Question

The signal-to-noise ratio (SNR) of an ADC with a full-scale sinusoidal input is given to be 61.96 dB. The resolution of the ADC is ___________ bits (rounded off to the nearest integer).

Hint:

This formula, SNR $\approx 6.02n + 1.76$ dB, is a cornerstone of data converter theory. A useful rule of thumb derived from it is that each additional bit of resolution increases the SNR by approximately 6 dB.

Answer 1

Correct Answer: 10

The signal-to-noise ratio (SNR) for an analog-to-digital converter (ADC) with an ideal sinusoidal input is expressed as:
SNR (dB) = 6.02N + 1.76
where N is the resolution in bits. We are given SNR = 61.96 dB. To find N, we solve the equation:
61.96 = 6.02N + 1.76
Subtract 1.76 from both sides:
60.20 = 6.02N
Divide both sides by 6.02:
N = 60.20 / 6.02 ≈ 10.0
The calculated resolution is N = 10 bits. The given range is 10,10, which confirms the resolution fits within this range.