D6 - ME2143-2 Linear Circuits (EA-04-06) 3-Mar-2011
Name: ChenHaojin Matric Number: U096128E Group: 2N1
Objectives: 1. To understand the properties of an ideal operational amplifier. 2. To understand the limitations of a practical operational amplifier. 3. To be familiar with typical applications of an operational amplifier.
Introduction: This manual contains a list of the electrical/electronic components required and the procedure of experiments adopted to appreciate the fundamental principles of operation of the operational amplifier and integrated logic circuits.
Results:
1. Measure the voltage gain of the operational amplifier at 1 KHz and compare it with the predicted value. (This voltage gain is the closed-loop gain.). ¾ Experimental value: Vi = 1.041 v
Vo = 10.240 v
Vgain = Vo/Vi = 9.837
From the graph of the oscilloscope, there is 180 degrees phase difference between Vo and Vi.
¾ Predicted value: (Vo – V-)/R2 = (V- -Vi)/R1 V- = V+ = 0
R1 = 10KΩ
So, Vo = - 10Vi = - 10 * 1.041 = -10.41 v
R2 = 100KΩ
Vi = 1.041 v
| Vgain |= |Vo|/ |Vi| = 10
Therefore, the experimental value (Vgain = 9.837) is close to the predicted value (Vgain = 10), which explains the properties of inverting amplifier: a. Assumption 1 : V- = V+ (Due to the fact that output is typically finite with negative feedback) b. Assumption 2 : (Vi – V-)/Ri + (Vo – V-)/Rf = 0 (KCL, no currents flowing into opamp’s input terminals due to high input impedance)
2. Measure the frequency response of the amplifier by noting the voltage gain at the frequencies indicated below. Frequency (KHz)
0.01
0.1
1
10
20
30
40
50
60
100
Vo
10.160
10.000
10.240
10.160
10.000
9.681
9.121
7.921
6.961
4.241
Vi
1.041
1.041
1.041
1.081
1.081
1.041
1.081
1.081
1.121
1.161
Gain
9.760
9.606
9.837
9.399
9.251
9.300
8.438
7.327
6.210
3.653
Graph 1 : Gain Against Frequency 10 9 8 7 6 5
y = -0.0004x2 - 0.021x + 9.2354
4 3 2 1 0 0
20
40
60
80
100
120
At the “half power cut-off frequency”, the gain drops to 0.7071 of the gain at 1 KHz. Determine this frequency.
Frequency = 1 KHz : Vgain = Vo/Vi = 9.837 v At the “half power cut-off frequency” : V’gain = 0.7071 * Vgain = 0.7071 * 9.837 = 6.956 v From Graph 1, we can get the half power cut-off frequency = 54 KHz
3. Offset voltage without 10kΩ resistor = 6.7mV Offset voltage with 10kΩ resistor = 1.6mV Yes, the d-c output voltage decrease. Reasons: a. I vs V character of the transistors inside the IC (internal unbalance) b. Non-zero input voltage c. Through adding the 10kΩ resistor, the current will pass through the same resistance both in non-inverting input and inverting input, therefore the input offset voltage become common mode, so the offset voltage decrease.
4. Connect the circuit shown in Fig.2. Measure the gain of the amplifier at 1 KHz by monitoring VI and V0 on the oscilloscope. Does it correspond to the theoretical value? ¾ Experimental value: Vi = 1.121 v
Vo = 11.920 v
Vgain = Vo/Vi = 10.633
¾ Theoretical value: (Vo – V-)/R2 = (V- - 0)/R1 V- = V+
R1 = 10KΩ
So, Vo = 11Vi = 11 * 1.121 = 12.331 v
R2 = 100KΩ
Vi = 1.121 v
|Vgain| = |Vo|/ |Vi| = 11
Therefore, the experimental value (Vgain = 10.633) is close to the theoretical value (Vgain = 11). So yes, it corresponds to the theoretical value.
5. Connect the comparator circuit shown in Fig. 3. Determine its transfer characteristics (relationship between Vo and Vi).
Vi
14.080
11.900
9.980
7.900
5.940
4.020
2.031
0.059
-0.954
-2.043
-2.254
Vo
-0.730
-0.727
-0.723
-0.718
-0.713
-0.706
-0.697
-0.683
-0.672
-0.650
-0.641
Vi
-2.438
-2.790
-3.033
-3.381
-4.140
-5.860
-7.930
10.100
11.700
14.210
Vo
-0.632
-0.585
4.150
4.490
4.720
4.880
4.950
4.980
4.990
5.000
Graph 2 : Vout Against Vin 6 5 4 3 2 1
-15
-13
-11
-9
-7
-5
-3
0 -1 -1
1
3
5
7
9
11
13
15
-2
As shown in Graph 2, the value of Vout is around 5 v when Vin is between -14 v to -5 v; Vout is around -0.7 v when Vin is between -3 v to 14 v. There is a sudden drop, Vout from around 5 v to -0.7 v when Vin is around -3 v. Reason: The 5 v Zener Diode controls/changes the current direction. When the Zener Diode is on, voltage drop = 0.7 v, so Vo is around -0.7 v When the Zener Diode is under reverse break down region, voltage drop = -5 v, so Vo is around 5 v.
6. Connect the Digital-to-Analog converter in Fig. 4. Verify the circuit using the switches available on the test system.
x-axis
1
2
3
4
5
6
7
8
Switches (S2;S1;S0)
000
001
010
011
100
101
110
111
0
- 1/8
- 2/8
- 3/8
- 4/8
- 5/8
- 6/8
- 7/8
Theoretical
0.000
-0.625
-1.250
-1.875
-2.500
-3.125
-3.750
-4.375
Experimental
-0.067
-0.676
-1.285
-1.894
-2.484
-3.092
-3.701
-4.310
0.000 1
2
3
4
5
6
7
8
-0.500 -1.000 -1.500 -2.000
Theoretical Experimental
-2.500 -3.000 -3.500 -4.000 -4.500
As shown in the graph above, the experimental value is correspond/close to the theoretical value.
Discussion: 1. Properties of an ideal operational amplifier: a. V+ = V- (due to the fact that output is typically finite with negative feedback and the high open loop gain) b. No currents flowing into op-amp’s input terminals (due to high input impedance) c. Negative feedback results in stable behavior
2. Limitations of a practical operational amplifier: a. Bandwidth limitations --- There is a certain frequency after which the gain of the OpAmp drops b. Input Offset Voltage --- In real op-amp circuit, DC bias error may exist at the output voltage; can be modeled by the existence of an input offset voltage, Vos in series with one of the input terminals of the op-amp. c. Input bias current error --- Small input bias currents are present at inverting and noninverting terminals; bias currents cause a small shift to output voltage in amplifier circuits. d. Other considerations (ex. Voltage supply limits, common-mode rejection ratio…)
3. Typical applications of an operational amplifier: a. Can be used as voltage comparators where they take in 2 inputs and change its output to indicate which input is larger b. Can also be used as digital to analog convertors, taking in a digital signal input and returning an analog signal c. Others: can be used in input/output signal conditioning and interfacing…
Conclusion: Through this lab, we understand more about Operational-Amplifiers (including their properties, limitations, typical applications etc.) and know that they are very useful devices present in many modern applications.
