GATE 2016 EC (EC2) – Question 53
An N-bit flash ADC drives $2^N-1$ comparator inputs simultaneously. The input voltage source has resistance 75 Ω and each comparator input capacitance is 8 pF. Settling to within 1/2 LSB after a full-scale change is required; encoder time is negligible. For 8-bit resolution, which is closest to the maximum sampling rate?
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Correct answer: (A) 1 megasample/s
Explanation
There are 255 comparators, so their parallel input capacitance is $255(8)=2040$ pF. The source time constant is $75(2040\ \mathrm{pF})=153$ ns.
A full-scale exponential residual must be at most $1/512$ of full scale. Thus $e^{-t/\tau}\le1/512$, requiring $t\ge153\ln512=954.46$ ns.
The corresponding maximum sampling rate is about 1.048 megasamples/s, closest to **1 megasample/s, A**.