(a) Show that V. ref i0 = R b, +.+ 2N 21 22 (b) Which bit is the LSB? Which is the MSB? (c) For Vref - 10 V, R - 10 k2, and N - 8, find the maximum value of io obtained.

Electricity for Refrigeration, Heating, and Air Conditioning (MindTap Course List)
10th Edition
ISBN:9781337399128
Author:Russell E. Smith
Publisher:Russell E. Smith
Chapter17: Commercial And Industrial Air-conditioning Control Systems
Section: Chapter Questions
Problem 22RQ
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1.42 Figure P1.42 shows the circuit of an N-bit DAC. Each of the N bits of the digital word to be converted controls
one of the switches. When the bit is 0, the switch is in the position labeled 0; when the bit is 1, the switch is in the
position labeled 1. The analog output is the current io. Vref is a constant reference voltage.
ref
2R
4R
8R
2NR
(a) Show that
Vt (b,, b,
ref
...
R
21
22
2N
(b) Which bit is the LSB? Which is the MSB?
(c) For Vref = 10 V, R = 10 k2, and N = 8, find the maximum value of io obtained. What is the change in io
resulting from the LSB changing from 0 to 1?
Transcribed Image Text:1.42 Figure P1.42 shows the circuit of an N-bit DAC. Each of the N bits of the digital word to be converted controls one of the switches. When the bit is 0, the switch is in the position labeled 0; when the bit is 1, the switch is in the position labeled 1. The analog output is the current io. Vref is a constant reference voltage. ref 2R 4R 8R 2NR (a) Show that Vt (b,, b, ref ... R 21 22 2N (b) Which bit is the LSB? Which is the MSB? (c) For Vref = 10 V, R = 10 k2, and N = 8, find the maximum value of io obtained. What is the change in io resulting from the LSB changing from 0 to 1?
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