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:

For ideal ADCs, use $SNR_{dB} \approx 6.02N + 1.76$. Each extra bit of resolution improves SNR by about 6 dB.

Answer 1

Step 1: Formula for SNR of an ideal ADC.
For an $N$-bit ADC, the theoretical SNR is given by: \[ SNR_{dB} = 6.02N + 1.76 \] Step 2: Substitute given SNR.
\[ 61.96 = 6.02N + 1.76 \] Step 3: Solve for $N$.
\[ 6.02N = 61.96 - 1.76 = 60.2 \] \[ N = \frac{60.2}{6.02} = 10.0 \] Step 4: Round to nearest integer.
$N = 10$ bits.
\[ \boxed{10} \]