Question

A 1 mW signal having a bandwidth of 100 MHz is transmitted to a receiver through cable that has 40 dB loss. If the effective one side noise spectral density at the receiver is 10^-20 Watt/Hz, then the signal to noise ratio at the receiver is
1. 50 dB
2. 30 dB
3. 40 dB
4. 60 dB

Answer 1

Correct Answer - Option 1 : 50 dB

Noise power \({\rm{N}} = {{\rm{N}}_0}{\rm{W}} = {10^{ - 20}} \times {10^8}\)

\({{\rm{P}}_{{\rm{loss}}}} = 40{\rm{dB}} = {10^4}\)

\({{\rm{S}}_{\rm{i}}} = \frac{{{{\rm{P}}_{\rm{t}}}}}{{{{\rm{P}}_{{\rm{loss}}}}}} = \frac{{0.001}}{{{{10}^4}}} = {10^{ - 7}}\)

Signal to Noise Ratio \(\frac{{\rm{S}}}{{\rm{N}}} = \frac{{{{10}^{ - 7}}}}{{{{10}^{ - 12}}}} = {10^5} = 50{\rm{dB}}\)