Topic: Communication Systems
In communication system, if for a given rate of information transmission requires channel bandwidth, $B_{1}$ and signal-to-noise ratio $SNR_{1}$. If the channel bandwidth is doubled for same rate of information then new signal-to-noise ratio will be
- A. $SNR_{1}$
- B. $2SNR_{1}$
- C. $\sqrt{SNR_{1}}$
- D. $SNR_{1}/2$
Answer: C. $\sqrt{SNR_{1}}$
Explanation: Using Shannon's Channel Capacity theorem: $C = B \log_2(1 + SNR) \approx B \log_2(SNR)$ for large SNR. If the bandwidth is doubled for the same capacity, $C = 2B \log_2(SNR')$. Equating them gives $B \log_2(SNR) = 2B \log_2(SNR') \Rightarrow \log_2(SNR') = \frac{1}{2}\log_2(SNR) \Rightarrow SNR' = \sqrt{SNR}$.