ADC and DAC


Question 1
Consider the circuit shown with an ideal OPAMP. The output voltage V_o is __________V (rounded off to two decimal places).

A
0.5
B
0.75
C
-0.5
D
-0.75
GATE EC 2022   Digital Circuits
Question 1 Explanation: 


V_A=\frac{V_R}{2} \; and R_{th}=R
V_B=\frac{V_B}{2}

V_C=\frac{(V_R+V_R/4)}{2}=\frac{5}{8}V_R
R_{th}=2R||2R=R
Similarly,
V_D=\frac{V_C}{2}=\frac{5}{16}V_R
So, \frac{S}{16}V_R=\frac{5}{16} \times 1.6V
V_o=\frac{-3R}{(2R+R)} \times \frac{5}{16} \times 1.6=-\frac{3}{2} \times \frac{5}{16} \times 1.6
V_o=-0.5V
Question 2
An 8-bit unipolar (all analog output values are positive) digital-to-analog converter (DAC) has a full-scale voltage range from 0\; V to 7.68\:V. If the digital input code is 10010110 (the leftmost bit is \text{MSB}), then the analog output voltage of the DAC (rounded off to one decimal place) is ___________ V.
A
2.4
B
4.5
C
8.4
D
5.4
GATE EC 2021   Digital Circuits
Question 2 Explanation: 
\begin{aligned} \text { Given: } \qquad \qquad V_{p s}&=7.68 \mathrm{~V} \\ n &=8 \mathrm{bit} \\ \text { Resolution }(k) &=\frac{V_{F S}}{2^{n}-1}=\frac{7.68}{2^{8}-1}=0.03\\ \text { Now, } \quad V_{\mathrm{DAC}}&=k \times\{\text { Decimal equivalent }\}\\ &=0.03 \times\{150\} \\ &=4.5 \mathrm{~V} \end{aligned}


Question 3
A 10-bit D/A converter is calibrated over the full range from 0 to 10 V. If the input to the D/A converter is 13A (in hex), the output (rounded off to three decimal places) is _________ V.
A
3.069
B
1.214
C
2.124
D
0.257
GATE EC 2020   Digital Circuits
Question 3 Explanation: 
Given, n=10
V_{FS}=10\, V
Input Voltage=(13A)_{16}=(314)_{10}
Output Voltage=Resolution X Decimal Equivalent of input
V_{o}=\frac{10}{2^{10}-1}\times 314=3.069\, V
Question 4
In an N bit flash ADC, the analog voltage is fed simultaneously to 2^{N}-1 comparators. The output of the comparators is then encoded to a binary format using digital circuits. Assume that the analog voltage source V_{in} (whose output is being converted to digital format) has a source resistance of 75 \Omega as shown in the circuit diagram below and the input capacitance of each comparator is 8 pF. The input must settle to an accuracy of 1/2 LSB even for a full scale input change for proper conversion. Assume that the time taken by the thermometer to binary encoder is negligible.

If the flash ADC has 8 bit resolution, which one of the following alternatives is closest to the maximum sampling rate ?
A
1 megasamples per second
B
6 megasamples per second
C
64 megasamples per second
D
256 megasamples per second
GATE EC 2016-SET-2   Digital Circuits
Question 5
Consider a four bit D to A converter. The analog value corresponding to digital signals of values 0000 and 0001 are 0 V and 0.0625 V respectively. The analog value (in Volts) corresponding to the digital signal 1111 is ________.
A
0.7
B
0.93
C
1.13
D
1.07
GATE EC 2015-SET-1   Digital Circuits
Question 5 Explanation: 
Step size =0.0625 \mathrm{V}
Decimal equivalent =15
Analog output =15 \times 0.0625=0.9375 Volts


There are 5 questions to complete.