What is the quantization noise power for N bit uniform quantizer with full scale input voltage 2B?

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This question was previously asked in

ISRO Scientist Electronics 2024 Official Paper

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Answer 1

Concept:

The quantization noise power P_q for a uniform quantizer is given by:

P_q = \(\frac{{\Delta^2}}{12}\)

where \(\Delta\) is the quantization step size.

Given:

Full-scale input voltage = 2B

Number of quantization levels = 2^N

Calculation:

Quantization step size:

\(\Delta = \frac{2B}{2^N} = \frac{B}{2^{N-1}}\)

Quantization noise power:

\(\frac{\Delta^2}{12} = \frac{1}{12} \cdot \left(\frac{B}{2^{N-1}}\right)^2 = \frac{B^2}{12 \cdot 2^{2(N-1)}} = \frac{B^2}{3 \cdot 2^{2N}}\)

Hence, the correct answer is option 1) \(\rm \frac{B^{2}}{3\left(2^{2 N}\right)}\)