Answered: SNR of a quantized signal depends on…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

See similar textbooks

Related questions

Concept explainers

Question

SNR of a quantized signal depends on the number of bits. Explain how the number of bits should be chosen for a quantization process.

Expert Solution

Step 1

When an Analog to Digital converter converts any continuous signal to discreet form, a range of input values produce the same output due to rounding of of the signal in discreet form. This leads to an error called as Quantization error it's RMS value is given by the below expression,

$v_{q n} = \frac{Q}{\sqrt{12}} Where, Q = Quantum (The range of input values that produces the same output)$

Let, us assume that the input signal is a sinusoidal signal with the maximum value of V_m , where 2V_m is the reference voltage for an N-Bit Analog to digital converter

Step 2

$RMS value = \frac{2 V_{m}}{2 \sqrt{2}} = \frac{2^{N} Q}{2 \sqrt{2}} where, N = number of bits for discretization$

Signal to noise ratio can be calculated as:

$\begin{array}{rcl} S N R & = & 20 \log (\frac{V_{r m s}}{v_{q n}}) \\ = & 20 \log (\frac{\frac{2^{N} Q}{2 \sqrt{2}}}{\frac{Q}{\sqrt{12}}}) \\ = & 20 \log (\frac{2^{N} \sqrt{12}}{2 \sqrt{2}}) \\ = & 20 \log (2^{N}) + 20 \log (\frac{\sqrt{6}}{2}) \\ = & 6.02 N + 1.76 d B \end{array}$

Step by step

Solved in 3 steps

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.

Similar questions