Nabeela Z. Khan
Experim Experiment ent 5 : Digital to Analog Converter
Objective: study of digital to analog converter using R–2R ladder circuit. Equipments:
Trainer board. OpAmp 741 Resistors Wires
Theory: In elect electron ronics, ics, a digital-to-analog converter (DAC or D-to-A) is a device that converts a digital (usually binary binary)) code to to an analog signal(curr signal(current ent,, voltage, voltage, or electric electric charge charge). ). An analog-to-dig analog-to-digit ital al convert converter er (ADC) (ADC ) performs performs the reverse reverse operation. Signals are easily stored and and transmit transmitted ted in digital digital form, form, but a DAC is needed for the signal to to be recognized by human senses or other non-digital system systems. s. A common use of digital-to-analog converters is generation of audio signals from digital information in music music players. players. Digital Digital video video signals are conver converted ted to to analog in television televisions s and mobile phones phones to display display colors and shades. Digital-to-analog conversion can degrade degrade a signal, so conversion conversion details details are normally normally chosen so that the errors are negligible. Due to cost and the need for matched matched components, components, DAC DA Cs are almost exclusively manufactur manufactured ed on integr integrated ated circuit circuits s (ICs). (IC s). There are many many DAC archite architectu ctures res which which have have different different adva advant ntages ages and disadvantages. The suitability of a particular DAC for an application is determined by a variety of measurements including speed and resolution.
DACs are very important to system performance. The most important characteristics of these devices are: Resolution
The The number of possi ossib ble out output lev levels els the DAC DAC is is desig esign ned to repr eprodu oduce. ce. This This is usual sually ly sta stated as the the number number of bits bits it uses, uses, which is the base two two logarith logarithm m of the the number number of levels. levels. For F or instance instance a 1
8
1 bit DAC is designed to reproduce 2 (2 ) levels while an 8 bit DAC is designed for 256 (2 ) levels. Resolution R esolution is related to to the effective number number of bits bits which is a measuremen measurementt of the actual resolution attained attained by the the DAC. DAC . Resolution Resolution determ determines ines color depth depth in video video applications and audio audio bit depth depth in audio audio applications. applications. Maximum Maximum sampling rate
A measurement of the maximum speed at which the DACs circuitry can operate and still produce the correct correct output. output. As stated in tthe he Nyquist–S hannon sampling theorem theorem defines a relationship relationship between between the the sampling frequency frequency and bandwidth bandwidth of the sampled signal.
Digital and Analog Representations
An analog signal can be represented with digital values at some time interval.
Four binary positions = 4-bit resolution
16 different representations
Eight binary positions = 8-bit resolution
256 different representations
Operational amplifiers are important building blocks in analog-to-digital (A/D) and digital-to-analog (D/A) converters. They provide a means for summing currents at the input and converting a current to a voltage at the output of converter circuits. The operational amplifier is used in the circuit for scaling the value of output voltage. Operational Amplifier Basics
Very high input impedance
Very high voltage gain
Very low output impedance
DAC DACs are electronic circuits that convert digital, (usually binary) signals (for example, 1000100) to analog electrical quantities (usually voltage) directly related to the digitally encoded input number. DACs are used in many other applications, such as voice synthesizers, automatic test system, and process control actuator. In addition, they allow computers to communicate with the real (analog) world. Input Binary Number Analog Voltage Output r e t s i g e R
Voltage Switch
Resistive Summing Network
Amplifier
Register: Use to store the digital input (let it remain a constant value) during the conversion period. Voltage: Similar to an ON/OFF switch. It is ‘closed’ when the input is ‘1’. It is ‘opened’ when the input is
‘0’. Resisti ve Summi ng Netwo rk : Summation of the voltages according to different weighting. Am pl if ier : Amplification of the analog according to a pre-determined output voltage range. For example-
an operation amplifier. The two most popular types of resistive summing networks are: 1) Weighted binary resistance type, and 2) Ladder resistance (R-2R) type DAC types
The binary-weighted DAC, which contains individual electrical components for each bit of the DAC connected to a summing point. These precise voltages or currents sum to the correct output value. This is one of the fastest conversion methods but suffers from poor accuracy because of the high precision required for each individual voltage or current. Such high-precision components are expensive, so this type of converter is usually limited to 8-bit resolution or less
The R-2R ladder DAC which is a binary-weighted DAC that uses a repeating cascaded structure of resistor values R and 2R. This improves the precision due to the relative ease of producing equal valued-matched resistors (or current sources). However, wide converters perform slowly due to increasingly large RC-constants for each added R-2R link.
Binary-Weighted Digi tal-to-Analog Converters
Sum of the currents from the input resistors
Binary weighting factor
Disadvantages of B inary-Weight ed Digital-to-Analog Converters
Accurate resistance over a wide range is difficult
Not practical for conversions greater than 4-bit
R/2R Ladder Digital-to-Analog Converters
Only two resistor values
8, 10, 12, 14, and 16 bit resolutions are common
The R/2R ladder D/A converter uses only two different resistor values, no matter how many binary input bits are included. This allows for very high resolution and ease of fabrication in integrated-circuit form.
Current division
analog output versus digital input
The process of translation of digital information into equivalent analog information is called as digital to analog conversion. Such converter is also called as decoding device. There are two types of
such converters –
the
weighted
resistor
DAC
and
the
R–2R
ladder
DAC.
The R–2R ladder (binary ladder) is a resistive network whose output voltage is a properly weighted sum of the digital inputs. It uses resistors of only two values, the R and the 2R. The input to a DAC is a binary word of n-bits and the output is an analog value, as schematically shown in Figure a.
Figure : (a) DAC block diagram; (b) input-output characteristic of a DAC The n-bit word (or digital code) is a digital representation of a signal. The relationship between the analog output value and the binary word is for the case of a 3-bit code (b2,b1,bo), as follows: VDAC =K 1 (b2/2 +b1 /4 +bo/8) Vref where
K 1=Rf /R
VDAC =(b 2/2 + b 1 /4 + b o /8) FS
in which K 1 is a scale factor, Vref is a reference voltage, FS stands for Full Scale (=K 1xVref ) and bi is the ith bit of the digital word. The bit bo is called the least significant bit (LSB) and b 3 is the most significant bit (MSB). Each time the LSB changes the analog output will change by a value equal to 3
N
FS/2 for a three bit DAC (or by FS/2 for a N bit DAC). As an example, lets assume that the digital input is equal to (101), K 1 =1 and the reference Vref =5V. The output voltage will then be: VDAC =K(1/2 +0/4 +1/8) Vref =5/8xVref =5/8xFS =3.125 V 3
For each digital input (b2,b1,bo) there will be a corresponding output as shown in Figure b for a total of 2 = 8 possible digital words. Notice that only discrete values of the output signal are possible. The more bits the input word has, the smaller the steps of the output signal will be (or the better the resolution).
Reference: 1. Pages 922, 923, 924, 925, 926 of Chapter 9 of Microelectronic Circuits by Sedra/Smith. 2. http://seminarprojects.com/Thread-study-the-working-of-4%E2%80%93bitr%E2%80%932r-ladder-d-a-converter-circuit 3. http://en.wikipedia.org/wiki/Resistor_ladder 4. http://www.seas.upenn.edu/~ese206/labs/adc206/adc206.html
Circuit diagram:
2
2
2
2 U6
1
1
R4 1k
1k
R3 1k R1
R2
1k
1k
1
R7
1k
R6 1k
R5 1k
1
R9
1k
R10
1k
1k
1k R15
1k
R14
R11
1k
R8
R13 R12
uA741 2 -
1k 3
+ U2
4 V-OS1 1 6 OUT V OS2 5 7
Data: R 1KΩ
Truth Table:
Observation
D3
D2
D1
D0
1
0
0
0
0
2
0
0
0
1
3
0
0
1
0
4
0
0
1
1
5
0
1
0
0
6
0
1
0
1
7
0
1
1
0
Vout
#
Nabeela Z. Khan
8
0
1
1
1
9
1
0
0
0
10
1
0
0
1
11
1
0
1
0
12
1
0
1
1
13
1
1
0
0
14
1
1
0
1
15
1
1
1
0
16
1
1
1
1
Calculation
Questions: 1.
Name some applications of DAC.
2.
The DAC circuit implemented in experiment 8 used what type of resistive summing network ?
3.
What was the resolution of the DAC circuit? Which circuit element gives the resolution?
4.
How many levels can it reproduce ?
5.
Determine Vout.
Nabeela Z. Khan
6.
What are the disadvantages of Binary-Weighted DAC?
7.
What is the advantage of R-2R ladder DAC?
8.
What is the purpose of the OpAmp in the circuit?
9.
For the following circuit find out K 1, FS and VDAC for input 1010. [2 points]
Nabeela Z. Khan