Question:
A full-scale sinusoidal signal is applied to a 10-bit ADC. The fundamental signal component in the ADC output has a normalized power of 1 W, and the total noise and distortion normalized power is \(10 \, \mu {W}\). The effective number of bits (rounded off to the nearest integer) of the ADC is \(\_\_\_\_\).
A full-scale sinusoidal signal is applied to a 10-bit ADC. The fundamental signal component in the ADC output has a normalized power of 1 W, and the total noise and distortion normalized power is \(10 \, \mu {W}\). The effective number of bits (rounded off to the nearest integer) of the ADC is \(\_\_\_\_\).
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The Effective Number of Bits (ENOB) represents the practical resolution of an analog-to-digital converter (ADC) while accounting for the impact of noise and distortion. Understanding SINAD is essential to evaluate ADC performance.
Updated On: Jan 31, 2025
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The Correct Option is B
Solution and Explanation
Step 1: Calculate the Signal-to-Noise and Distortion Ratio (SINAD).
The formula for SINAD is:
\[
{SINAD} = 10\log_{10} \left(\frac{{Signal Power}}{{Noise + Distortion Power}}\right).
\]
By substituting the given values:
\[
{SINAD} = 10\log_{10} \left(\frac{1}{10 \times 10^{-6}}\right) = 50 \, {dB}.
\]
Step 2: Determine the Effective Number of Bits (ENOB).
The ENOB is given by:
\[
{ENOB} = \frac{{SINAD} - 1.76}{6.02}.
\]
Substitute \({SINAD} = 50\):
\[
{ENOB} = \frac{50 - 1.76}{6.02} = 8 \, {bits}.
\]
Final Answer:
\[
\boxed{{(2) } 8}
\]
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