
Chapter 9
Text and image sources, contributors, and licenses 9.1 Text • Transistor Source: http://en.wikipedia.org/wiki/Transistor?oldid=625165861 Contributors: Mav, The Anome, Taw, Rjstott, Jkominek, Sandos, Youssefsan, RAD, Little guru, Mudlock, Ray Van De Walker, SimonP, Maury Markowitz, Ellmist, Gbraad, Heron, RTC, JohnOwens, Michael Hardy, Tim Starling, Cprompt, Nixdorf, Ixfd64, Ahoerstemeier, Cyp, ZoeB, Stevenj, Suisui, Iammaxus, Александър, Kaeslin, Julesd, Glenn, Bogdangiusca, Cyan, Nikai, Tristanb, Jiang, Lommer, HolIgor, Wikiborg, Reddi, Stone, Dfeuer, Andrewman327, Gutza, Zoicon5, PeterGrecian, Timc, Tpbradbury, Marshman, Maximus Rex, Grendelkhan, Omegatron, ReciprocityProject, Thue, Stormie, Bloodshedder, Raul654, Dpbsmith, Flockmeal, Ldo, Phil Boswell, Maheshkale, Robbot, Pigsonthewing, Jakohn, Owain, Fredrik, Pjedicke, Babbage, Jondel, Bkell, Hadal, UtherSRG, Galexander, Jleedev, Alan Liefting, David Gerard, Enochlau, Wjbeaty, Ancheta Wis, Giftlite, DavidCary, Mat-C, Ferkelparade, Brian Kendig, COMPATT, Fleminra, Capitalistroadster, Dratman, Chowbok, Gadfium, Plutor, Sonjaaa, Antandrus, Mako098765, Jossi, Untifler, Avihu, Dcandeto, Qdr, Jimaginator, Mike Rosoft, Vesta, Mindspillage, Zed, Discospinster, Rich Farmbrough, Rhobite, Rmalloy, Pjacobi, ArnoldReinhold, Xezbeth, Mani1, Dmeranda, Dyl, Kbh3rd, Klenje, Plugwash, Jindrich, Srivatsaaithal, CanisRufus, Sfahey, El C, Lankiveil, Barfooz, Sietse Snel, Neilrieck, Spoon!, Bobo192, EricBarbour, R. S. Shaw, Elipongo, Matt Britt, Mikel Ward, Jojit fb, Kjkolb, Wikinaut, DanB, Haham hanuka, Hooperbloob, Nsaa, Nazli, Alansohn, Orimosenzon, Jared81, Interiot, Eric Kvaalen, Barium, Atlant, WTGDMan1986, Ashley Pomeroy, Mr snarf, Brinkost, Snowolf, Blobglob, Oneliner, Wtshymanski, Knowledge Seeker, Cburnett, Suruena, Cal 1234, TenOfAllTrades, DV8 2XL, Gene Nygaard, MIT Trekkie, Redvers, TheCoffee, Ahseaton, HenryLi, Flying fish, Begemotv2718, Veemonkamiya, Polyparadigm, Matijap, MONGO, Pyrosim, Cbdorsett, Eyreland, Bar0n, Zzyzx11, CPES, Palica, Msiddalingaiah, Graham87, Magister Mathematicae, Haikupoet, Snafflekid, Coneslayer, JVz, Mjm1964, Bernard van der Wees, Tangotango, Colin Hill, Vegaswikian, DonSiano, Ligulem, LjL, Rbeas, Yamamoto Ichiro, FlaBot, Naraht, Arnero, Ysangkok, Nihiltres, AJR, Gparker, RexNL, Gurch, DavideAndrea, RobyWayne, Alvin-cs, Kri, JonathanFreed, Jidan, Chobot, Krishnavedala, DVdm, Cornellrockey, Bubbachuck, YurikBot, Wavelength, Marginoferror, Hairy Dude, Jimp, SpuriousQ, Stephenb, Gaius Cornelius, Yyy, Shaddack, Brejc8, Pseudomonas, NawlinWiki, Rohitbd, ONEder Boy, RazorICE, Jpbowen, Speedevil, Scs, Misza13, Scottfisher, DeadEyeArrow, Bota47, Jeh, Searchme, Light current, 21655, Ninly, Theda, Closedmouth, Arthur Rubin, Vdegroot, Cronostvg, Emc2, Wbrameld, Katieh5584, Kungfuadam, GrinBot, Zvika, ModernGeek, Elliskev, That Guy, From That Show!, Minnesota1, Attilios, Siker, SmackBot, YellowMonkey, RockMaestro, Dovo, Reedy, Thorseth, Delldot, StephenJMuir, Unforgettableid, Magwich77, Gilliam, Simoxxx, Andy M. Wang, Lindosland, QEDquid, Master Jay, Avin, @modi, Thumperward, Oli Filth, EncMstr, Papa November, SEIBasaurus, DHNbot, Squibman, Audriusa, WDGraham, Foogod, HeKeRnd, Can't sleep, clown will eat me, Writtenright, Sephiroth BCR, KaiserbBot, Lantrix, Yidisheryid, Rrburke, VMS Mosaic, Chcknwnm, Nakon, Valenciano, MichaelBillington, BWDuncan, Repairscircuitboards, Jklin, DMacks, Rspanton, Ligulembot, Ohconfucius, The undertow, SashatoBot, Kuru, NeilUK, Danorux, Lazylaces, Evenios, JorisvS, Scetoaux, IronGargoyle, CyrilB, Loadmaster, MarkSutton, Slakr, Optimale, George The Dragon, Rogerbrent, Dicklyon, Waggers, Mets501, EEPROM Eagle, Softice6, Caiaffa, Tsolosmi, Kvng, KJS77, Cmcginnis, Iridescent, Drlegendre, Yves-Laurent, Paul Foxworthy, DarkCell, Aeons, IanOfNorwich, Tawkerbot2, Daniel5127, G-W, Chetvorno, Elekas, Compy 386, David Carron, ThisIsMyUsername, CmdrObot, Irwangatot, Chrumps, Ilikefood, JohnCD, Rohan2kool, Zureks, Old Guard, Casper2k3, Cydebot, Verdy p, Tawkerbot4, DumbBOT, Editor at Large, Splateagle, Charlvn, Malleus Fatuorum, 6pence, Jessemonroy650, Epbr123, Pcu123456789, Headbomb, Electron9, Gerry Ashton, Nezzadar, Leon7, CboneG5, Natalie Erin, Escarbot, AntiVandalBot, Luna Santin, Firespray, EarthPerson, Scientific American, RapidR, Dvandersluis, Farosdaughter, Rico402, JAnDbot, Xhienne, Dan D. Ric, Em3ryguy, Harryzilber, MER-C, CosineKitty, Ericoides, Dagnabit, Britcom, Dricherby, Snowolfd4, PhilKnight, Denimadept, Acroterion, I80and, Bongwarrior, VoABot II, Verkhovensky, BigChicken, Robcotton, Schily, Sub40Hz, Bleh999, Allstarecho, Canyouhearmenow, Clipjoint, Matt B., Species8471, Cocytus, Gjd001,
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Hall, Sabbah67, MichaelVernonDavis, Mild Bill Hiccup, Somwk, Alkamid, Brews ohare, Maarschalk, 7, Addbot, Furiousgreencloud, Мыша, Jncraton, MrOllie, Lightbot, Heinzelmann, Biezl, Legobot, Luckas-bot, Yobot, Andreasmperu, Kamran engineer, AnomieBOT, Ciphers, ^musaz, Kingpin13, Пика Пика, Materialscientist, Citation bot, Frankenpuppy, LilHelpa, Xqbot, Gilo1969, Isheden, Panagea, GrouchoBot, Prunesqualer, Javirosa, Sophus Bie, Dougofborg, FrescoBot, Luke831, Jc3s5h, Roman12345, Austria156, Adlerbot, SpaceFlight89, Inderpeet singh, Lissajous, Vertpox, Aesthe, Extra999, MrSnoot, Qtipium, AndyHe829, EmausBot, John of Reading, Beatnik8983, Dltwaddell, Tommy2010, Matthewbeckler, Traxs7, MigueldelosSantos, Dffgd, Kgsbot, Jbergste, 28bot, Rocketrod1960, Mikhail Ryazanov, ClueBot NG, Zelpld, Satellizer, Dywindel, Cntras, Mehtablocham, Helpful Pixie Bot, Wbm1058, Trunks ishida, Patwal.manish, CitationCleanerBot, Piet De Pauw, MrBill3, Pratyya Ghosh, Tkaret, Dexbot, Mogism, Manish cfc, Makecat-bot, Lightfoot54, Ndikumana, Michipedian, Jianhui67, Shipandreceive, Teerthram and Anonymous: 416 • Field-effect transistor Source: http://en.wikipedia.org/wiki/Field-effect_transistor?oldid=626735374 Contributors: Sandos, Mudlock, Heron, Michael Hardy, Tim Starling, Dgrant, Stw, Stevenj, Kaeslin, Glenn, Nikai, EdH, Rob Hooft, Lommer, Colin Marquardt, Ozuma, Omegatron, Jerzy, Donarreiskoffer, Robbot, Jakohn, Altenmann, Moink, Wikibot, Wjbeaty, Nunh-huh, Cantus, Jaan513, Glengarry, Bobblewik, Mako098765, Supaari, Simson, Sillydragon, Klemen Kocjancic, Clemwang, Qdr, TedPavlic, Rmalloy, Pjacobi, Clawed, Deelkar,
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Mithoon, Skr15081997, Tinkerer02, Anubhavawasthi05 and Anonymous: 231 • Silicon Source: http://en.wikipedia.org/wiki/Silicon?oldid=627479860 Contributors: AxelBoldt, CYD, Mav, The Anome, Stephen Gilbert, Jeronimo, Rjstott, LA2, Josh Grosse, XJaM, PierreAbbat, Ortolan88, William Avery, Ktsquare, DrBob, Heron, Fonzy, Stevertigo, Dwmyers, RTC, Kchishol1970, Erik Zachte, Ixfd64, Miciah, Eric119, Shimmin, Dgrant, Card, Looxix, Ahoerstemeier, Cyp, Mac, Suisui, Poor Yorick, Andres, Mxn, Andfarm, MedievalFreak, Schneelocke, Emperorbma, Tantalate, Stone, David Latapie, DJ Clayworth, Vancouverguy, Grendelkhan, Omegatron, Shafei, Denelson83, Donarreiskoffer, Robbot, Hankwang, Moriori, Jotomicron, Romanm, Naddy, Modulatum, Smallweed, Bkell, Hadal, Raeky, JerryFriedman, Carnildo, Alan Liefting, Giftlite, Inter, Lupin, Timpo, No Guru, Gracefool, AlistairMcMillan, Solipsist, Khalid hassani, Brockert, Darrien, Jackol, Glengarry, Delta G, Golbez, Wmahan, Knutux, Quadell, Antandrus, Ravikiran r, Lvl, Icairns, Karl-Henner, Nielmo, Wyllium, Jh51681, Deglr6328, Trevor MacInnis, Canterbury Tail, Ultratomio, Discospinster, FT2, Vsmith, Spundun, Paul August, DcoetzeeBot, Bender235, ESkog, Sunborn, Plugwash, Brian0918, RJHall, JustinWick, CanisRufus, MBisanz, El C, Kwamikagami, Hayabusa future, Chairboy, Remember, Femto, Bobo192, Mike Schwartz, Smalljim, Matt Britt, SpeedyGonsales, Trevj, Rje, Merope, HasharBot, Melah Hashamaim, Jumbuck, Etrigan, Storm Rider, Jérôme, Danski14, Alansohn, Gary, PaulHanson, Patrick Bernier, Arthena, Atlant, Rd232, Sl, Redfarmer, Bantman, Snowolf, Twisp, RainbowOfLight, Dirac1933, TenOfAllTrades, Skatebiker, Gene Nygaard, Iustinus, HenryLi, Adrian.benko, Rossheth, Dismas, Megan1967, Isfisk, Woohookitty, Mindmatrix, TigerShark, Myleslong, Benbest, Polyparadigm, Fbriere, WadeSimMiser, Miss Madeline, Schzmo, Z303, Terence, Sengkang, GregorB, Mr. Qwert, Alec Connors, Palica, Dysepsion, Mandarax, DePiep, Jclemens, Saperaud, Rjwilmsi, Coemgenus, MZMcBride, Tawker, 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Aldaron, Reid A., Cybercobra, Makemi, Nakon, Savidan, RandomP, PokeTIJeremy, Polonium, Imaginateca, Doodle77, Airwolf, PeterJeremy, Bartholomeyczik, Ck lostsword, Pilotguy, Ohconfucius, Chymicus, SashatoBot, Bcasterline, DA3N, Archimerged, Kuru, Khazar, John, Heimstern, Linnell, AB, JorisvS, KristianMolhave, Ckatz, Jamix, Slakr, Beetstra, Haasl, Condem, Jose77, Ndittert, Caiaffa, Pejman47, Quaeler, Sfgagnon, Iridescent, Paul Koning, JayZ, Tmangray, Shoeofdeath, Igoldste, Thricecube, Tawkerbot2, Daniel5127, Poolkris, JForget, Stifynsemons, Thermochap, The Librarian, Dycedarg, JohnCD, R9tgokunks, Logical2u, Reywas92, A876, Mike Christie, Astrochemist, Hyperdeath, Rifleman 82, Gogo Dodo, Farzaneh, DumbBOT, Jay32183, FastLizard4, Omicronpersei8, EvocativeIntrigue, Thijs!bot, Epbr123, Barticus88, NJPharris, Norman Yarvin, TheFearow, Communisthamster, Headbomb, Marek69, DmitTrix, West Brom 4ever, John254, E. Ripley, EdJohnston, CharlotteWebb, Dawnseeker2000, Natalie Erin, SparhawkWiki, Escarbot, Porqin, AntiVandalBot, Opelio, AlexOvShaolin, Danger, Michael.j.sykora, Gökhan, Res2216firestar, JAnDbot, Deflective, Leuko, Plantsurfer, Planetary, Mcorazao, Instinct, Jabam, 03272, Andonic, Hut 8.5, Time3000, .anacondabot, Karlhahn, Bongwarrior, VoABot II, AuburnPilot, Rhadamante, Dichrra, CTF83!, SwiftBot, Animum, Adrian J. Hunter, Ciaccona, Allstarecho, P.B. Pilhet, User A1, The Real Marauder, Vssun, DerHexer, Kraxler, Cocytus, Ratherhaveaheart, Hdt83, MartinBot, ChemNerd, ItaniuMatrix, R'n'B, Dgwohu, AlexiusHoratius, Leyo, Siliconov, Peterheis, Watch37264, J.delanoy, Captain panda, Abby, NightFalcon90909, Pursey, 12dstring, Thaurisil, Eskimospy, Acalamari, Shawn in Montreal, Mahewa, Gman124, Oldboltonian, Coppertwig, Hessammehr, AntiSpamBot, Warut, NewEnglandYankee, Touch Of Light, Juliancolton, Cometstyles, STBotD, Vanished user 39948282, Sarregouset, Squids and Chips, CardinalDan, Idioma-bot, Wikieditor06, VolkovBot, CWii, ABF, Science4sail, Luzheng, Jeff G., Ryan032, Philip Trueman, TXiKiBoT, Zidonuke, The Original Wildbear, Malinaccier, Miranda, Park70, Ann Stouter, Kumorifox, Seraphim, Axiosaurus, Kirsten07734, Jackfork, LeaveSleaves, ^demonBot2, Psyche825, Cremepuff222, Cbaker9552, Hastings007, Smartdude122, Vaubin, Lamro, Redyoshi49q, Go-in, Falcon8765, Enviroboy, Sevela.p, AlleborgoBot, TheBendster, Lando5, LuigiManiac, Petergans, EmxBot, CMBJ, SieBot, PlanetStar, WereSpielChequers, Ktulu6, ToePeu.bot, Cwkmail, Yintan, Goron1130, Oda Mari, It.franciscus, Oxymoron83, Nuttycoconut, Pooeater69, RooZ, Steven Zhang, Helikophis, Colboi, JackSchmidt, Hobartimus, Hak-kâ-ngìn, Robertan, Dzukman2000, StaticGull, Double Vigie, Squirmymcphee, Nergaal, Denisarona, Martarius, ClueBot, Andrew Nutter, WilliamRoper, Naaa127, The Thing That Should Not Be, Zach4636, Arakunem, Mild Bill Hiccup, Doseiai2, CounterVandal-
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ismBot, Blanchardb, Neverquick, DragonBot, Souseiseki42, Excirial, Alexbot, CrazyChemGuy, LeoCRogers, Aubriexoxo, Bloodofjing, Aristotle28, Hunt ice, Abrech, Dspark76, Yim00, Arjayay, The Red, Kakofonous, Enricoros, Kariboo, Plasmic Physics, Versus22, SoxBot III, Glacier Wolf, Crazy Boris with a red beard, Usaf2222, XLinkBot, Rror, Little Mountain 5, Skarebo, Noctibus, MystBot, HexaChord, Willking1979, Some jerk on the Internet, Twaz, Fieldday-sunday, Biskuvi, SpillingBot, Download, CarsracBot, Zomgadonggs, Numbo3-bot, VASANTH S.N., Tide rolls, David0811, HerculeBot, LuK3, FSIM, Alfie66, Luckas-bot, Yobot, 2D, Lethalgeek, Fraggle81, Cflm001, Davduff, KamikazeBot, Elizgoiri, Eudialytos, Daniel 1992, Synchronism, AnomieBOT, Pkenriquez, Marauder40, Kristen Eriksen, Master of Pies, Rubinbot, Galoubet, AdjustShift, Richnotts, Crystal whacker, Flewis, Materialscientist, Citation bot, Djtrimz, 45Factoid44, Rockoprem, Frankenpuppy, LilHelpa, Andrewmc123, Xqbot, Zad68, Sketchmoose, Kojiki1976, Sionus, Capricorn42, Br77rino, Delphonic, Supermansbutt, Srich32977, Ubcule, GrouchoBot, Call me Bubba, MC Steel, Doulos Christos, Shadowjams, Erik9, Nixón, R8R Gtrs, FrescoBot, Thatsjustnotcricket, Eldin raigmore, Citation bot 1, DrilBot, Pinethicket, A8UDI, Fentlehan, Xeworlebi, Jauhienij, FoxBot, Double sharp, TobeBot, Ticklewickleukulele, Intrr, Hbec, Mattiee'x, Doggy69, Ritter17055, Alteo255, Askud99, RjwilmsiBot, EmausBot, Cricobr, ITshnik, Dewritech, GoingBatty, RA0808, Solarra, P. S. F. Freitas, Chuck Baggett, Liquidmetalrob, Shuipzv3, StringTheory11, Chemicalinterest, 1 of 6818119630, Wikfr, GianniG46, Wayne Slam, ChemMater, Bulkhardon, L1A1 FAL, Donner60, Mentibot, ChuispastonBot, Peter Karlsen, DASHBotAV, Xanchester, ClueBot NG, Michael2707, Matthiaspaul, This lousy T-shirt, Andrewsailer, Parcly Taxel, Kasirbot, TheFame123, Pilularis, Diyar se, Helpful Pixie Bot, Geo7777, JohnSRoberts99, HMSSolent, Wbm1058, Bibcode Bot, DBigXray, Lowercase sigmabot, M0rphzone, PTJoshua, Rijinatwiki, MusikAnimal, Alanmcruickshank, AdventurousSquirrel, Doggydodo, Too0003, Sam881030, Azurelcorrupted, Bplppl, Glacialfox, Brendonwalsh27, TheFinniest, Trollinboss, BattyBot, DarafshBot, Th4n3r, Ellebellyjelly, NitRav, BrightStarSky, Dexbot, JZNIOSH, Lugia2453, Gwitz13, Graphium, Sowlos, Jnargus, The Anonymouse, Roman Champ, Reatlas, Hermespeed, Mr funky clouds, Percyjvalgal, Epicgenius, Mcatee.jesse, Gruvinnz, Wedgeline, Ankhsoprah, Ramendoctor, Rahuljohn77, Ebag7125, Lolydolly, Username469, Cinaeth1, Rotaryphone111, Keelyellenmarie, BethNaught, Lalalalalalalala1231231231234, Dorkakiin and Anonymous: 1025 • Germanium Source: http://en.wikipedia.org/wiki/Germanium?oldid=623792123 Contributors: AxelBoldt, CYD, Mav, Bryan Derksen, LA2, Josh Grosse, PierreAbbat, William Avery, DrBob, David spector, Bdesham, RTC, Tim Starling, Erik Zachte, Gdarin, Shellreef, Graue, Minesweeper, Ahoerstemeier, Mac, Jimfbleak, Mgimpel, Suisui, Poor Yorick, Schneelocke, Emperorbma, Tantalate, Stone, David Latapie, Greenrd, Tpbradbury, Grendelkhan, SEWilco, Thue, Jerzy, Donarreiskoffer, Robbot, Chris 73, Romanm, Naddy, Hadal, Carnildo, Giftlite, Graeme Bartlett, AJim, Guanaco, Yekrats, Darrien, Jaan513, Jackol, Delta G, R. fiend, OldZeb, Antandrus, Qleem, Thincat, Icairns, Gscshoyru, B.d.mills, Joyous!, Trevor MacInnis, Plexust, Discospinster, Guanabot, Vsmith, Nvj, Paul August, DcoetzeeBot, Bender235, Sunborn, RJHall, CanisRufus, El C, Joanjoc, Kwamikagami, Remember, Art LaPella, Triona, Femto, Krellis, Jumbuck, Alansohn, Abe Lincoln, Sl, PhazZ, Staeiou, Bsadowski1, Woohookitty, Linas, StradivariusTV, Benbest, Sengkang, Graham87, BD2412, DePiep, Grammarbot, Sjö, Saperaud, Rjwilmsi, WCFrancis, XLerate, NeonMerlin, FlaBot, Ground Zero, Nihiltres, Srleffler, King of Hearts, Chobot, Jaraalbe, YurikBot, Wavelength, Mukkakukaku, Petiatil, Hellbus, Hydrargyrum, Yyy, Shaddack, Alex Bakharev, Bovineone, NawlinWiki, Janke, The Ogre, Ospalh, Bota47, Ms2ger, Tetracube, Lt-wiki-bot, E Wing, GraemeL, Geoffrey.landis, Anclation, Curpsbotunicodify, GrinBot, Luk, ChemGardener, Itub, Amalthea, SmackBot, Alexdeh, KocjoBot, Delldot, Edgar181, Eloil, Kdliss, Kurykh, Persian Poet Gal, Thumperward, MalafayaBot, Deli nk, Dlohcierekim’s sock, Sbharris, Gyrobo, Tsca.bot, Can't sleep, clown will eat me, Sergio.ballestrero, Kaimiddleton, Rrburke, SundarBot, PsychoCola, Cybercobra, Nibuod, Smokefoot, Doodle77, DMacks, PeterJeremy, Captainbeefart, SashatoBot, Archimerged, John, Buchanan-Hermit, Edwy, Beetstra, Avs5221, Jopusbob, Novangelis, Jose77, Sifaka, KJS77, Iridescent, LeyteWolfer, Igoldste, FelisSchrödingeris, Thricecube, Cryptic C62, Poolkris, Zubaexy, JForget, Stifynsemons, CmdrObot, R9tgokunks, FlyingToaster, MarsRover, Intelligentguest, Christian75, Roberta F., Thijs!bot, Epbr123, Barticus88, Irishleprechaun, Runch, Kablammo, Headbomb, WillMak050389, Phopon, D.H, BlytheG, Escarbot, Eleuther, Mentifisto, Ju66l3r, AntiVandalBot, WinBot, Opelio, JAnDbot, Deflective, Plantsurfer, East718, Acroterion, Magioladitis, WolfmanSF, Karlhahn, Bongwarrior, VoABot II, Keithpoole, Verkhovensky, TARBOT, Ling.Nut, Aka042, Giggy, LorenzoB, Somearemoreequal, STBot, Rricci, ChemNerd, Trevor f, Watch37264, J.delanoy, Dshenai, Gman124, Warut, NewEnglandYankee, Ljgua124, Potatoswatter, STBotD, Ja 62, Squids and Chips, GrahamHardy, Vranak, VolkovBot, ABF, Butwhatdoiknow, Mightyhansa, Philip Trueman, TXiKiBoT, Oshwah, GimmeBot, Oudegeest, Qxz, Retiono Virginian, Axiosaurus, Vladsinger, Falcon8765, AlleborgoBot, LuigiManiac, Legoktm, EmxBot, Biscuittin, SaltyBoatr, SieBot, PlanetStar, WereSpielChequers, Keilana, Scorpion451, Avnjay, Hak-kâ-ngìn, The Hemp Necktie, StaticGull, Sean.hoyland, Mygerardromance, Nergaal, Laburke, MarsmanRom, Church, ClueBot, Knepflerle, DanielDeibler, CounterVandalismBot, Blanchardb, Piledhigheranddeeper, Ottava Rima, Acolorpink1, DragonBot, AssegaiAli, Lugh23, Juanathan, Ottre, Tylerdmace, NuclearWarfare, Jotterbot, New4325, LarryMorseDCOhio, Ember of Light, The Red, Thingg, Aitias, Plasmic Physics, Versus22, Dana boomer, RexxS, Badinfinity, TravisAF, SkyLined, Mr0t1633, Willking1979, Some jerk on the Internet, DOI bot, NjardarBot, CarsracBot, PranksterTurtle, Loveandprotect, Novel tubes, Alchemist-hp, Numbo3-bot, Tide rolls, Lightbot, Trevas, Margin1522, Luckas-bot, Yobot, EchetusXe, Lethalgeek, Berkay0652, II MusLiM HyBRiD II, Obscuranym, Cjp24, Tempodivalse, Magog the Ogre, AnomieBOT, Jim1138, Galoubet, Commander Shepard, Kingpin13, Hcaz11, Materialscientist, Digitalfear, Citation bot, Frankenpuppy, ArthurBot, LovesMacs, Obersachsebot, Andrewmc123, Xqbot, TheAMmollusc, Ywaz, Jslefo, JimVC3, Capricorn42, Srich32977, Abce2, RibotBOT, Nedim Ardoğa, Fromjarod, FrescoBot, Scott940603, Hgjghjh, Hedgerhedger, Wik1ped1a is meant 2 be vanda1ised, Barathrumm, Spindocter123, Finalius, Citation bot 1, Pinethicket, A8UDI, RedBot, Phearson, Wikitanvir, Jhbuk, Jauhienij, ActivExpression, FoxBot, Double sharp, TobeBot, Vrenator, DracaenaFragrans, Tbhotch, Slipknot1018, AXRL, RjwilmsiBot, Regancy42, DASHBot, EmausBot, Rbaselt, Richard.danylyuk, Racerx11, K6ka, Kaimakides, Peterindelft, HiW-Bot, Daonguyen95, StringTheory11, Alpha Quadrant (alt), Sthubertus, Aschwole, Donner60, ChuispastonBot, Zenhomeenergy, Mikhail Ryazanov, ClueBot NG, Feedintm, Leeroyjenkins1996, Mouse20080706, Helpful Pixie Bot, Bibcode Bot, Charouili, ElphiBot, Supernerd11, Zombieslayer523, Shisha-Tom, Murcielago7, ChrisGualtieri, CarrieVS, Dexbot, TrollTrollTrollTroll, Frosty, Jamesx12345, T42N24T, Jnargus, Eyesnore, Handoman123210, Kogge, Ramendoctor, Partymarty21, Prof.Haddock, Scooby1961, Monkbot, Hardkhora, Mtbrandon and Anonymous: 393 • Gallium arsenide Source: http://en.wikipedia.org/wiki/Gallium_arsenide?oldid=617335450 Contributors: Maury Markowitz, Hep-
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CHAPTER 9. TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES
haestos, Edward, Tim Starling, Collabi, Dgrant, Mac, Strebe, Julesd, Samw, HolIgor, Tantalate, Stone, Andrewman327, Denelson83, Donarreiskoffer, Gentgeen, Hankwang, Psychonaut, Giftlite, Eequor, Jabowery, Gadfium, Karl-Henner, N328KF, Cacycle, Femto, Matt Britt, Keenan Pepper, Benjah-bmm27, Walkerma, Ynhockey, Suruena, Gene Nygaard, Japanese Searobin, Firsfron, DuncanWidman, Benbest, Polyparadigm, Alan Canon, CronoDAS, Nanite, Rjwilmsi, TheGWO, FlaBot, SchuminWeb, Jeepo, Fresheneesz, Physchim62, Jaraalbe, YurikBot, Conscious, Alexmorgan, Rada, Shaddack, DragonHawk, ArséniureDeGallium, BOT-Superzerocool, RyanJones, Calaschysm, Sbyrnes321, Attilios, SmackBot, Ququ, Thorseth, The Photon, Jrockley, Lainagier, Commander Keane bot, Hugo-cs, Bluebot, Thumperward, Oli Filth, Plotnick, AndrewBuck, Miquonranger03, Papa November, Gruzd, Rrburke, Phudga, Smokefoot, Doodle77, Mion, Chymicus, Beetstra, Norm mit, Thricecube, Eastlaw, DangerousPanda, CmdrObot, Corp1117, Thijs!bot, Barticus88, Peter gk, Brianthegiant, Rehnn83, JAnDbot, MER-C, Plantsurfer, Flippin42, VoABot II, Keithpoole, R'n'B, T.vanschaik, R!SC, LordAnubisBOT, Billr wiki, Atropos235, Jim Swenson, VolkovBot, Bry9000, Nicholasnice, Axiosaurus, Razvan NEAGOE, Why Not A Duck, Kbrose, AIMetalsResearcher, Da Joe, Debussy Agutter, Chem-awb, Swisskitt, JSVickers, CohesionBot, ChardonnayNimeque, Wilso418, Wikimedes, Plasmic Physics, Addbot, Mortense, Frankhindle, Cantaloupe2, Some jerk on the Internet, Laser Razor, Hudavendigar, Lightbot, Legobot, Luckas-bot, Bunnyhop11, CheMoBot, KamikazeBot, Materialscientist, Peterdx, GrouchoBot, Pinethicket, Tiananmen 8888, RedBot, MastiBot, Mikespedia, RjwilmsiBot, EmausBot, Dcirovic, Chemicalinterest, Sthubertus, Tolly4bolly, Joeblanda, Mikhail Ryazanov, ClueBot NG, Rycecube57, Snotbot, Dsperlich, Ntansu, Helpful Pixie Bot, Wbm1058, BG19bot, Moonx, CeraBot, Senor Spandex, Monkbot, La2O3 and Anonymous: 91 • Voltage-controlled oscillator Source: http://en.wikipedia.org/wiki/Voltage-controlled_oscillator?oldid=623210713 Contributors: Glenn, Radiojon, Omegatron, Phil Boswell, DavidCary, Ds13, MFNickster, Ary29, Mike Rosoft, Hooperbloob, Atlant, Wtshymanski, Miq, Vegaswikian, FlaBot, Chobot, YurikBot, PinothyJ, Gaius Cornelius, Alynna Kasmira, Brandon, Light current, Donald Albury, JLaTondre, SmackBot, Telestylo, Maliaydin, Chris the speller, Mailmerge, Vina-iwbot, Wmattis, Kvng, Chetvorno, Chrumps, Boardhead, Electron9, AkosSzoboszlay, EP111, JAnDbot, Pi.1415926535, Nikevich, HL-SDK, Japo, Bissinger, Glrx, Cuddlyable3, Spinningspark, AlleborgoBot, SieBot, BotMultichill, A. Carty, Zdilli, Vahid avr, IR-TCI, Firefly322, PlantTrees, Denisarona, Dp67, BOTarate, Dim4ik, Thingg, XLinkBot, AgnosticPreachersKid, WikHead, Addbot, Ravindra 20, Redheylin, Zorrobot, Ronaldo.nunez, Luckas-bot, Yobot, Ptbotgourou, Fraggle81, AnomieBOT, ^musaz, Materialscientist, Comt Till, Febert, Berrinkursun, Gbalasandeep, Anitauky, J. in Jerusalem, EmausBot, ZéroBot, Aportnoy, Akerans, 28bot, Vishalshindeelect, Rushikeshbansodeelec, Z-communications and Anonymous: 63 • Frequency-shift keying Source: http://en.wikipedia.org/wiki/Frequency-shift_keying?oldid=599753694 Contributors: The Anome, Michael Hardy, Ellywa, CatherineMunro, Glenn, Robbot, Ktims, Karn, Ssd, Ary29, Vishahu, Sonett72, ChrisJ, Mcpusc, Smalljim, Bsadowski1, Dan100, Camw, Jonnabuz, Murat40, BD2412, HappyCamper, FlaBot, Fresheneesz, Roboto de Ajvol, Willpo, Deville, David Biddulph, SDS, SmackBot, Moeron, KelleyCook, Oli Filth, Harumphy, Dougmc, Dicklyon, Tawkerbot2, Xcentaur, Wafulz, Chrumps, Tawkerbot4, Kozuch, Thijs!bot, Epbr123, Electron9, Tarnjp, Kauczuk, Alphachimpbot, Jim.henderson, Microsloth, Glrx, Haffner, J.delanoy, Dhaluza, Brianonn, CanOfWorms, LeaveSleaves, Stoneygirl45, Sv1xv, RFdave007, Djkryptyk, Addbot, Cuaxdon, Ramkumarvecsrv, Тиверополник, Legobot, Yobot, AnomieBOT, Living001, Jeffrey Mall, Omnipaedista, FrescoBot, 2A4Fh56OSA, Yahia.barie, DARTH SIDIOUS 2, RjwilmsiBot, RenamedUser01302013, Fæ, بدر الإسلام, ClueBot NG, MerlIwBot, Wbm1058, BG19bot, Mbpaz, Srinathkr3, ChrisGualtieri, Ginsuloft, MitchRandall and Anonymous: 82 • Amplifier Source: http://en.wikipedia.org/wiki/Amplifier?oldid=627607080 Contributors: AxelBoldt, Eloquence, Mav, Ray Van De Walker, SimonP, Waveguy, Heron, Kku, Ixfd64, Delirium, Docu, Kingturtle, Glenn, Nikai, GRAHAMUK, Jengod, Ww, Wik, Jessel, Maximus Rex, Omegatron, Bevo, Raul654, Lumos3, Friedo, RedWolf, Donreed, Dave Bass, Hcheney, David Gerard, Centrx, Giftlite, DocWatson42, Lunkwill, DavidCary, Laudaka, Lupin, Vk2tds, Markus Kuhn, Jcobb, AJim, Maroux, Jason Quinn, Nayuki, Wmahan, Chowbok, Sam Hocevar, Jcorgan, Abdull, Rich Farmbrough, TedPavlic, Guanabot, Pmsyyz, Pt, Meggar, Timl, Hooperbloob, Watsonladd, Malo, Osmodiar, Wtshymanski, Twisp, Crosbiesmith, Woohookitty, Uncle G, Pol098, CaptainTickles, BD2412, FreplySpang, Snafflekid, Koavf, Quiddity, Oblivious, Brighterorange, RobertG, Arnero, Margosbot, Alfred Centauri, Kolbasz, 121a0012, Bgwhite, Ahpook, The Rambling Man, Nol Aders, Matt512, Epolk, Bergsten, Chaser, Rohitbd, Bjf, Bou, Welsh, Howcheng, Thiseye, Dhollm, Speedevil, DeadEyeArrow, Searchme, Light current, Mattg2k4, Deville, Kungfuadam, Mebden, Jer ome, Kf4bdy, SmackBot, Reedy, Unyoyega, Freestyle, Daviddavid, Lindosland, Amatulic, Chris the speller, Bluebot, TimBentley, Cadmium, Thumperward, Papa November, Szidomingo, Sajendra, OrphanBot, Seduisant, Evilspoons, SnappingTurtle, DMacks, Pilotguy, Bn, Shields020, Breno, Minna Sora no Shita, CyrilB, Rogerbrent, Dicklyon, 2006mba, Kvng, Politepunk, OnBeyondZebrax, Iridescent, Walton One, Mihitha, Yves-Laurent, Chetvorno, JohnTechnologist, Xcentaur, CmdrObot, Chrumps, Nczempin, Lenilucho, Anoneditor, Doctormatt, Tubenutdave, Red Director, HermanFinster, Australian audio guy, FredYork, Gionnico, Editor at Large, Enter The Crypt, Pjvpjv, Saimhe, Guy Macon, Mccartyp, CPMartin, CosineKitty, TAnthony, MegX, Jahoe, Magioladitis, VoABot II, Askari Mark, JNW, JamesBWatson, Faizhaider, MichaelSHoffman, Black Stripe, Ngwill, MartinBot, Sigmundg, Jim.henderson, Anaxial, Nono64, Masisnr1, M samadi, DrKiernan, AntiSpamBot, SophieCat, Vspengen, Colorbow, Ale2006, Mlewis000, Funandtrvl, Joeinwap, Meiskam, ICE77, Philip Trueman, The Original Wildbear, Zuperman, Smcreator, Henrydask, Anonymous Dissident, Afluent Rider, Someguy1221, Monkey Bounce, Don4of4, Jackfork, Billinghurst, Kilmer-san, Dragonkillernz, Spinningspark, Internetexploder, Biscuittin, Audioamp, Krawi, Hiddenfromview, Henry Delforn (old), Lightmouse, Nitram cero, StaticGull, Denisarona, Asher196, Thinkingatoms, ClueBot, Binksternet, The Thing That Should Not Be, GeoffreyHale, Jan1nad, GreenSpigot, AnnArborRick, Blanchardb, Linan0827, Gtstricky, Brews ohare, Arjayay, Versus22, Johnuniq, XLinkBot, Alexius08, Revancher, Srcloutier, Pedro magalhaes86, Addbot, Mortense, Olli Niemitalo, Avobert, Yobot, Jordsan, Bestiasonica, Dleger, P1ayer, Sarukum, AnomieBOT, Piano non troppo, B137, Materialscientist, Citation bot, LilHelpa, Justanothervisitor, Ubcule, Maitchy, Uusijani, GliderMaven, FrescoBot, Gog182, Jc3s5h, Nickw2066, Gdje je nestala duša svijeta, Icontech, I dream of horses, TechnoDanny, Anooshg, Jujutacular, Hessamnia, Orenburg1, Theo10011, Belledonne, Qianchq, John of Reading, Kodabmx, Cmavr8, TuomTuo, GoingBatty, Solarra, AnonymousNarrator, The Nut, ChunkyPastaSauce, Tuborama, Peterh5322, Lowkyalur, Jefffolly, Lakkasuo, Petrb, ClueBot NG, Jaanus.kalde, MelbourneStar, Piast93, Andreas.Persson, Historikeren, Robsuper, MerlIwBot, Helpful Pixie Bot, HMSSolent, Bibcode Bot, Supersam654, CitationCleanerBot, 1292simon, Braun walter, ChrisGualtieri, Dexbot, Frosty, Mark viking, Epicgenius, Acrislg, Jamesmcmahon0, Brzydalski,
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Spyglasses, Rewa, AddWittyNameHere, Jbolton07, Gerbenvaneerten, Barefootwhistler, MasterTriangle12, Grsh90 and Anonymous: 404 • Electron hole Source: http://en.wikipedia.org/wiki/Electron_hole?oldid=613374475 Contributors: Maury Markowitz, Tim Starling, Lkesteloot, Omegatron, Bevo, Robbot, Ojigiri, Wjbeaty, LiDaobing, Karol Langner, DragonflySixtyseven, Roo72, Tirthajyoti, PhilHibbs, Nigelj, Robotje, Ranveig, Capi crimm, Palica, Mandarax, Salleman, FlaBot, Arnero, Chobot, YurikBot, RobotE, Bambaiah, Archelon, Shaddack, Spike Wilbury, Ninly, Sbyrnes321, The Photon, Shai-kun, Betacommand, Jcarroll, Bluebot, Jprg1966, Lagrangian, DMacks, Jaganath, Robofish, JorisvS, Mgiganteus1, Noah Salzman, Tawkerbot2, Jh12, Chetvorno, Gogo Dodo, Delta Spartan, Envy0, Thijs!bot, Barticus88, Salgueiro, JAnDbot, Britcom, Savant13, Sir Link, Sqush101, Aboutmovies, Andejons, Kurosa, Captainlavender, JhsBot, Jack Naven Rulez, SieBot, Extremecircuitz, No such user, Addbot, Out of Phase User, Bob K31416, OlEnglish, דוד שי, Uroboros, Meisam, Legobot, Luckas-bot, LilHelpa, Xqbot, Leonardo Da Vinci, Erik9bot, Citation bot 1, Lissajous, EmausBot, K6ka, ClueBot NG, Crazymonkey1123, Bibcode Bot, Williammathew30, Iplaycards, Vanquisher.UA, YimmyYohnson and Anonymous: 59 • P–n junction Source: http://en.wikipedia.org/wiki/P–n_junction?oldid=627108074 Contributors: AxelBoldt, Waveguy, RTC, Dmd, Mac, HolIgor, Auric, Wjbeaty, Ancheta Wis, Rafaelgr, Armandino, Mako098765, Abdull, Jfraser, Matt Britt, Foobaz, Timl, Storm Rider, Keenan Pepper, Wtshymanski, Tebbb, Marudubshinki, Nanite, Amr Ramadan, Vegaswikian, LjL, Prgo, Alfred Centauri, Kolbasz, Tomer Ish Shalom, Chobot, YurikBot, Sceptre, Gaius Cornelius, Shaddack, NawlinWiki, Bota47, Light current, Chaiken, Katieh5584, Attilios, SmackBot, Jacek Kendysz, Mauls, JAn Dudík, Bluebot, Pieter Kuiper, MalafayaBot, Darth Panda, Apocryphite, Radagast83, Drphilharmonic, DMacks, Catani, Vriullop, Intellectnfun, JorisvS, CyrilB, Cikicdragan, Dicklyon, Filelakeshoe, Chetvorno, SkyWalker, Christian75, Maque, Thijs!bot, Headbomb, Electron9, Gerry Ashton, AntiVandalBot, Email4mobile, Dukebody, Kskowron, Gresszilla, TheNoise, MartinBot, Bissinger, Glrx, CommonsDelinker, LordAnubisBOT, NewEnglandYankee, Cmichael, DorganBot, PowerWill500, VolkovBot, Larryisgood, Scholzilla, Someguy1221, Lerdthenerd, Andy Dingley, AlleborgoBot, Nagy, SieBot, VVVBot, Delu 85, Pratik mallya, Nopetro, Wilson44691, Arjen Dijksman, Siyamraj, Anchor Link Bot, ClueBot, Brews ohare, Vboo-belarus, XLinkBot, Terry0051, MystBot, Zinger0, Addbot, Mortense, Napy1kenobi, ProperFraction, Download, Jamesrei, Shrikul joshi, ScAvenger, Cesaar, Luckas-bot, Yobot, Senator Palpatine, Choij, Materialscientist, Citation bot, Darcovian, DSisyphBot, Igorpark, Raffamaiden, Rickproser, Jangirke, FrescoBot, Jc3s5h, BenzolBot, Youarefunny, MJ94, SpaceFlight89, Lowrybob, Javaidphy, علی ویکی, TheGrimReaper NS, MrSnoot, Bhawani Gautam, EmausBot, Beatnik8983, Dewritech, Monterey Bay, TyA, Xiutwel-0003, Noophilic, ClueBot NG, Starshipenterprise, Jbolte, Widr, Helpful Pixie Bot, Wbm1058, Helloakshaypoddar, Metricopolus, Satishb.elec, Tarunselec, Ulidtko, C susil, Aloysius314, IngenieroLoco, Ginsuloft, Mattkevmd, Jadecatz, Kirasan5 and Anonymous: 186 • Bipolar transistor biasing Source: http://en.wikipedia.org/wiki/Bipolar_transistor_biasing?oldid=608294834 Contributors: BrianWilloughby, Natrij, TedPavlic, Wtshymanski, Bruce1ee, Toffile, RadioFan, Moe Epsilon, Phil Holmes, Derek Andrews, Steve carlson, Ohconfucius, Robofish, Rogerbrent, Dicklyon, Iridescent, Jaksmata, Xcentaur, Circuit dreamer, Alaibot, Qwyrxian, Marek69, Deficit, Dr. Blofeld, Magioladitis, GreenSpigot, Brews ohare, Spitfire, Paushali, WikHead, Airplaneman, Addbot, Anypodetos, ThermalCat, Nasnema, Shadowjams, FrescoBot, Enery the 8th, Vrenator, Retro917, Peter Karlsen, 28bot, ClueBot NG, 220 of Borg, ChrisGualtieri, Ekren, Azeezur rahman and Anonymous: 61 • 555 timer IC Source: http://en.wikipedia.org/wiki/555_timer_IC?oldid=627217654 Contributors: Damian Yerrick, AxelBoldt, Scipius, Heron, RTC, Stw, Ahoerstemeier, Glenn, Nikai, Tomv, PeterGrecian, Omegatron, Huangdi, Alan Liefting, Giftlite, Brouhaha, Leonard G., Nielmo, Sonett72, Abdull, Grunt, ThreeE, NathanHurst, Discospinster, Pak21, Pmsyyz, Jcmaco, Alistair1978, Kaisershatner, Kwamikagami, Bobo192, Longhair, Towel401, Hooperbloob, Nazli, Alansohn, Keenan Pepper, Wtmitchell, Wtshymanski, Mikeo, SteveLetwin, Gene Nygaard, Kay Dekker, Mindmatrix, Sdschulze, Jacj, Palica, Pfalstad, Mandarax, Dubkiller, Pbeens, Brighterorange, Ptdecker, FlaBot, Nihiltres, RexNL, Turidoth, Gwernol, YurikBot, Adam1213, RussBot, Hellbus, Toffile, Hyjwei, Mikebest, Mikeblas, Speedevil, Ninly, Nkendrick, Ataub2qf, SmackBot, Elonka, The Photon, Stefan506, Colin99, Bromskloss, Gilliam, Hlovdal, MrDrBob, Thumperward, Oli Filth, Papa November, Audriusa, Can't sleep, clown will eat me, Frap, Aznium, Weregerbil, Flsp70, DireWolf, IronGargoyle, Llamadog903, CyrilB, Dicklyon, MTSbot, Dl2000, Hu12, Jachim, Tawkerbot2, Mikiemike, Ubernerd, Circuit dreamer, WeggeBot, **mech**, Bill (who is cool!), A876, After Midnight, Click23, Foil166, Sprhodes, Dtgriscom, Marek69, Electron9, Mallred, Dgies, Mihtjel, Escarbot, Hmrox, AntiVandalBot, Luna Santin, Ndyguy, MER-C, Wser, Hut 8.5, RebelRobot, .anacondabot, VoABot II, Mondebleu, Chkno, ArmadilloFromHell, Welle4, Mermaid from the Baltic Sea, Keith D, Jerry teps, The Canadian Roadgeek, J.delanoy, Jcurie, Vesa Linjaaho, NightFalcon90909, Flicovent, Kraftlos, Pundit, Potatoswatter, Bonadea, Ripper-b, VolkovBot, ICE77, Lexein, Quentonamos, Philip Trueman, Hqb, Olly150, Jack1993jack, Inductiveload, Suriel1981, PeterEasthope, Truthanado, Jtcampbell, Josh the Nerd, Yintan, Fduraibi, Jp314159, Oda Mari, JSpung, Ebarnett, Allmightyduck, XU-engineer, Shooke, Superbeecat, Prasanthv88, Bekuletz, ClueBot, Tim Forcer, Avenged Eightfold, Snigbrook, The Thing That Should Not Be, WaltBusterkeys, SuperHamster, Kiu77, (void*), Somno, Excirial, Rswarbrick, RexxS, Against the current, Rror, AbstractBeliefs, Actam, Avoided, Thatguyflint, Addbot, Technicalpic, Ronhjones, Jncraton, Eivindbot, Glane23, Favonian, Heshamdiab116, Numbo3-bot, Ettrig, SLourenco, Quadrescence, Yobot, CSSINC, Motif user, Materialscientist, Xqbot, Ywaz, Bubble-boy-115, JWBE, Jmundo, SassoBot, Jacksonmiss, Prari, FrescoBot, 6hug99ko, ZenerV, Tetraedycal, 42murr42, DrilBot, Kimphill, A8UDI, Btilm, MinimanDragon32, Mikespedia, Jrkemerer, Lissajous, ApusChin, Segal’sLaw, Techwetpaintwiki, Vikasjois, Nikhilpatel4488, DARTH SIDIOUS 2, Gloomofdom, EmausBot, WikitanvirBot, Immunize, Sophie, VOG-NevaDA, Colin555, John Cline, East of Borschov, Sbmeirow, Raghavendrabsrg, DASHBotAV, Petrb, ClueBot NG, Terry caborn, 3000farad, Reifytech, Mtmcdaid, Ercrt, Jupiter Kasparov, ChrisGammell, MusikAnimal, Satishb.elec, Colin5555, Trevayne08, Mattsains, Hcamen, LordOider, Dhx1, Mogism, Techdude3331, Junbert hular, Guanta37201, AnthonyRobinson123, Sravan75, Nattsukhdeep, Sureshkumar.suraj, Wasdichsoveraenderthat, ElectronicKing888, Jelabon123 and Anonymous: 335 • Operational amplifier Source: http://en.wikipedia.org/wiki/Operational_amplifier?oldid=627316180 Contributors: Mav, The Anome, WillWare, Malcolm Farmer, Heron, Edward, RTC, Michael Hardy, Mahjongg, Wapcaplet, Julesd, Glenn, Ghewgill, GRAHAMUK, Bemoeial, Dysprosia, Andrewman327, Omegatron, Wernher, AnonMoos, AlexPlank, Hankwang, RedWolf, Donreed, Smither, Pengo, Giftlite, DavidCary, Mintleaf, Inkling, Ds13, CyborgTosser, Leonard G., Frencheigh, Rpyle731, Mboverload, Foobar, Mike R, Aulis
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Eskola, DRE, Eranb, KeithTyler, Clemwang, M1ss1ontomars2k4, Adashiel, TedPavlic, ArnoldReinhold, Sn0wflake, ESkog, Plugwash, Dpotter, CanisRufus, Bdieseldorff, Shanes, Bobo192, Nigelj, .:Ajvol:., Foobaz, Hooperbloob, Musiphil, Neonumbers, Atlant, Keenan Pepper, Wtmitchell, Wtshymanski, Gene Nygaard, Alai, DSatz, Unixxx, Weyes, Woohookitty, Mindmatrix, Pol098, Cbdorsett, Gimboid13, Cataclysm, Msiddalingaiah, Snafflekid, Bvankuik, Sjakkalle, Arabani, Alejo2083, Chris Pressey, Ground Zero, Margosbot, Efficacy, Alfred Centauri, RexNL, Enon, Fresheneesz, Srleffler, YurikBot, Borgx, Gaius Cornelius, Rohitbd, Synaptidude, Grafen, 48v, Sparkinark, TDogg310, Voidxor, Supten, DeadEyeArrow, Elkman, Searchme, Bakkster Man, Light current, Super Rad!, Closedmouth, Mike1024, Mebden, Luk, Peranders, SmackBot, Igtorque, Thelukeeffect, Speight, Man with two legs, Jwestbrook, Lindosland, QEDquid, KD5TVI, Chris the speller, Bluebot, Oli Filth, EncMstr, Papa November, DHN-bot, FredStrauss, Audriusa, 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Philip Trueman, DoorsAjar, Draurbilla, Ianr44, Bizarro Bull, Inductiveload, Andy Dingley, Spinningspark, SieBot, Caltas, Charles.small, Roy hu, Jjwilkerson, Jp314159, Opamp, M Puddick, OsamaBinLogin, Evaluist, Faradayplank, PHermans, OscarJuan, PerryTachett, ClueBot, Smart Viral, Binksternet, ArthurOgawa, Mild Bill Hiccup, Srinivasbt, Alexbot, Jusdafax, Brews ohare, Sldghmmr, La Pianista, Wstorr, Aitias, Johnuniq, SoxBot III, Analogkidr, Salam32, Alexius08, ZooFari, Skonieczny, Gggh, Addbot, Mortense, Some jerk on the Internet, Olli Niemitalo, Theleftorium, Sudeepa123, Ppj4, Punkguitar, AnnaFrance, Favonian, LinkFA-Bot, Bruno gouveia rodrigues, Supav1nnie, Eng general, OlEnglish, Pietrow, Zorrobot, RobertTanzi, Luckas-bot, Yobot, Ptbotgourou, Annomination, AnomieBOT, Paulthomas2, Jim1138, JackieBot, Piano non troppo, LiuyuanChen, Materialscientist, Citation bot, Akilaa, Xqbot, Sellyme, XZeroBot, دانقولا, Dprabhu, Maitchy, Endothermic, GliderMaven, FrescoBot, LucienBOT, Ong saluri, Berrinkursun, Anitauky, Wikigayburgers, Roman12345, Vhann, Gdje je nestala duša svijeta, I dream of horses, Jonesey95, Hoo man, Ezhuttukari, Mikespedia, Abhishekchavan79, Æneas, Dinamik-bot, Overjive, PleaseStand, DARTH SIDIOUS 2, Teravolt, Breezeboy, EmausBot, John of Reading, Kasper Meerts, Torturella, Tawsifkhan, Solarra, Meht7860, Fæ, East of Borschov, Aflafla1, Thine Antique Pen, Rcsprinter123, Sbmeirow, Peterh5322, L Kensington, Danielop-NJITWILL, VictorianMutant, Petrb, Sudheerp99, ClueBot NG, Jaanus.kalde, Grottolese, Muon, Iinvnt, Widr, Lain.cai, Oddbodz, Helpful Pixie Bot, Wbm1058, Czar44, Sodaant, Minsbot, Yogirox234, Hghyux, MarinSwimmer, ChrisGualtieri, SD5bot, Dexbot, Jamesx12345, Visitor01, Monkbot, Pcrengnr, TerryAlex, MorganBEAST, AntonKrugerAtUiowa, Madphysics and Anonymous: 445 • Phase-locked loop Source: http://en.wikipedia.org/wiki/Phase-locked_loop?oldid=626157396 Contributors: Bryan Derksen, The Anome, Ap, PierreAbbat, Heron, Michael Hardy, Karada, CesarB, PingPongBoy, Mac, Glenn, Raven in Orbit, Technopilgrim, Dcoetzee, Lkesteloot, Omegatron, Maheshkale, Robbot, Jotomicron, Naddy, Mirv, Iain.mcclatchie, Cutler, Alan Liefting, Giftlite, Brouhaha, Neffk, Sarex, Tietew, BrianWilloughby, Abdull, RevRagnarok, D6, JGeld, Rich Farmbrough, Xezbeth, CanisRufus, Cmdrjameson, Timl, Iltseng, Hooperbloob, Tom Yates, Arthena, Wtshymanski, Brholden, DV8 2XL, Gene Nygaard, Alai, Linas, Sburke, Ruud Koot, Burgher, Jonnabuz, Msiddalingaiah, Snafflekid, Kotukunui, Rjwilmsi, Leeyc0, Tawker, Mbutts, FlaBot, Chris Pressey, Mel Gibson, Gurch, RobyWayne, WriterHound, YurikBot, Encyclops, Prometheus235, Toffile, Hydrargyrum, Brandon, Guerberj, Mikeblas, Mysid, Light current, Deville, Ninly, Alanb, LeonardoRob0t, Whaa?, Zvika, Pankkake, SmackBot, H2eddsf3, Reedy, Unyoyega, Fulldecent, Larrykoen, Lindosland, Chris the speller, Bluebot, Oli Filth, Papa November, Can't sleep, clown will eat me, Frap, OrphanBot, Shanid, Nakon, Wirbelwind, Dr. Crash, Viyh, Kvng, Paul Koning, Yenhsrav Keviv, Tudy77, Blehfu, Chetvorno, Emote, Eastlaw, Philshea, Chrumps, Requestion, Johnlogic, Mattisse, Alex Forencich, DmitTrix, Electron9, Prolog, Hmo, Beabroad, User A1, Glrx, R'n'B, Huzzlet the bot, Kar.ma, Rod57, Ganymedstanek, Vanished user 47736712, Jrolston, Rex07, Frodo avr, Squids and Chips, Anton Rakitskiy, TXiKiBoT, ElinorD, ChooseAnother, Jpat34721, Billgordon1099, Wangyiliu99, Dirkbb, Faduman, AlleborgoBot, Plan10, SieBot, Cwkmail, Mwaisberg, EngineerSteve, HURRICANE1415, WWStone, Vahid avr, IR-TCI, WakingLili, Dp67, ClueBot, PipepBot, Yegorius, 718 Bot, Stevenmyan, Alexbot, PixelBot, Jimfordbroadcom, Peter.C, SchreiberBike, DumZiBoT, Apps guy, Feinoha, MystBot, J 0JFCfrmAyw59oVFk, Dsimic, Addbot, AVand, Duketron, H92Bot, Mitch feaster, Lightbot, Wireless friend, Sechinsic, Legobot, Luckas-bot, OrgasGirl, Castagna, AnomieBOT, LilHelpa, Obersachsebot, Grim23, Devanney, Feldhaus, Jangirke, Prosaicpat, MastiBot, Merlinsorca, Renatyv, HitiABC, Cetsurfer, EmausBot, John of Reading, Tolly4bolly, Orange Suede Sofa, ClueBot NG, Daithiob, Helpful Pixie Bot, Emresearch13, Neøn, LeonovGA, Kuznetsov N.V., Frogging101, Rabachand, 08Peter15, Dexbot, Bizet74, Vicentealvarez2, Ehud.ahissar, Avinash701, Drjimbonobo, Lizbel123, AntonKrugerAtUiowa, Crystallizedcarbon and Anonymous: 217 • Voltage regulator Source: http://en.wikipedia.org/wiki/Voltage_regulator?oldid=627175051 Contributors: BlckKnght, Heron, Bdonlan, Glenn, GRAHAMUK, Zoicon5, Maximus Rex, Omegatron, Hankwang, Henrygb, DavidCary, Scott MacLean, Sonett72, Jcmaco, Rubicon, Jaberwocky6669, Plugwash, RoyBoy, Nigelj, Timl, Hooperbloob, Jakew, Mareino, 1-1111, Tpikonen, Atlant, Wtshymanski, Pol098, Mandarax, Tizio, Brighterorange, Yamamoto Ichiro, Margosbot, Alfred Centauri, Srleffler, Jidan, Visor, DMahalko, Toffile, Gaius Cornelius, Rohitbd, Ethan, Spike Wilbury, Mikeblas, LeoNerd, Hirak 99, Ninly, SmackBot, Unyoyega, Gilliam, Lindosland, Chris the speller, Oli Filth, Spacemeng, Audriusa, 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Hart, Eirik1231, DexDor, AndyHe829, Wyatte Gillette, EmausBot, Orphan Wiki, Dcirovic, ZéroBot, Mkratz, Pgarg78, Sbmeirow, Mohsen.1987, Donner60, ClueBot NG, Akashacharyak, Ulrich67, Rezabot, MerlIwBot, Helpful Pixie Bot, Aholyokeb, Wbm1058, Mataresephotos, Mpalframan, Tiscando, Vydeoatpict, Jschnabs, Jamietwells, Nilay.pant, Tentinator, Buntybhai, Monkbot, GinAndChronically, RoyPijnenburg, Mario Castelán Castro, ChamithN and Anonymous: 205 Comparator Source: http://en.wikipedia.org/wiki/Comparator?oldid=627647264 Contributors: Heron, Edward, Ahoerstemeier, Glenn, Smack, Schneelocke, Omegatron, Dbroadwell, Stuuf, Jaan513, Discospinster, Sietse Snel, Hooperbloob, Andrewpmk, Cburnett, Jannex, Matthew Platts, Mandarax, Maxim Razin, Arnero, Crazycomputers, Stassats, Guerberj, Katieh5584, Bmearns, Lindosland, Bluebot, Daydreamer302000, Af1218, Barney Stratford, S Roper, Jeff Wheeler, Paul Rako, Avé, 16@r, Dicklyon, Daharde, Chetvorno, Mikiemike, Circuit dreamer, TAB, Thijs!bot, CosineKitty, Adilsm, Scottr9, R'n'B, Amikake3, Grantdj, Miwanya, Inductiveload, AlleborgoBot, Flyer22, Sokari, ClueBot, The Thing That Should Not Be, Optics guy07, VQuakr, Mild Bill Hiccup, Somno, Three-quarter-ten, ChardonnayNimeque, PixelBot, SpikeToronto, Analogkidr, Addbot, Mortense, Yobot, Xqbot, NSK Nikolaos S. Karastathis, FrescoBot, Febert, Smurfettekla, Berrinkursun, Cannolis, I dream of horses, Calmer Waters, Chotugubbi, Eguru37, Wikieditorz, Reconsider the static, EmausBot, ZéroBot, East of Borschov, Derekleungtszhei, ChuispastonBot, ClueBot NG, Helpful Pixie Bot, CitationCleanerBot, BattyBot, Jaspritsgill, Imneerajgarg3, Monkbot, Ksumatrob and Anonymous: 109 Thermistor Source: http://en.wikipedia.org/wiki/Thermistor?oldid=626052477 Contributors: Sodium, Bryan Derksen, Zundark, Szopen, Ray Van De Walker, Heron, Tim Starling, Tango, Ellywa, Zoicon5, Maximus Rex, Omegatron, Carbuncle, Jni, Twang, Chuunen Baka, Donarreiskoffer, Robbot, Hankwang, Tonsofpcs, Sho Uemura, Alan Liefting, Buster2058, Centrx, BenFrantzDale, Tsca, Leonard G., Bobblewik, Wmahan, DougEngland, Zondor, Grunt, Plugwash, Kjkolb, Hooperbloob, Alansohn, PAR, Velella, RainbowOfLight, Henry W. Schmitt, Gene Nygaard, Vadim Makarov, Jimgeorge, Ruud Koot, Graham87, War, Toki, Brighterorange, Unfocused, Allen Moore, FlaBot, Margosbot, Srleffler, Zotel, Chobot, Karch, Mhking, Cookie4869, CambridgeBayWeather, Shaddack, Veledan, Howcheng, Raven4x4x, RUL3R, Searchme, Light current, Morcheeba, Closedmouth, Tabby, Sbyrnes321, Finell, Grend3l, Waulfgang, SmackBot, Thorseth, Iopq, Papep, Ohnoitsjamie, Oscarthecat, Bluebot, Oli Filth, SchfiftyThree, Милан Јелисавчић, BullRangifer, Doodle77, Mircealutic, Mion, Shirifan, Dicklyon, Komeil, Tawkerbot2, Bemasher, CmdrObot, Zureks, Requestion, NickFr, Ussensor, Yaris678, PureGenius, NascarEd, N5iln, James086, Drigz, Greg L, Nemilar, Stannered, AntiVandalBot, Quintote, Myanw, JAnDbot, Txomin, Rob Kam, Mdurante, Magioladitis, Diablod666, VoABot II, Rivertorch, Chakri srivatsa, Madmanguruman, MartinBot, Manavbhardwaj, Neeners, Jim.henderson, Tgmsfu, EliV, Choihei, Ashtead Tutor, Dhaluza, Halmstad, Ibdelfest, Funandtrvl, Nasanbat, VolkovBot, ABF, Constant314, TXiKiBoT, Oh Snap, Salvar, Brian Helsinki, Broadbot, Jackfork, Madhero88, Triesault, AlleborgoBot, Neparis, SieBot, God Emperor, Masgatotkaca, Seraphal, ClueBot, Janz94b, Mardetanha, Awickert, Plainman, Estirabot, Dittos12, Paulienator, Karpouzi, Teslaton, Rob-bob70, SkyLined, Kbdankbot, Addbot, Mortense, Willking1979, Captain-tucker, AkhtaBot, West.andrew.g, Jnmurfin, Lou Mueller, Cesaar, Legobot, Luckas-bot, Yobot, Ptbotgourou, Amirobot, QueenCake, Tempodivalse, AnomieBOT, Rubinbot, Ndgrahams, Aditya, Materialscientist, ArthurBot, Xqbot, Vichou, Nedim Ardoğa, Yoganate79, Jangirke, IShadowed, Idyllic press, Pinethicket, SpaceFlight89, Mayank2507, TjBot, EmausBot, Dewritech, GoingBatty, Tommy2010, Hhhippo, Back0ut, Jwortzel, SamuelFreli, ClueBot NG, MelbourneStar, Lochlan1, Widr, Helpful Pixie Bot, Ramaksoud2000, Piguy101, Klilidiplomus, Mrt3366, MadCowpoke, Yukichen, Isarra (HG), BeaumontTaz, Sihuapilapa, Chestercheryl, RogerDulhunty, Epicgenius, R.Mann66, Jodosma, Yardimsever, 99kmg365, Zeniu17, AMWEI Thermistor and Anonymous: 254 Photodiode Source: http://en.wikipedia.org/wiki/Photodiode?oldid=627766575 Contributors: Css, Perry Bebbington, Heron, Frecklefoot, Bdesham, RTC, Tim Starling, Rabin, Liftarn, Sannse, Glenn, Nikai, Andres, Epo, Reddi, Omegatron, Francs2000, Robbot, Fredrik, Roscoe x, Giftlite, Ferkelparade, Mako098765, Rdsmith4, Nickptar, Deglr6328, Murtasa, Shanes, Bookofjude, Giraffedata, BigRiz, Hooperbloob, Atlant, Wtshymanski, DV8 2XL, Linas, Pol098, Palica, RuM, Snafflekid, Rjwilmsi, KaiMartin, Weihao.chiu, Srleffler, Chobot, Jaraalbe, YurikBot, Jeffthejiff, Hede2000, Jhchang, Kkmurray, Morcheeba, Pb30, GrinBot, KnightRider, SmackBot, Terry1944, The Photon, Fulldecent, Ohnoitsjamie, Vercalos, Lindosland, HenrikS, Oli Filth, A. B., Audriusa, LouScheffer, DinosaursLoveExistence, Nakon, Xagent86, Rcopley, DJIndica, Anachron, NANOIDENT, Breno, Minna Sora no Shita, MadScientistVX, Beetstra, Dicklyon, Spiel496, Kvng, Moonkey, Ddcc, Tarchon, Nilfanion, Shadwstalkr, Dancter, Mitjaprelovsek, Thijs!bot, Electron9, Tellyaddict, Big Bird, KrakatoaKatie, Whogue, Gh5046, Em3ryguy, Vanished user ty12kl89jq10, Vssun, DerHexer, Kevglynn, MartinBot, Ctroy36, J.delanoy, Pharaoh of the Wizards, Jstahley, Zen-in, Dlegros, Sgc2002, Philip Trueman, Srdhrp vict, Daisydaisy, Adam C C, LeaveSleaves, Silverbone, Tmaull, Andy Dingley, AledJames, WingkeeLEE, Cyfal, ClueBot, Robertmuil, Lucas the scot, Nrnkpeukdzr, AlanM1, H0dges, Addbot, Mathieu Perrin, A0602336, Download, Shkirenko edik, Favonian, Bwrs, Semiwiki, Yobot, Amirobot, Fotodiod, SwisterTwister, AnomieBOT, Jim1138, Materialscientist, Xqbot, Erud, Capricorn42, RibotBOT, Nedim Ardoğa, Chn Andy, FrescoBot, Arande2, Evan 124, Tóraí, Scwks, Devindunseith, Texasron, EmausBot, John of Reading, WikitanvirBot, Giant12111, Sbmeirow, Karthikndr, Atcold, Tls60, Puffin, Intellec7, Staticd, ClueBot NG, Fulvio314, Helpful Pixie Bot, OAnimosity, Djjhs, Himu.arif, Fathpour, Phadd, JaunJimenez, GoLiang, Jogi.sreeram and Anonymous: 218 Photoresistor Source: http://en.wikipedia.org/wiki/Photoresistor?oldid=624078563 Contributors: Heron, Bdesham, RTC, Tim Starling, Egil, Iain, Julesd, Glenn, Andres, Bemoeial, ElusiveByte, Omegatron, Raul654, Eugene van der Pijll, Robbot, Hankwang, Aechols, Glenn Koenig, Adashiel, Mike Rosoft, Jiy, Neko-chan, Gilgamesh he, Femto, Billymac00, Giraffedata, Samadam, Hooperbloob, Alansohn, Gary, Atlant, Evil Monkey, Gene Nygaard, UFu, Cbdorsett, Cyberman, K3wq, Rjwilmsi, Ademkader, Alfred Centauri, Kolbasz, Srleffler, YurikBot, Adam1213, Hydrargyrum, Gaius Cornelius, Havok, NawlinWiki, Wiki alf, Mssetiadi, Elkman, Ikonen, Tabby, Donald Albury, Kevin, Neilgravir, Sbyrnes321, KnightRider, Gigs, Erbbysam, Relaxing, Wheatleya, Oli Filth, Pevarnj, Akendall, CyrilB, OZOO, E-Kartoffel, Yves-Laurent, Dancter, Thijs!bot, Frozenport, Jojan, Marek69, Zaiken, AntiVandalBot, Luna Santin, Âme Errante, Ioeth, JAnDbot, MER-C, CosineKitty, Hut 8.5, VoABot II, Kharkless, MartinBot, Aragorn450, Gzkn, Paulvermillion, Jim Swenson, Jennavecia, Amikake3, Ulfbastel, Clarince63, Melsaran, Yk Yk Yk, KyleSinghSaini, SieBot, Flyer22, Richgoddard, Cameron7935, C4udy, ClueBot, PaulLowrance, Heracletus, DragonBot, PixelBot, BOTarate, HumphreyW, DumZiBoT, Teslaton, Addbot, Mortense, Willking1979, Element16, Ronhjones, Sploshy100, Glane23, Chzz, Semiwiki, Luckas-bot, TaBOT-zerem, Muranesenema, KDS4444, Ciphers, Poetman22,
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Cachao, Duhos, RibotBOT, Prari, FrescoBot, Jc3s5h, MGA73bot, PigFlu Oink, Kutayzorlu, Pinethicket, SpaceFlight89, Dinamik-bot, Soulhack, دالبا, EmausBot, Go82102, Mkratz, HawkMcCain, TYelliot, Mikhail Ryazanov, ClueBot NG, O.Koslowski, Widr, Helpful Pixie Bot, HMSSolent, Vaibhavsg.elec, Quickshivam, FynnM, Chip123456, Phillip mcfuzz, Lxdcn, SFK2, Arunwebber, Tentinator, Ruprecht27, JaunJimenez and Anonymous: 190 • Analogue switch Source: http://en.wikipedia.org/wiki/Analogue_switch?oldid=624623726 Contributors: SimonP, Waveguy, Heron, Colin Marquardt, Zoicon5, Omegatron, Robbot, Mintleaf, Everyking, Glogger, Hooperbloob, Gene Nygaard, Uncle G, Josh Parris, KaiMartin, Bmicomp, Light current, SmackBot, Oli Filth, Mion, Catapult, Pi.1415926535, Mild Bill Hiccup, Addbot, Erik9bot, Febert, Berrinkursun, Gbalasandeep, Anitauky, EmausBot, Kuashio, Rangoon11, Thawk59 and Anonymous: 10 • Decibel Source: http://en.wikipedia.org/wiki/Decibel?oldid=628262911 Contributors: Tobias Hoevekamp, DrBob, Heron, Spiff, Edward, Patrick, Michael Hardy, Iluvcapra, Ahoerstemeier, Hpa, BAxelrod, Smack, Timwi, Pheon, Furrykef, Omegatron, Indefatigable, Pakaran, Hankwang, Pigsonthewing, Peak, Academic Challenger, Rsduhamel, Pabouk, Giftlite, DocWatson42, DavidCary, Mintleaf, BenFrantzDale, Zigger, Karn, Abqwildcat, Jason Quinn, Mboverload, Rchandra, AlistairMcMillan, Antandrus, Cihan, Icairns, Sonett72, BrianWilloughby, Mormegil, Jayjg, Abar, Rich Farmbrough, Guanabot, Florian Blaschke, Xezbeth, Alistair1978, Bender235, ZeroOne, A purple wikiuser, Plugwash, Petersam, Mark R Johnson, Alansohn, Vslashg, Duffman, RPaschotta, Andrewpmk, SlimVirgin, !melquiades, Kotasik, Hu, Benjamin.Heasly, Hessi, Wtshymanski, Cburnett, Stephan Leeds, Gene Nygaard, Peter Hanes, Nuno Tavares, Mário, LOL, Pol098, Walker44, Kristaga, MONGO, Kgrr, Pyrosim, Cbdorsett, Scm83x, Jwoodger, E090, Deltabeignet, BD2412, Rjwilmsi, Joffan, Aechris, Wesley R. Elsberry, N0YKG, Titoxd, Ianharvey, RexNL, Ayla, DrVeghead, Fresheneesz, Skierpage, Srleffler, Glenn L, Epitome83, King of Hearts, Chobot, DVdm, Crovax, Oh2mqk, Whosasking, Rmo13, Wolfmankurd, RussBot, Muchness, Peter S., Xihr, Splash, JabberWok, BlongerBros, Hydrargyrum, Manop, Sixteen Left, Burek, Accurrent, Wiki alf, Razer64, Dhollm, Zephalis, Asbl, Eurosong, Ke6jjj, Light current, Noclip, Open2universe, Knotnic, Nikkimaria, Pb30, Esprit15d, David Biddulph, Thesleepwalker, GrinBot, Bo Jacoby, Cmglee, Sbyrnes321, DVD R W, CIreland, SmackBot, Tgoose, Bobet, Xephael, CelticJobber, Hydrogen Iodide, Fuchsia Groan, Cutter, RichGibson, GraemeMcRae, Bromskloss, Commander Keane bot, Gilliam, Skizzik, JAn Dudík, Lindosland, PeterCooperJr, Bluebot, Kurykh, Oli Filth, Greatgavini, Nbarth, Colonies Chris, Dual Freq, Emurphy42, GeeksHaveFeelings, Microfrost, Rrburke, Spectrogram, Cybercobra, MichaelBillington, Kneale, Gurnec, Fitzhugh, Romanski, Daniel.Cardenas, Mostlyharmless, Ugur Basak Bot, Rklawton, Straif, Hefo, Jidanni, Henry’s Cat, Beta34, JustinSmith, Dicklyon, Tobyw87, SolarAngel, Dr.K., Noleander, Kvng, Samstayton, Dl2000, ILovePlankton, Smsaladi, Emote, TheHorseCollector, Bungledb, Myncknm, Desrt, Tarchon, Cydebot, MC10, JJC1138, Zginder, Rajkiran g, DumbBOT, Ehudzel, Centuriono, Thijs!bot, Yhevhe, Epbr123, Mdberg1, Headbomb, Dtgriscom, Sobreira, Marek69, Chris01720, Neil916, Electron9, CharlotteWebb, Uruiamme, Auralcircuitry, AntiVandalBot, Luna Santin, RapidR, Rutuag, Chill doubt, Alphachimpbot, Ingolfson, JackSparrow Ninja, JAnDbot, MER-C, Magioladitis, Bongwarrior, VoABot II, Catslash, SHCarter, Stotan, Ling.Nut, MarcusMaximus, Enquire, Waninge, Pan Dan, WLU, The Sanctuary Sparrow, Amphedu, MartinBot, IgorSF, Ephracis, Jim.henderson, Rettetast, Anaxial, R'n'B, Bjerke, SSSidhu, M samadi, Mange01, Ali, Poopface666, Nolaiz, Floaterfluss, Pcfjr9, Kraftlos, Robinparfitt, Juliancolton, Davecrosby uk, Mlewis000, Sapphire12758, Jeff G., Toddles29, EchoBravo, Boute, Philip Trueman, The Original Wildbear, Oric.gr, Link, Vipinhari, A4bot, Hqb, Pediacycle, Tonyjeffs, Billydee84, J.C. Roberts, Dendodge, Greg searle, Hanjabba, Jhawkinson, Alexjliu, Spinningspark, Insanity Incarnate, NMTPhysics, Tbmoney1000, Thunderbird2, Mr. PIM, Markwads, Bluemouse2306, Thomas EL Smith, Kbrose, Bohemian simian, Caltas, Yintan, Ygramul, Permacultura, Bsherr, Antonio Lopez, Kielhofer, AMCKen, OscarJuan, Kudret abi, Gomertrash, Dellr, Jjefferp, ClueBot, Rumping, Binksternet, Eric Wester, EoGuy, Thubing, Meekywiki, Uncle Milty, TimmmmCam, Klenod, Sun Creator, Dirt Tyrant, Madkaugh, Jonverve, Fmiser, GeoffMacartney, DumZiBoT, JKeck, AlanM1, Avoided, Superbirk, Subversive.sound, Kace7, HexaChord, Addbot, Caden, Ocdnctx, Fgnievinski, Computer Guy 990, GyroMagician, CanadianLinuxUser, C6H3N3O3, NjardarBot, Redheylin, Glane23, LemmeyBOT, Numbo3-bot, Ehrenkater, Fundamentisto, Didie, Legobot, Yobot, AnomieBOT, Götz, Jeni, Bently64, Ipatrol, Materialscientist, Citation bot, Foreman1280, Richard Jay Morris, Nifky?, Oshasafety, Jeffrey Mall, Heddmj, Nasa-verve, WaysToEscape, Dave3457, Dogbert66, Jc3s5h, Euc, Oalp1003, Citation bot 1, Pinethicket, PrincessofLlyr, 10metreh, RedBot, SpaceFlight89, Dtrx, North8000, Vrenator, Fastilysock, Goph'r, Marie Poise, DARTH SIDIOUS 2, Caffeein, Jaguarondi, EmausBot, Immunize, Mordgier, Dewritech, Roshamboz, O'DaveY, Wikipelli, BrianServis, Josve05a, Shofus, Dondervogel 2, H3llBot, Glockenklang1, ChemMater, Mltinus, Divineale, Mxctor, ClueBot NG, DieSwartzPunkt, Widr, Helpful Pixie Bot, Kurtdebille, Rsercher, Kamerrill, BG19bot, Gurt Posh, Emayv, Yuanquan74, Daleshirk, J991, Planetary Chaos Redux, Mark Arsten, CitationCleanerBot, NotWith, Aisteco, BattyBot, Pad3509, Brownb 22, ChrisGualtieri, GoShow, Garamond Lethe, Khazar2, Ntmbeast, Riccardo4444, Smit 58, Reatlas, Hoodecho, Faizan, Epicgenius, Seanhalle, BreakfastJr, Frozenprakash, Lolguy9, Babitaarora, Spyglasses, Quadlou, Jackmcbarn, W. P. Uzer, Coreyemotela, 22lsufan, MrsBentonsclass, Swarhili, Jayakumar RG, Simplexdave and Anonymous: 635 • Noise (electronics) Source: http://en.wikipedia.org/wiki/Noise_(electronics)?oldid=628056538 Contributors: William Avery, Heron, Omegatron, Smither, Alan Liefting, Ancheta Wis, Giftlite, DavidCary, Vadmium, Keenan Pepper, Penwhale, Gene Nygaard, TheArmadillo, Kosher Fan, Pol098, Rjwilmsi, Bruce1ee, Lmatt, Splintercellguy, Toffile, Daniel C, Light current, Deville, Tevildo, Kle0012, SmackBot, Ssbohio, Macintosh User, Lindosland, Oli Filth, SchfiftyThree, Il palazzo, Scwlong, Dreadstar, RickO5, Rogerbrent, Dicklyon, Waggers, Chetvorno, TristanJ, Tbone2001, Cydebot, Martin Hedegaard, JAnDbot, Mytomi, Rich257, STBot, Glrx, Mange01, RSRScrooge, Maurice Carbonaro, Rod57, Jeepday, Funandtrvl, Jamelan, Improve, Yngvarr, SieBot, Pitoutom, Flyer22, Paolo.dL, Chemawb, Vcaeken, YSSYguy, Arjayay, Johnuniq, Rror, DOI bot, Fyrael, GyroMagician, Yobot, AnomieBOT, Valueyou, Materialscientist, Nasa-verve, RibotBOT, Nedim Ardoğa, Aandroyd, Miyagawa, FrescoBot, Nageh, Michael93555, Throwaway85, DexDor, Ok2ptp, Riichrd, Hhhippo, ClueBot NG, Helpful Pixie Bot, Bibcode Bot, Htavroh, Ahmedmustafamahmoud, BattyBot, Mcginnsc, ChrisGualtieri, Tagremover, Frosty, Atul hbk and Anonymous: 61 • Switched capacitor Source: http://en.wikipedia.org/wiki/Switched_capacitor?oldid=611735228 Contributors: HelgeStenstrom, Heron, TedPavlic, Magister Mathematicae, Guerberj, Jaycarlson, SmackBot, Katanzag, Bluebot, Savidan, Jeff Wheeler, Reza mirhosseini,
9.1. TEXT
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EdGl, Yves-Laurent, Biscay, Mikiemike, CmdrObot, Underpants, Thijs!bot, RobBrisbane, Mubed, Phosphoricx, User A1, RockMFR, VolkovBot, Deki mg, Rob hagan, Treekids, Mreza v, Addbot, Willplatts, EconoPhysicist, Redheylin, Yobot, Theorih, Catwikionline, EmausBot, Hanjifi, ClueBot NG, Snotbot, KLBot2, BrunoHaider and Anonymous: 37 • H bridge Source: http://en.wikipedia.org/wiki/H_bridge?oldid=625428917 Contributors: RTC, DavidCary, BenFrantzDale, Vadmium, Sarex, Publunch, Roo72, Jcmaco, Fuxx, Sanctum, Nasukaren, Magetoo, Marudubshinki, Vegaswikian, Ademkader, FlaBot, Arnero, DVdm, WriterHound, Hellbus, Speedevil, !jrb, SmackBot, Oli Filth, OrphanBot, CyrilB, Dicklyon, Wizard191, Brwilliams, Amalas, Hans.vdb, Pro crast in a tor, CosineKitty, Donny3000, Americanhero, Matt B., Glrx, Smial, Leyo, TSullivan, Roboto1148, SoCalSuperEagle, Ikalogic, Noformation, Spinningspark, Biscuittin, Envergure, Cupzonia, Spuzzdawg, Treekids, ClueBot, Snigbrook, Pelesl, DumZiBoT, XLinkBot, Ijayasin, Sisera, Addbot, Mortense, Semiwiki, Luckas-bot, Yobot, Fraggle81, Xqbot, GliderMaven, HRoestBot, Steve2011, John of Reading, WikitanvirBot, Bamyers99, John Smith 104668, خالقیان, ClueBot NG, Kubing, Clampower, Helpful Pixie Bot, Wbm1058, BG19bot, JYBot, Vamfun, Tony Mach, Creation911, Jodosma, Spyglasses, Nchiazza, 8BitTRex and Anonymous: 82 • Hall effect sensor Source: http://en.wikipedia.org/wiki/Hall_effect_sensor?oldid=627806864 Contributors: Magnus Manske, Glenn, Smack, Omegatron, BenFrantzDale, Geeoharee, Ot, Karol Langner, Sam Hocevar, Cacycle, Android79, Bobo192, Remuel, Enric Naval, A-Day, Hooperbloob, Alansohn, Hohum, Evil Monkey, IMeowbot, Angr, Alvis, Sjakkalle, Mbutts, Anthony81212, Srleffler, YurikBot, RussBot, Sillybilly, Stephenb, Janke, Mikeblas, Attilios, SmackBot, Bluebot, Tsca.bot, DMacks, Mion, Es330td, Yves-Laurent, Vanisaac, Thijs!bot, Adams13, JAnDbot, Cubaexplorer, Rewolff, Nyq, Nposs, DadaNeem, Inwind, Funandtrvl, TXiKiBoT, David Condrey, SieBot, Antzervos, ClueBot, Danpeirce, Mralik, ALLurGroceries, Pocketrocket24, Little Mountain 5, Addbot, Kongr43gpen, Grahamatwp, OlEnglish, AnomieBOT, Materialscientist, Xqbot, GrouchoBot, Trurle, RibotBOT, Zhangzhe0101, Ksk2005, John of Reading, Jnanadevm, Joe Gazz84, Josve05a, , Aeonx, Jwortzel, Sbmeirow, Djapa84, Bcaulf, RockMagnetist, ClueBot NG, JohnTsams, Muon, Rezabot, Dsperlich, Helpful Pixie Bot, BG19bot, Alangar Manickam, CitationCleanerBot, Samhuntvid, Riyasmydheen, Magnetic models and Anonymous: 70 • Low-pass filter Source: http://en.wikipedia.org/wiki/Low-pass_filter?oldid=623165965 Contributors: Mav, The Anome, Rjstott, Heron, Patrick, JohnOwens, Lexor, David Martland, Glenn, Palfrey, Dysprosia, Furrykef, Omegatron, ThereIsNoSteve, Giftlite, DavidCary, Wolfkeeper, Bensaccount, Vadmium, LucasVB, Antandrus, BrianWilloughby, Moxfyre, Rfl, Rich Farmbrough, TedPavlic, Mecanismo, ESkog, Teorth, Foobaz, Cavrdg, Hangjian, Hooperbloob, Dragoljub, Wtshymanski, Cburnett, Flying fish, Davidkazuhiro, Pol098, Akavel, Pfalstad, Torquil, Mikm, Alfred Centauri, Kri, Krishnavedala, Borgx, PinothyJ, Toffile, Gaius Cornelius, Brandon, Mikeblas, Searchme, Light current, Mickpc, Deville, Petri Krohn, LeonardoRob0t, Phil Holmes, RG2, Mejor Los Indios, EXonyte, KnightRider, Mitchan, Steve carlson, Pgk, Niehaus, Nbarth, RoysonBobson, Zvar, Soundsop, IE, P.o.h, Elzair, Dog Eat Dog World, Minna Sora no Shita, Rogerbrent, Dicklyon, Kvng, Ss181292, Unmitigated Success, Myasuda, Paddles, Editor at Large, Epbr123, Sobreira, Bobblehead, Brichcja, Majorly, Danroa, Lovibond, Ekkanant, JAnDbot, Xhienne, Drizzd, Time3000, Bongwarrior, VoABot II, Dics, Eus Kevin, Parijata, Kayau, MartinBot, Renski, Tgeairn, RockMFR, Mange01, Slamedsilver, LLcopp, VolkovBot, Inductiveload, Ahmedsaieed, Spinningspark, Anoko moonlight, Kbrose, Tetos, Tugjob, Dp67, ClueBot, Binksternet, Brews ohare, Thingg, 7, Dusen189, Johnuniq, XLinkBot, Mm40, ZooFari, Addbot, Howard Landman, Jojhutton, Redheylin, Parvejkhan, Nocal, Tide rolls, Gail, Legobot, Bdb112, Floquenbeam, Jim1138, B137, Materialscientist, Citation bot, Xqbot, Armstrong1113149, Pontificalibus, Christopherley, RibotBOT, Rb88guy, GliderMaven, ICEAGE, Jonesey95, RedBot, Piandcompany, December21st2012Freak, The Utahraptor, Mgclapé, Astro89, WikitanvirBot, Immunize, Dewritech, Catshome2000, Zueignung, Teapeat, Dweymouth, ClueBot NG, Satellizer, Widr, Varun varshney12, OceanEngineerRI, Kizzlebot, JYBot, Kroq-gar78, CsDix, My name is not dave, Quenhitran, Meteor sandwich yum, Monkbot and Anonymous: 221 • High-pass filter Source: http://en.wikipedia.org/wiki/High-pass_filter?oldid=611538221 Contributors: The Anome, Rjstott, PierreAbbat, Lexor, Glenn, Charles Matthews, Omegatron, Eugene van der Pijll, ThereIsNoSteve, Tonsofpcs, BenFrantzDale, Vadmium, Rfl, TedPavlic, Bobo192, Rbj, Foobaz, Hooperbloob, Dragoljub, RJFJR, Zawersh, Gene Nygaard, Bruce89, Thryduulf, Robert K S, GregorB, Waldir, Pfalstad, Rjwilmsi, Lockley, Arnero, PinothyJ, Alynna Kasmira, Mikeblas, Attilios, KnightRider, SmackBot, Vina-iwbot, P.o.h, Elzair, Soumyasch, Dicklyon, Shaunwhite000, Shoez, Myasuda, Scoofy, Sobreira, Drizzd, AndyBloch, .anacondabot, Magioladitis, Faizhaider, Baccyak4H, Katalaveno, Joerglwitsch, Ziounclesi, Spinningspark, Tresiden, Fibo1123581321, Bekuletz, ClueBot, Binksternet, Estirabot, Gciriani, XLinkBot, Addbot, Jojhutton, Olli Niemitalo, Redheylin, Legobot, Yobot, Fraggle81, Amirobot, EnTerr, Gianno, Citation bot, ShornAssociates, Armstrong1113149, RibotBOT, Mnmngb, Maitchy, Ll1324, JMS Old Al, Toriicelli, DARTH SIDIOUS 2, EmausBot, Xiutwel-0003, ChuispastonBot, ClueBot NG, Rezabot, Helpful Pixie Bot, Gfoltz9, AvocatoBot, ChrisGualtieri, Txnhockey3, CsDix, Monkbot and Anonymous: 79 • Band-pass filter Source: http://en.wikipedia.org/wiki/Band-pass_filter?oldid=625817556 Contributors: The Anome, Maury Markowitz, Patrick, Angela, Nanobug, Glenn, Poor Yorick, BAxelrod, Emmjade, Guaka, Omegatron, ThereIsNoSteve, Giftlite, Sword, Zowie, Rfl, CALR, Billlion, Shanes, Hooperbloob, SidP, Cburnett, OwenX, Cbdorsett, Pfalstad, Zbxgscqf, Sango123, Ianthegecko, Arnero, Antikon, DVdm, Martin Hinks, YurikBot, Splash, PinothyJ, Toffile, Brandon, Hakeem.gadi, Deville, KNfLrPnKNsT, LeonardoRob0t, Poulpy, Machtzu, RG2, Henrikb4, Binarypower, Commander Keane bot, Oli Filth, Vina-iwbot, Clicketyclack, Robofish, Mofomojo, Dicklyon, Tawkerbot2, Nalvage, Sobreira, AlienBlancmange, CosineKitty, Email4mobile, RisingStick, STBot, Mange01, Acalamari, VolkovBot, Cuddlyable3, Inductiveload, Spinningspark, Benjwgarner, Dp67, Binksternet, PipepBot, ChrisHodgesUK, Johnuniq, Addbot, Alexandra Goncharik, Redheylin, OlEnglish, B137, Citation bot, GrouchoBot, Ebrambot, Lorem Ip, ClueBot NG, Rezabot, Helpful Pixie Bot, Flyguy53, Ankitd.elec, Chetan.meshram, Omegaoptical, Forestrf, CsDix, Ugog Nizdast, Joshua Mahesh Inayathullah and Anonymous: 63
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9.2 Images • File:1st_Order_Lowpass_Filter_RC.svg Source: http://upload.wikimedia.org/wikipedia/commons/e/e0/1st_Order_Lowpass_Filter_ RC.svg License: Public domain Contributors: Own work Original artist: Inductiveload • File:555_Astable_Diagram.svg Source: http://upload.wikimedia.org/wikipedia/commons/3/3d/555_Astable_Diagram.svg License: Public domain Contributors: Own drawing, made in Inkscape 0.43 Original artist: jjbeard • File:555_Bistable.svg Source: http://upload.wikimedia.org/wikipedia/commons/7/78/555_Bistable.svg License: CC0 Contributors: Own work Original artist: AbstractBeliefs • File:555_Monostable.svg Source: http://upload.wikimedia.org/wikipedia/commons/1/19/555_Monostable.svg License: Public domain Contributors: Own work Original artist: Inductiveload • File:555_Pinout.svg Source: http://upload.wikimedia.org/wikipedia/commons/c/c7/555_Pinout.svg License: Public domain Contributors: Own work Original artist: Inductiveload • File:75_Hz_HPF_on_Smaart.jpg Source: http://upload.wikimedia.org/wikipedia/commons/4/4d/75_Hz_HPF_on_Smaart.jpg License: CC-BY-SA-3.0-2.5-2.0-1.0 Contributors: Own work Original artist: Binksternet • File:7812_voltage_regulator.jpg Source: http://upload.wikimedia.org/wikipedia/commons/c/ce/7812_voltage_regulator.jpg License: CC-BY-3.0 Contributors: http://traveler.com.br/photos/matarese/photo/435-a-7812-voltage-regulator-chip/ Original artist: Mataresephotos • File:AFSK_1200_baud.ogg Source: http://upload.wikimedia.org/wikipedia/commons/2/27/AFSK_1200_baud.ogg License: CC-BYSA-3.0 Contributors: ? Original artist: ? • File:Active_Highpass_Filter_RC.png Source: http://upload.wikimedia.org/wikipedia/commons/8/87/Active_Highpass_Filter_RC.png License: Public domain Contributors: Own work by Toriicelli Original artist: Toriicelli • File:Active_Lowpass_Filter_RC.svg Source: http://upload.wikimedia.org/wikipedia/commons/5/59/Active_Lowpass_Filter_RC.svg License: Public domain Contributors: http://en.wikipedia.org/wiki/File:Active_Lowpass_Filter_RC.svg Original artist: Inductiveload • File:Amplifier_Circuit_Small.svg Source: http://upload.wikimedia.org/wikipedia/commons/f/fd/Amplifier_Circuit_Small.svg License: Public domain Contributors: This vector image was created with Inkscape. Original artist: Twisp • File:Approximated_Ebers_Moll.svg Source: http://upload.wikimedia.org/wikipedia/commons/e/eb/Approximated_Ebers_Moll.svg License: CC-BY-SA-3.0 Contributors: File:Ebers-Moll model schematic (NPN).svg Original artist: Original uploader was Krishnavedala at en.wikipedia derivative work: Inductiveload (talk) • File:BJT_NPN_symbol.svg Source: http://upload.wikimedia.org/wikipedia/commons/6/66/BJT_NPN_symbol.svg License: CC-BYSA-3.0-2.5-2.0-1.0 Contributors: Created by User:Omegatron Original artist: Omegatron • File:BJT_NPN_symbol_(case).svg Source: http://upload.wikimedia.org/wikipedia/commons/c/cb/BJT_NPN_symbol_%28case%29. svg License: Public domain Contributors: Own work Original artist: Zedh • File:BJT_PNP_symbol.svg Source: http://upload.wikimedia.org/wikipedia/commons/9/9b/BJT_PNP_symbol.svg License: CC-BYSA-3.0-2.5-2.0-1.0 Contributors: Created by User:Omegatron Original artist: Omegatron • File:BJT_PNP_symbol_(case).svg Source: http://upload.wikimedia.org/wikipedia/commons/a/ab/BJT_PNP_symbol_%28case%29. svg License: CC-BY-SA-3.0-2.5-2.0-1.0 Contributors: Own work Original artist: Zedh • File:BJT_h-parameters_(generalised).svg Source: http://upload.wikimedia.org/wikipedia/commons/9/9f/BJT_h-parameters_ %28generalised%29.svg License: CC-BY-SA-3.0 Contributors: • H-parameters.gif Original artist: H-parameters.gif: Original uploader was Rohitbd at en.wikipedia • File:BandDiagram-Semiconductors-E.PNG Source: http://upload.wikimedia.org/wikipedia/commons/8/85/ BandDiagram-Semiconductors-E.PNG License: CC-BY-SA-2.5 Contributors: ? Original artist: ? • File:Bandpass_Filter.svg Source: http://upload.wikimedia.org/wikipedia/commons/b/bd/Bandpass_Filter.svg License: Public domain Contributors: Own work Original artist: Inductiveload • File:Bandstruktur_GaAs_en.svg Source: http://upload.wikimedia.org/wikipedia/commons/6/67/Bandstruktur_GaAs_en.svg License: CC-BY-SA-3.0 Contributors: • Bandstruktur_GaAs.svg Original artist: Bandstruktur_GaAs.svg: Cepheiden. • File:Bandwidth_2.svg Source: http://upload.wikimedia.org/wikipedia/commons/6/6b/Bandwidth_2.svg License: Public domain Contributors: Own work Original artist: Inductiveload
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• File:Bardeen_Shockley_Brattain_1948.JPG Source: http://upload.wikimedia.org/wikipedia/commons/c/c2/Bardeen_Shockley_ Brattain_1948.JPG License: Public domain Contributors: eBay item Original artist: AT&T; photographer: Jack St. (last part of name not stamped well enough to read), New York, New York. • File:Butterworth_response.svg Source: http://upload.wikimedia.org/wikipedia/commons/6/60/Butterworth_response.svg License: CCBY-SA-3.0-2.5-2.0-1.0 Contributors: • Butterworth_response.png Original artist: • derivative work: Krishnavedala (talk) • File:C555_Internal_Circuit.svg Source: http://upload.wikimedia.org/wikipedia/commons/2/29/C555_Internal_Circuit.svg License: CC-BY-3.0 Contributors: Own work Original artist: Wdwd • File:ClassG.svg Source: http://upload.wikimedia.org/wikipedia/commons/4/48/ClassG.svg License: CC-BY-SA-3.0 Contributors: • ClassG.GIF Original artist: --- Tiger66 --- derivative work:Henrydask • File:ClassH.svg Source: http://upload.wikimedia.org/wikipedia/commons/f/f1/ClassH.svg License: CC-BY-SA-3.0 Contributors: • ClassH.GIF Original artist: Tiger66 • File:Classe_E.svg Source: http://upload.wikimedia.org/wikipedia/commons/1/11/Classe_E.svg License: CC-BY-SA-3.0 Contributors: own work/travail personnel Original artist: Yves-Laurent Allaert • File:Clutch_with_Hall_Effect_sensor.jpg Source: http://upload.wikimedia.org/wikipedia/commons/4/4f/Clutch_with_Hall_Effect_ sensor.jpg License: CC-BY-2.0 Contributors: Flickr Original artist: Ð¤Ð¸Ð³Ñ Ñ ÐºÐ¸ • File:Collector_to_base_bias.PNG Source: http://upload.wikimedia.org/wikipedia/commons/7/79/Collector_to_base_bias.PNG License: Public domain Contributors: Transferred from en.wikipedia; transferred to Commons by User:Sfan00_IMG using CommonsHelper. Original artist: Original uploader was Xcentaur at en.wikipedia • File:Common_Hall_Sensor_Symbol.png Source: http://upload.wikimedia.org/wikipedia/commons/1/1e/Common_Hall_Sensor_ Symbol.png License: CC-BY-SA-3.0 Contributors: Created in gEDA and exported Previously published: http://www.turbo-electric.com Original artist: Grahamatwp • File:Commons-logo.svg Source: http://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg License: ? Contributors: ? Original artist: ? • File:Comparators_stuuf.jpg Source: http://upload.wikimedia.org/wikipedia/commons/1/1d/Comparators_stuuf.jpg License: CC-BYSA-3.0 Contributors: Own work Original artist: Stuuf • File:Cscr-featured.svg Source: http://upload.wikimedia.org/wikipedia/en/e/e7/Cscr-featured.svg License: ? Contributors: ? Original artist: ? • File:Current-Voltage_relationship_of_BJT.png Source: http://upload.wikimedia.org/wikipedia/commons/3/33/Current-Voltage_ relationship_of_BJT.png License: CC-BY-SA-3.0 Contributors: Own work Original artist: AlexHe34 • File:Cylinders_with_Hall_sensors.png Source: http://upload.wikimedia.org/wikipedia/commons/9/9c/Cylinders_with_Hall_sensors. png License: CC-BY-SA-3.0 Contributors: Own work by the original uploader Original artist: User:IMeowbot • File:Darlington_transistor_MJ1000.jpg Source: http://upload.wikimedia.org/wikipedia/commons/d/d9/Darlington_transistor_ MJ1000.jpg License: Attribution Contributors: Transferred from de.wikipedia; transferred to Commons by User:Wdwd using CommonsHelper. Original artist: thomy_pc. • File:Dependent_Sources.PNG Source: http://upload.wikimedia.org/wikipedia/commons/6/6a/Dependent_Sources.PNG License: CCBY-SA-3.0-2.5-2.0-1.0 Contributors: Own work Original artist: Brews ohare • File:Diamond_Cubic-F_lattice_animation.gif Source: http://upload.wikimedia.org/wikipedia/commons/2/22/Diamond_Cubic-F_ lattice_animation.gif License: CC0 Contributors: http://www.msm.cam.ac.uk/phase-trans/2003/MP1.crystals/MP1.crystals.html ; English Wikipedia Original artist: original uploader: Brian0918 • File:Discrete_opamp.png Source: http://upload.wikimedia.org/wikipedia/commons/8/85/Discrete_opamp.png License: CC-BY-SA-3.0 Contributors: Op Amp Applications Handbook Original artist: Analog Devices • File:Divide_4.png Source: http://upload.wikimedia.org/wikipedia/commons/6/64/Divide_4.png License: CC-BY-3.0 Contributors: Own work Original artist: Jon Guerber • File:Dynamic_Comparator.png Source: http://upload.wikimedia.org/wikipedia/commons/c/c1/Dynamic_Comparator.png License: CC-BY-SA-3.0 Contributors: Transferred from en.wikipedia. Original artist: Guerberj at en.wikipedia • File:ECC83_Glow.jpg Source: http://upload.wikimedia.org/wikipedia/commons/5/5a/ECC83_Glow.jpg License: CC0 Contributors: Own work Original artist: Olli Niemitalo
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• File:EMRI_LXCOS_Voltage_Regulator.jpg Source: http://upload.wikimedia.org/wikipedia/commons/5/53/EMRI_LXCOS_ Voltage_Regulator.jpg License: CC-BY-SA-3.0 Contributors: Own work Original artist: RoyPijnenburg • File:Early_effect_(NPN).svg Source: http://upload.wikimedia.org/wikipedia/commons/4/49/Early_effect_%28NPN%29.svg License: Public domain Contributors: Own work Original artist: Inductiveload • File:Ebers-Moll_model_schematic_(NPN).svg Source: http://upload.wikimedia.org/wikipedia/commons/8/8a/Ebers-Moll_model_ schematic_%28NPN%29.svg License: CC-BY-SA-3.0 Contributors: • Ebers-Moll_Model_NPN.PNG Original artist: Ebers-Moll_Model_NPN.PNG: Original uploader was Krishnavedala at en.wikipedia • File:Ebers-Moll_model_schematic_(PNP).svg Source: http://upload.wikimedia.org/wikipedia/commons/e/ec/Ebers-Moll_model_ schematic_%28PNP%29.svg License: CC-BY-SA-3.0 Contributors: • Ebers-Moll_Model_PNP.PNG Original artist: Ebers-Moll_Model_PNP.PNG: Original uploader was Krishnavedala at en.wikipedia • File:Edit-clear.svg Source: http://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg License: ? Contributors: ? Original artist: ? • File:Electron-hole.svg Source: http://upload.wikimedia.org/wikipedia/commons/d/d6/Electron-hole.svg License: Public domain Contributors: Own derivative work of wikipedia:Image:ElectronHole.JPG Original artist: User:Sir_Link • File:Electronic_Amplifier_Class_A.png Source: http://upload.wikimedia.org/wikipedia/commons/9/9b/Electronic_Amplifier_Class_ A.png License: CC-BY-SA-3.0 Contributors: en:Image:Electronic_Amplifier_Class_A.png Original artist: GRAHAMUK with modification of Yves-Laurent Allaert • File:Electronic_Amplifier_Class_B_fixed.png Source: http://upload.wikimedia.org/wikipedia/commons/b/b6/Electronic_Amplifier_ Class_B_fixed.png License: CC-BY-SA-3.0 Contributors: Transferred from en.wikipedia; transferred to Commons by User:Logan using CommonsHelper. Original artist: Nitram cero at en.wikipedia • File:Electronic_Amplifier_Class_C.png Source: http://upload.wikimedia.org/wikipedia/commons/e/e1/Electronic_Amplifier_Class_ C.png License: CC-BY-SA-3.0 Contributors: en:Image:Electronic_Amplifier_Class_C.png Original artist: GRAHAMUK with modification of Yves-Laurent Allaert • File:Electronic_Amplifier_Push-pull.svg Source: http://upload.wikimedia.org/wikipedia/commons/b/b4/Electronic_Amplifier_ Push-pull.svg License: CC-BY-SA-3.0-2.5-2.0-1.0 Contributors: File:Electronic Amplifier Push-pull.png Original artist: Lakkasuo • File:Emitter_bias.PNG Source: http://upload.wikimedia.org/wikipedia/commons/3/39/Emitter_bias.PNG License: Public domain Contributors: Transferred from en.wikipedia; transferred to Commons by User:Sfan00_IMG using CommonsHelper. Original artist: Original uploader was Xcentaur at en.wikipedia • File:FET_comparison.png Source: http://upload.wikimedia.org/wikipedia/commons/c/c0/FET_comparison.png License: Public domain Contributors: ? Original artist: ? • File:Ferrosilicon.JPG Source: http://upload.wikimedia.org/wikipedia/commons/5/51/Ferrosilicon.JPG License: CC-BY-SA-3.0-2.52.0-1.0 Contributors: Own work Original artist: FocalPoint • File:Fixed_bias.PNG Source: http://upload.wikimedia.org/wikipedia/commons/7/79/Fixed_bias.PNG License: Public domain Contributors: Transferred from en.wikipedia; transferred to Commons by User:Sfan00_IMG using CommonsHelper. Original artist: Original uploader was Xcentaur at en.wikipedia • File:Fixed_bias_with_emitter_resistor.PNG Source: http://upload.wikimedia.org/wikipedia/commons/b/b2/Fixed_bias_with_ emitter_resistor.PNG License: Public domain Contributors: Transferred from en.wikipedia; transferred to Commons by User:Sfan00_IMG using CommonsHelper. Original artist: Original uploader was Xcentaur at en.wikipedia • File:Folder_Hexagonal_Icon.svg Source: http://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg License: ? Contributors: ? Original artist: ? • File:Fotodio.jpg Source: http://upload.wikimedia.org/wikipedia/commons/e/e6/Fotodio.jpg License: CC-BY-SA-3.0 Contributors: ? Original artist: ? • File:Fsk.svg Source: http://upload.wikimedia.org/wikipedia/commons/3/39/Fsk.svg License: CC-BY-SA-3.0 Contributors: ? Original artist: ? • File:GHS-pictogram-pollu.svg Source: http://upload.wikimedia.org/wikipedia/commons/b/b9/GHS-pictogram-pollu.svg License: ? Contributors: EPS file pollu.eps from UNECE web site converted with ImageMagick convert and with potrace, edited in inkscape Original artist: Torsten Henning • File:GHS-pictogram-skull.svg Source: http://upload.wikimedia.org/wikipedia/commons/5/58/GHS-pictogram-skull.svg License: ? 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• File:Gallium_arsenide_crystal.jpg Source: http://upload.wikimedia.org/wikipedia/commons/6/6f/Gallium_arsenide_crystal.jpg License: CC-BY-SA-3.0 Contributors: http://woelen.homescience.net/science/index.html Original artist: W. Oelen • File:General_Microwave_VCO.png Source: http://upload.wikimedia.org/wikipedia/commons/5/5b/General_Microwave_VCO.png License: CC-BY-SA-3.0 Contributors: http://www.herley.com/index.cfm?act=product&prd=481 Original artist: en:Herley Industries • File:Generic_741_pinout_top.png Source: http://upload.wikimedia.org/wikipedia/commons/7/72/Generic_741_pinout_top.png License: CC-BY-SA-3.0 Contributors: Own work by uploader (derived from other own (Creative Commons) work from uploader at http://www.tedpavlic.com/teaching/osu/ece209/support/part_pinouts.pdf) Original artist: TedPavlic • File:Germane-2D-dimensions.png Source: http://upload.wikimedia.org/wikipedia/commons/c/ca/Germane-2D-dimensions.png License: Public domain Contributors: Own work Original artist: Ben Mills • File:Gnome-mime-sound-openclipart.svg Source: http://upload.wikimedia.org/wikipedia/commons/8/87/ Gnome-mime-sound-openclipart.svg License: Public domain Contributors: Own work. Based on File:Gnome-mime-audio-openclipart. svg, which is public domain. Original artist: User:Eubulides • File:H_bridge.svg Source: http://upload.wikimedia.org/wikipedia/commons/d/d4/H_bridge.svg License: CC-BY-SA-3.0 Contributors: Own work Original artist: Cyril BUTTAY • File:H_bridge_operating.svg Source: http://upload.wikimedia.org/wikipedia/commons/f/f2/H_bridge_operating.svg License: CC-BYSA-3.0 Contributors: own work, made using inkscape Original artist: Cyril BUTTAY • File:Hall_sensor_tach.gif Source: http://upload.wikimedia.org/wikipedia/commons/7/7e/Hall_sensor_tach.gif License: CC-BY-SA-3.0 Contributors: ? Original artist: ? • File:Hazard_N.svg Source: http://upload.wikimedia.org/wikipedia/commons/6/6a/Hazard_N.svg License: Public domain Contributors: Converted from EPS file at http://forum.cptec.org/index.php?showtopic=368 Original artist: See historic • File:Hazard_T.svg Source: http://upload.wikimedia.org/wikipedia/commons/3/39/Hazard_T.svg License: Public domain Contributors: ? Original artist: ? • File:High_Pass_Filter_Example.jpg Source: http://upload.wikimedia.org/wikipedia/commons/c/ca/High_Pass_Filter_Example.jpg License: CC0 Contributors: Own work Original artist: Ll1324 • File:High_pass_filter.svg Source: http://upload.wikimedia.org/wikipedia/commons/f/fe/High_pass_filter.svg License: Public domain Contributors: ? Original artist: ? • File:Hybrid-pi_detailed_model.svg Source: http://upload.wikimedia.org/wikipedia/en/2/2f/Hybrid-pi_detailed_model.svg License: ? Contributors: ? Original artist: ? • File:Hybrid_opamp.png Source: http://upload.wikimedia.org/wikipedia/commons/8/84/Hybrid_opamp.png License: CC-BY-SA-3.0 Contributors: Op Amp Applications Handbook Original artist: Analog Devices • File:IGFET_N-Ch_Dep_Labelled.svg Source: http://upload.wikimedia.org/wikipedia/commons/e/e8/IGFET_N-Ch_Dep_Labelled. svg License: Public domain Contributors: From Scratch in Inkcape 0.43 Original artist: jjbeard • File:IGFET_N-Ch_Enh_Labelled.svg Source: http://upload.wikimedia.org/wikipedia/commons/6/62/IGFET_N-Ch_Enh_Labelled. svg License: Public domain Contributors: ? Original artist: ? • File:IGFET_N-Ch_Enh_Labelled_simplified.svg Source: http://upload.wikimedia.org/wikipedia/commons/6/61/IGFET_N-Ch_ Enh_Labelled_simplified.svg License: CC-BY-SA-3.0-2.5-2.0-1.0 Contributors: Based on Image:IGFET N-Ch Enh Labelled.svg, Created by User:Omegatron Original artist: User:Omegatron • File:IGFET_P-Ch_Dep_Labelled.svg Source: http://upload.wikimedia.org/wikipedia/commons/1/1b/IGFET_P-Ch_Dep_Labelled. svg License: Public domain Contributors: From Scratch in Inkcape 0.43 Original artist: jjbeard • File:IGFET_P-Ch_Enh_Labelled.svg Source: http://upload.wikimedia.org/wikipedia/commons/0/0c/IGFET_P-Ch_Enh_Labelled. svg License: Public domain Contributors: From Scratch in Inkcape 0.43 Original artist: jjbeard • File:IGFET_P-Ch_Enh_Labelled_simplified.svg Source: http://upload.wikimedia.org/wikipedia/commons/c/c4/IGFET_P-Ch_Enh_ Labelled_simplified.svg License: CC-BY-SA-3.0-2.5-2.0-1.0 Contributors: Based on Image:IGFET P-Ch Enh Labelled.svg, Created by User:Omegatron Original artist: User:Omegatron • File:Inside_of_a_Boss_Audio_DD3600_Class_D_mono_block_amp.jpg Source: http://upload.wikimedia.org/wikipedia/commons/ 2/26/Inside_of_a_Boss_Audio_DD3600_Class_D_mono_block_amp.jpg License: CC-BY-3.0 Contributors: Transferred from en.wikipedia; transferred to Commons by User:Logan using CommonsHelper. Original artist: Daniel Christensen (talk). Original uploader was Daniel Christensen at en.wikipedia • File:Inverting_Amplifier_Signal_Clipping.png Source: http://upload.wikimedia.org/wikipedia/commons/9/9f/Inverting_Amplifier_ Signal_Clipping.png License: CC0 Contributors: Own work Original artist: Super Rad!
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• File:JFET_N-Channel_Labelled.svg Source: http://upload.wikimedia.org/wikipedia/commons/4/46/JFET_N-Channel_Labelled.svg License: Public domain Contributors: From Scratch in Inkcape 0.43 Original artist: jjbeard • File:JFET_N-dep_symbol.svg Source: http://upload.wikimedia.org/wikipedia/commons/6/6d/JFET_N-dep_symbol.svg License: CCBY-SA-3.0-2.5-2.0-1.0 Contributors: Own work Original artist: Zedh • File:JFET_P-Channel_Labelled.svg Source: http://upload.wikimedia.org/wikipedia/commons/0/09/JFET_P-Channel_Labelled.svg License: Public domain Contributors: From Scratch in Inkcape 0.43 Original artist: jjbeard • File:JFET_n-channel_en.svg Source: http://upload.wikimedia.org/wikipedia/commons/5/50/JFET_n-channel_en.svg License: CC-BYSA-3.0-2.5-2.0-1.0 Contributors: • JFET_n-channel.svg Original artist: JFET_n-channel.svg: Phirosiberia • File:K2-w_Vacuum_Tube_Op-amp.jpg Source: http://upload.wikimedia.org/wikipedia/commons/1/15/K2-w_Vacuum_Tube_ Op-amp.jpg License: CC-BY-SA-3.0 Contributors: Own work Original artist: Bdieseldorff • File:Konstanze.jpg Source: http://upload.wikimedia.org/wikipedia/commons/f/f0/Konstanze.jpg License: Public domain Contributors: Own work Original artist: Ulfbastel • File:L298_IMGP4533_wp.jpg Source: http://upload.wikimedia.org/wikipedia/commons/2/23/L298_IMGP4533_wp.jpg License: FAL Contributors: Own work Original artist: Smial • File:LM741CN.jpg Source: http://upload.wikimedia.org/wikipedia/commons/9/95/LM741CN.jpg License: CC0 Contributors: Own work Original artist: Olli Niemitalo • File:Lateral_mosfet.svg Source: http://upload.wikimedia.org/wikipedia/commons/7/79/Lateral_mosfet.svg License: CC-BY-SA-3.0 Contributors: ? Original artist: ? • File:MDAC.png Source: http://upload.wikimedia.org/wikipedia/en/3/3c/MDAC.png License: ? Contributors: ? Original artist: ? • File:Mergefrom.svg Source: http://upload.wikimedia.org/wikipedia/commons/0/0f/Mergefrom.svg License: Public domain Contributors: ? Original artist: ? • File:MidSTAR-1.jpg Source: http://upload.wikimedia.org/wikipedia/commons/a/a0/MidSTAR-1.jpg License: Public domain Contributors: • MidSTAR.jpg Original artist: MidSTAR.jpg: United States Naval Academy • File:Modular_opamp.png Source: http://upload.wikimedia.org/wikipedia/commons/9/97/Modular_opamp.png License: CC-BY-SA3.0 Contributors: Op Amp Applications Handbook Original artist: Analog Devices • File:Monokristalines_Silizium_für_die_Waferherstellung.jpg Source: http://upload.wikimedia.org/wikipedia/commons/2/23/ Monokristalines_Silizium_f%C3%BCr_die_Waferherstellung.jpg License: CC-BY-SA-3.0 Contributors: ? Original artist: ? • File:Moving_Coil_Voltage_Regulator.png Source: http://upload.wikimedia.org/wikipedia/en/7/79/Moving_Coil_Voltage_Regulator. png License: ? Contributors: ? Original artist: ? • File:NE555_Bloc_Diagram.svg Source: http://upload.wikimedia.org/wikipedia/commons/1/17/NE555_Bloc_Diagram.svg License: Public domain Contributors: Own work Original artist: BlanchardJ • File:NE555_Internal_Circuit.svg Source: http://upload.wikimedia.org/wikipedia/commons/1/1c/NE555_Internal_Circuit.svg License: CC-BY-3.0 Contributors: Own work Original artist: Wdwd • File:NE555_Monotable_Waveforms_(English).png Source: http://upload.wikimedia.org/wikipedia/commons/d/dc/NE555_ Monotable_Waveforms_%28English%29.png License: Public domain Contributors: • NE555_Monostable_Waveforms_fr.png Original artist: NE555_Monostable_Waveforms_fr.png: BlanchardJ • File:NPN_BJT_(Planar)_Cross-section.svg Source: http://upload.wikimedia.org/wikipedia/commons/6/6b/NPN_BJT_%28Planar% 29_Cross-section.svg License: Public domain Contributors: Own work Original artist: Inductiveload • File:NPN_BJT_-_Structure_&_circuit.svg Source: http://upload.wikimedia.org/wikipedia/commons/4/49/NPN_BJT_-_Structure_ %26_circuit.svg License: CC-BY-SA-3.0 Contributors: • Based on File:Npn-structure.png, by User:Heron at the English Wikipedia Original artist: Inductiveload • File:NPN_BJT_Basic_Operation_(Active).svg Source: http://upload.wikimedia.org/wikipedia/commons/1/13/NPN_BJT_Basic_ Operation_%28Active%29.svg License: Public domain Contributors: Own drawing, done in Inkscape Original artist: Inductiveload • File:NPN_Band_Diagram_Active.svg Source: http://upload.wikimedia.org/wikipedia/commons/4/4b/NPN_Band_Diagram_Active. svg License: Public domain Contributors: Own drawing, done in Inkscape Original artist: Inductiveload • File:NPN_Band_Diagram_Equilibrium.svg Source: http://upload.wikimedia.org/wikipedia/commons/a/a3/NPN_Band_Diagram_ Equilibrium.svg License: Public domain Contributors: Own drawing, done in Inkscape Original artist: Inductiveload • File:NPN_common_emitter_AC.svg Source: http://upload.wikimedia.org/wikipedia/commons/8/8c/NPN_common_emitter_AC.svg License: CC-BY-SA-3.0-2.5-2.0-1.0 Contributors: Own work Original artist: Zedh
9.2. IMAGES
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• File:NTC_bead.jpg Source: http://upload.wikimedia.org/wikipedia/commons/3/3b/NTC_bead.jpg License: CC-BY-SA-2.0-de Contributors: photo taken with Canon PowerShot G3 Original artist: Ansgar Hellwig • File:Npn_heterostructure_bands.svg Source: http://upload.wikimedia.org/wikipedia/commons/b/b1/Npn_heterostructure_bands.svg License: CC-BY-SA-3.0 Contributors: Own work Original artist: Matthewbeckler • File:NucleophilicAdditionWithOrganogermanium.png Source: http://upload.wikimedia.org/wikipedia/commons/e/e3/ NucleophilicAdditionWithOrganogermanium.png License: CC-BY-SA-3.0 Contributors: Transferred from en.wikipedia; transferred to Commons by User:T.vanschaik using CommonsHelper. Original artist: Original uploader was V8rik at en.wikipedia. Later version(s) were uploaded by Mahahahaneapneap at en.wikipedia. • File:Nuvola_apps_edu_science.svg Source: http://upload.wikimedia.org/wikipedia/commons/5/59/Nuvola_apps_edu_science.svg License: LGPL Contributors: http://ftp.gnome.org/pub/GNOME/sources/gnome-themes-extras/0.9/gnome-themes-extras-0.9.0.tar.gz Original artist: David Vignoni / ICON KING • File:Nuvola_apps_ksim.png Source: http://upload.wikimedia.org/wikipedia/commons/8/8d/Nuvola_apps_ksim.png License: LGPL Contributors: http://icon-king.com Original artist: David Vignoni / ICON KING • File:Office-book.svg Source: http://upload.wikimedia.org/wikipedia/commons/a/a8/Office-book.svg License: Public domain Contributors: This and myself. Original artist: Chris Down/Tango project • File:Op-Amp_Comparator.svg Source: http://upload.wikimedia.org/wikipedia/commons/0/0d/Op-Amp_Comparator.svg License: Public domain Contributors: Own work Original artist: Inductiveload • File:Op-Amp_Internal.svg Source: http://upload.wikimedia.org/wikipedia/commons/0/0d/Op-Amp_Internal.svg License: Public domain Contributors: Own work Original artist: Inductiveload • File:Op-Amp_Inverting_Amplifier.svg Source: http://upload.wikimedia.org/wikipedia/commons/4/41/Op-Amp_Inverting_ Amplifier.svg License: Public domain Contributors: Own work Original artist: Inductiveload • File:Op-Amp_Non-Inverting_Amplifier.svg Source: http://upload.wikimedia.org/wikipedia/commons/4/44/Op-Amp_ Non-Inverting_Amplifier.svg License: Public domain Contributors: Own work Original artist: Inductiveload • File:Op-amp_open-loop_1.svg Source: http://upload.wikimedia.org/wikipedia/commons/8/8e/Op-amp_open-loop_1.svg License: CCBY-SA-3.0 Contributors: my drawing Original artist: Ong saluri • File:Op-amp_symbol.svg Source: http://upload.wikimedia.org/wikipedia/commons/9/97/Op-amp_symbol.svg License: CC-BY-SA3.0-2.5-2.0-1.0 Contributors: Own work Original artist: User:Omegatron • File:OpAmpTransistorLevel_Colored_Labeled.svg Source: http://upload.wikimedia.org/wikipedia/commons/e/e0/ OpAmpTransistorLevel_Colored_Labeled.svg License: CC-BY-2.5 Contributors: redrawn png file (from User:Omegatron), datasheet Original artist: Daniel Braun • File:Operational_amplifier_noninverting.svg Source: http://upload.wikimedia.org/wikipedia/commons/6/66/Operational_amplifier_ noninverting.svg License: CC-BY-SA-3.0 Contributors: my drawing Original artist: Ong saluri • File:P45N02LD.jpg Source: http://upload.wikimedia.org/wikipedia/commons/a/af/P45N02LD.jpg License: CC-BY-SA-3.0 Contributors: ? Original artist: ? • File:PD-icon.svg Source: http://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg License: ? Contributors: ? Original artist: ? • File:PLL,usage.png Source: http://upload.wikimedia.org/wikipedia/commons/0/0f/PLL%2Cusage.png License: CC-BY-SA-3.0 Contributors: Transferred from en.wikipedia; transfer was stated to be made by User:IngFrancesco. Original artist: Original uploader was Iain.mcclatchie at en.wikipedia Later version(s) were uploaded by Vahid avr at en.wikipedia. • File:PLL_generic_inline_optional_N.png Source: http://upload.wikimedia.org/wikipedia/commons/6/60/PLL_generic_inline_ optional_N.png License: CC-BY-SA-4.0 Contributors: Own work Original artist: Crystallizedcarbon, Iain.mcclatchie, Mysid, Yegorius • File:PNP_BJT_-_Structure_&_circuit.svg Source: %26_circuit.svg License: CC-BY-SA-3.0 Contributors:
http://upload.wikimedia.org/wikipedia/commons/9/90/PNP_BJT_-_Structure_
• Based on File:Pnp-structure.png, by User:Heron at the English Wikipedia Original artist: Inductiveload • File:PN_Junction_in_Reverse_Bias.png Source: http://upload.wikimedia.org/wikipedia/commons/0/01/PN_Junction_in_Reverse_ Bias.png License: GFDL 1.2 Contributors: ? Original artist: ? • File:PN_band.gif Source: http://upload.wikimedia.org/wikipedia/commons/2/22/PN_band.gif License: CC-BY-3.0 Contributors: GIF:http://nanohub.org/resources/8797/ , Tool link: https://nanohub.org/tools/pntoy/ Original artist: Saumitra R Mehrotra & Gerhard Klimeck • File:PN_diode_with_electrical_symbol.svg Source: http://upload.wikimedia.org/wikipedia/commons/7/79/PN_diode_with_ electrical_symbol.svg License: CC-BY-SA-3.0 Contributors: Own work Original artist: Raffamaiden • File:Padlock-silver.svg Source: http://upload.wikimedia.org/wikipedia/commons/f/fc/Padlock-silver.svg License: ? Contributors: http: //openclipart.org/people/Anonymous/padlock_aj_ashton_01.svg Original artist: This image file was created by AJ Ashton. Uploaded from English WP by User:Eleassar. Converted by User:AzaToth to a silver color.
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• File:Parasitic_Sensative_Inverter.png Source: http://upload.wikimedia.org/wikipedia/en/7/76/Parasitic_Sensative_Inverter.png License: ? Contributors: ? Original artist: ? • File:Pdms.png Source: http://upload.wikimedia.org/wikipedia/commons/6/6a/Pdms.png License: CC-BY-SA-3.0 Contributors: selfmade with ChemDraw and Photoshop Original artist: Jesse • File:Pet_Flasche.JPG Source: http://upload.wikimedia.org/wikipedia/commons/e/ea/Pet_Flasche.JPG License: CC-BY-SA-3.0-2.52.0-1.0 Contributors: ? Original artist: ? • File:Philco_Surface_Barrier_transistor=1953.jpg Source: http://upload.wikimedia.org/wikipedia/commons/e/e8/Philco_Surface_ Barrier_transistor%3D1953.jpg License: CC-BY-SA-3.0 Contributors: Own work Original artist: Historianbuff • File:Photodiode_array_chip.jpg Source: http://upload.wikimedia.org/wikipedia/commons/c/ce/Photodiode_array_chip.jpg License: CC-BY-SA-3.0 Contributors: Own work Original artist: Fulvio314 • File:Photodiode_operation.png Source: CC-BY-SA-3.0 Contributors:
http://upload.wikimedia.org/wikipedia/commons/0/06/Photodiode_operation.png License:
• Kennlinie_Photodiode_1.png Original artist: Kennlinie_Photodiode_1.png: Gregor Hess (Ghe42) • File:Photodiode_symbol.svg Source: http://upload.wikimedia.org/wikipedia/commons/2/2b/Photodiode_symbol.svg License: CC-BYSA-3.0-2.5-2.0-1.0 Contributors: ? Original artist: ? • File:Photoresistor.svg Source: http://upload.wikimedia.org/wikipedia/commons/1/13/Photoresistor.svg License: Public domain Contributors: Own work Original artist: Горовато • File:PhototransistorSymbol.png Source: http://upload.wikimedia.org/wikipedia/commons/5/57/PhototransistorSymbol.png License: CC-BY-3.0 Contributors: WikiProject Wikipedia Original artist: myself • File:Pink.noise.png Source: http://upload.wikimedia.org/wikipedia/commons/7/72/Pink.noise.png License: Public domain Contributors: Transferred from de.wikipedia; transferred to Commons by User:Leyo using CommonsHelper. Original artist: Original uploader was Bautsch at de.wikipedia • File:Pn-junction-equilibrium-graphs.png Pn-junction-equilibrium-graphs.png License: nal artist: en:User:TheNoise
Source: CC-BY-SA-3.0 Contributors:
http://upload.wikimedia.org/wikipedia/commons/f/fa/ en:Image:Pn-junction-equilibrium-graphs.png Origi-
• File:Pn-junction-equilibrium.png Source: http://upload.wikimedia.org/wikipedia/commons/d/d6/Pn-junction-equilibrium.png License: CC-BY-SA-3.0 Contributors: Transferred from en.wikipedia; Transfer was stated to be made by User:Mu301. Original artist: Original uploader was TheNoise at en.wikipedia • File:Polycrystalline_silicon_rod.jpg Source: http://upload.wikimedia.org/wikipedia/commons/5/59/Polycrystalline_silicon_rod.jpg License: CC-BY-SA-3.0-2.5-2.0-1.0 Contributors: Own work Original artist: Warut Roonguthai • File:Pwm_amp.svg Source: http://upload.wikimedia.org/wikipedia/commons/4/4c/Pwm_amp.svg License: CC-BY-SA-3.0 Contributors: English Wikipedia Original artist: Rohitbd • File:Quartz,_Tibet.jpg Source: http://upload.wikimedia.org/wikipedia/commons/1/14/Quartz%2C_Tibet.jpg License: CC-BY-SA-2.5 Contributors: Own work Original artist: JJ Harrison (
[email protected]) • File:Question_book-new.svg Source: http://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg License: ? Contributors: ? Original artist: ? • File:RC_Divider.svg Source: http://upload.wikimedia.org/wikipedia/commons/3/3b/RC_Divider.svg License: Public domain Contributors: SVG work by uploader Original artist: ZooFari • File:Radiolaria3434.JPG Source: http://upload.wikimedia.org/wikipedia/commons/c/c1/Radiolaria3434.JPG License: CC-BY-SA-3.0 Contributors: ? Original artist: ? • File:Relationship_between_dBu_and_dBm.png Source: http://upload.wikimedia.org/wikipedia/commons/c/c7/Relationship_ between_dBu_and_dBm.png License: CC-BY-SA-3.0-2.5-2.0-1.0 Contributors: ? Original artist: ? • File:Renierit.JPG Source: http://upload.wikimedia.org/wikipedia/commons/e/ea/Renierit.JPG License: CC-BY-SA-2.0-de Contributors: Own work Original artist: Alchemist-hp (
talk) (www.pse-mendelejew.de) • File:Replica-of-first-transistor.jpg Source: http://upload.wikimedia.org/wikipedia/commons/b/bf/Replica-of-first-transistor.jpg License: Public domain Contributors: ? Original artist: ? • File:Response_silicon_photodiode.svg Source: http://upload.wikimedia.org/wikipedia/commons/4/41/Response_silicon_photodiode. svg License: CC-BY-SA-3.0 Contributors: Own work Original artist: KaiMartin • File:SI_base_unit.svg Source: http://upload.wikimedia.org/wikipedia/commons/c/c8/SI_base_unit.svg License: CC-BY-SA-3.0 Contributors: I (Dono (talk)) created this work entirely by myself. Base on http://www.newscientist.com/data/images/archive/2622/26221501.jpg Original artist: Dono (talk) • File:SMD_Cystal_Oscillator_TCXO.png Source: http://upload.wikimedia.org/wikipedia/commons/2/2c/SMD_Cystal_Oscillator_ TCXO.png License: CC-BY-3.0 Contributors: Own work Original artist: Appaloosa
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• File:STM-NE556-HD.jpg Source: http://upload.wikimedia.org/wikipedia/commons/c/c3/STM-NE556-HD.jpg License: CC-BY-3.0 Contributors: http://zeptobars.ru/en/read/open-microchip-asic-what-inside-II-msp430-pic-z80 Original artist: ZeptoBars • File:Schematic_of_class_H_current_amplifier.gif Source: http://upload.wikimedia.org/wikipedia/commons/a/aa/Schematic_of_ class_H_current_amplifier.gif License: CC-BY-SA-3.0 Contributors: Own work Original artist: Braun walter • File:Signetics_NE555N.JPG Source: http://upload.wikimedia.org/wikipedia/commons/2/21/Signetics_NE555N.JPG License: CC-BYSA-3.0 Contributors: Own work Original artist: de:User:Stefan506 • File:Silicon-unit-cell-3D-balls.png Source: http://upload.wikimedia.org/wikipedia/commons/f/f1/Silicon-unit-cell-3D-balls.png License: Public domain Contributors: Own work Original artist: Ben Mills • File:Silicon_wafer_with_mirror_finish.jpg Source: http://upload.wikimedia.org/wikipedia/commons/5/5d/Silicon_wafer_with_ mirror_finish.jpg License: Public domain Contributors: NASA Glenn Research Center Original artist: NASA Glenn Research Center • File:Silizium_pulver.jpg Source: http://upload.wikimedia.org/wikipedia/commons/4/4a/Silizium_pulver.jpg License: CC-BY-SA-3.0 Contributors: eigenes Bild; de:Bild:Silizium pulver.jpg Original artist: Silane • File:Simple_electromechanical_regulation.PNG Source: http://upload.wikimedia.org/wikipedia/en/c/ca/Simple_electromechanical_ regulation.PNG License: ? Contributors: ? Original artist: ? • File:Simple_electromechanical_voltage_regulator.PNG Source: http://upload.wikimedia.org/wikipedia/en/3/38/Simple_ electromechanical_voltage_regulator.PNG License: ? Contributors: ? Original artist: ? • File:Sinc_function_(normalized).svg Source: http://upload.wikimedia.org/wikipedia/commons/d/d4/Sinc_function_%28normalized% 29.svg License: CC-BY-SA-3.0-2.5-2.0-1.0 Contributors: ? Original artist: ? • File:Singlemode_fibre_structure.svg Source: http://upload.wikimedia.org/wikipedia/commons/8/84/Singlemode_fibre_structure.svg License: CC-BY-SA-3.0 Contributors: derivative work by uploader Original artist: Original by Bob Mellish, SVG derivative by Benchill • File:Stabilizer.JPG Source: http://upload.wikimedia.org/wikipedia/commons/d/d5/Stabilizer.JPG License: Public domain Contributors: Originally uploaded by copyright holder Sriramk750 at English Wikipedia to http://en.wikipedia.org/wiki/File:Stabilizer.JPG Original artist: Sriramk750 at English Wikipedia • File:Streetlight_control.jpg Source: http://upload.wikimedia.org/wikipedia/commons/c/c8/Streetlight_control.jpg License: CC-BYSA-3.0 Contributors: Own work Original artist: MyName (Atlant) • File:Switching_capacitor_schematic.PNG Source: http://upload.wikimedia.org/wikipedia/commons/e/e3/Switching_capacitor_ schematic.PNG License: Public domain Contributors: en.wikipedia Original artist: en:Reza mirhosseini • File:Symbol_book_class2.svg Source: http://upload.wikimedia.org/wikipedia/commons/8/89/Symbol_book_class2.svg License: CCBY-SA-2.5 Contributors: Mad by Lokal_Profil by combining: Original artist: Lokal_Profil • File:Text_document_with_red_question_mark.svg Source: http://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_ with_red_question_mark.svg License: Public domain Contributors: Created by bdesham with Inkscape; based upon Text-x-generic.svg from the Tango project. Original artist: Benjamin D. Esham (bdesham) • File:Thermistor.svg Source: http://upload.wikimedia.org/wikipedia/commons/1/10/Thermistor.svg License: Public domain Contributors: Own drawing, made in Inkscape 0.43 Original artist: jjbeard • File:Transbauformen.jpg Source: http://upload.wikimedia.org/wikipedia/commons/e/e1/Transbauformen.jpg License: CC-BY-SA-3.0 Contributors: Own work Original artist: Ulfbastel • File:Transistor-die-KSY34.jpg Source: http://upload.wikimedia.org/wikipedia/commons/e/e2/Transistor-die-KSY34.jpg License: Public domain Contributors: ? Original artist: ? • File:Transistor_Simple_Circuit_Diagram_with_NPN_Labels.svg Source: http://upload.wikimedia.org/wikipedia/commons/9/91/ Transistor_Simple_Circuit_Diagram_with_NPN_Labels.svg License: CC-BY-SA-3.0 Contributors: I created a postscript file, and converted it to SVG using the pstoedit program. Original artist: Michael9422 • File:Transistor_as_switch.svg Source: http://upload.wikimedia.org/wikipedia/commons/5/5d/Transistor_as_switch.svg License: Public domain Contributors: Own work Original artist: FDominec • File:Transistor_on_portuguese_pavement.jpg Source: http://upload.wikimedia.org/wikipedia/commons/3/38/Transistor_on_ portuguese_pavement.jpg License: CC-BY-SA-3.0 Contributors: Own work Original artist: Joao.pimentel.ferreira • File:Transistorer_(croped).jpg Source: http://upload.wikimedia.org/wikipedia/commons/2/2c/Transistorer_%28croped%29.jpg License: CC-BY-SA-3.0 Contributors: Own work Original artist: Transisto at en.wikipedia • File:Transparent.gif Source: http://upload.wikimedia.org/wikipedia/commons/c/ce/Transparent.gif License: Public domain Contributors: Own work Original artist: Edokter • File:Ua741_opamp.jpg Source: http://upload.wikimedia.org/wikipedia/commons/4/43/Ua741_opamp.jpg License: CC-BY-3.0 Contributors: Transferred from en.wikipedia; transferred to Commons by User:BokicaK using CommonsHelper. Original artist: Teravolt (talk). Original uploader was Teravolt at en.wikipedia • File:VCO.jpg Source: http://upload.wikimedia.org/wikipedia/commons/a/af/VCO.jpg License: CC-BY-SA-3.0-2.5-2.0-1.0 Contributors: Own work Original artist: ^musaz
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• File:Voltage_divider_bias.PNG Source: http://upload.wikimedia.org/wikipedia/commons/f/f7/Voltage_divider_bias.PNG License: Public domain Contributors: Transferred from en.wikipedia; transferred to Commons by User:Sfan00_IMG using CommonsHelper. Original artist: Original uploader was Xcentaur at en.wikipedia • File:Voltage_divider_with_cap.PNG Source: http://upload.wikimedia.org/wikipedia/commons/1/13/Voltage_divider_with_cap.PNG License: Public domain Contributors: Transferred from en.wikipedia; transferred to Commons by User:Sfan00_IMG using CommonsHelper. Original artist: Original uploader was Xcentaur at en.wikipedia • File:Voltage_modulation_Class_H.jpg Source: http://upload.wikimedia.org/wikipedia/commons/7/7b/Voltage_modulation_Class_H. jpg License: CC-BY-SA-3.0 Contributors: Own work Original artist: Braun walter • File:Voltage_stabiliser_OA,_IEC_symbols.svg Source: http://upload.wikimedia.org/wikipedia/commons/f/fb/Voltage_stabiliser_ OA%2C_IEC_symbols.svg License: CC-BY-SA-3.0 Contributors: http://commons.wikimedia.org/wiki/File:Stab_ov.svg Original artist: German verison: Appaloosa, Translated by Eirik1231 • File:Voltage_stabiliser_transistor,_IEC_symbols.svg Source: http://upload.wikimedia.org/wikipedia/commons/c/c3/Voltage_ stabiliser_transistor%2C_IEC_symbols.svg License: CC-BY-SA-3.0 Contributors: http://commons.wikimedia.org/wiki/File:Ser_stab.svg Original artist: German verison: Appaloosa, Translated by Eirik1231 • File:Wikibooks-logo-en-noslogan.svg Source: http://upload.wikimedia.org/wikipedia/commons/d/df/Wikibooks-logo-en-noslogan. svg License: CC-BY-SA-3.0 Contributors: Own work Original artist: User:Bastique, User:Ramac et al. • File:Wikibooks-logo.svg Source: http://upload.wikimedia.org/wikipedia/commons/f/fa/Wikibooks-logo.svg License: CC-BY-SA-3.0 Contributors: Own work Original artist: User:Bastique, User:Ramac et al. • File:Wikiversity-logo.svg Source: http://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg License: ? Contributors: Snorky (optimized and cleaned up by verdy_p) Original artist: Snorky (optimized and cleaned up by verdy_p) • File:Wiktionary-logo-en.svg Source: http://upload.wikimedia.org/wikipedia/commons/f/f8/Wiktionary-logo-en.svg License: Public domain Contributors: Vector version of Image:Wiktionary-logo-en.png. Original artist: Vectorized by Fvasconcellos (talk · contribs), based on original logo tossed together by Brion Vibber • File:X_mark.svg Source: http://upload.wikimedia.org/wikipedia/commons/a/a2/X_mark.svg License: Public domain Contributors: Own work Original artist: User:Gmaxwell • File:Yes_check.svg Source: http://upload.wikimedia.org/wikipedia/en/f/fb/Yes_check.svg License: ? Contributors: ? Original artist: ?
9.3 Content license • Creative Commons Attribution-Share Alike 3.0
