Topic: Communication Systems
A 1 mW video signal having a bandwidth of 100 MHz is transmitted to a receiver through a cable that has 40 dB loss. If the effective one-sided noise spectral density at the receiver is $10^{-20}\text{ Watt/Hz}$, then the signal-to-noise ratio at the receiver is
- A. 50 dB
- B. 30 dB
- C. 40 dB
- D. 60 dB
Answer: A. 50 dB
Explanation: Input power $P_{in} = 1~\text{mW} = -30~\text{dBW}$.
Loss in cable = 40 dB, so received signal power $P_{out} = -30 - 40 = -70~\text{dBW}$.
Noise power $P_N = N_0 \times BW = 10^{-20} \times 100 \times 10^6 = 10^{-12}~\text{W} = -120~\text{dBW}$.
$SNR = P_{out} - P_N = -70 - (-120) = 50~\text{dB}$.