Topic: Communication Systems
A $1~V_{p-p}$ sinusoid is digitized by a 4 bit A-to-D converter with input dynamic range of $2V_{p-p}$. The signal to noise ratio of the digitized signal is
- A. 384
- B. 96
- C. 48
- D. 24
Answer: B. 96
Explanation: The step size is $S = \frac{2V_{m}}{M} = \frac{2V_{p-p}/2}{2^n} = \frac{2 \times 1}{2^4} = \frac{1}{8}\text{ V}$.
Quantization noise power $P_{n} = \frac{S²}{12} = \frac{(1/8)^2}{12} = \frac{1}{64 \times 12}$.
Signal power $P_{s} = \frac{V_{m}^2}{2} = \frac{(0.5)^2}{2} = \frac{1}{8}\text{ W}$.
SNR = $\frac{P_{s}}{P_{n}} = \frac{1/8}{1/(64 \times 12)} = \frac{64 \times 12}{8} = 8 \times 12 = 96$.