GATE EC 2023 Set 1 — Question 31
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Digital Circuits → Data Converters → Resolution & Quantization Error
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Question
The signal-to-noise ratio (SNR) of an ADC with a full-scale sinusoidal input is given to be dB. The resolution of the ADC is ________ bits (rounded off to the nearest integer).
Correct answer
10 to 10
Solution
The signal-to-noise ratio (SNR) for an ideal -bit Analog-to-Digital Converter (ADC) with a full-scale sinusoidal input is given by the formula:Given that the dB, we can substitute this value into the formula to find the resolution :Subtracting from both sides:Solving for :Thus, the resolution of the ADC is 10 bits.
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