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. 7
• B. 8
• C. 9
• D. 10

Hint:

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.

Answer 1

The Correct Option is B

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: \[ \boxed{{(2) } 8} \]