The signal input power to a receiver is 10 nW. The noise power is 0.1 nW. What are the S/N ratio and the S/N ratio in decibels, respectively?

Group of answer choices

10, 10 dB

0.01, -20 dB

0.1, -10 dB

100, 20 dB

1 answer

To calculate the Signal-to-Noise (S/N) ratio, you can use the formula:

\[ \frac{S}{N} = \frac{\text{Signal Power}}{\text{Noise Power}} \]

Given:

  • Signal power, \(S = 10 , \text{nW}\)
  • Noise power, \(N = 0.1 , \text{nW}\)

Calculating the S/N ratio:

\[ \frac{S}{N} = \frac{10 , \text{nW}}{0.1 , \text{nW}} = 100 \]

Next, to convert the S/N ratio to decibels (dB), you can use the following formula:

\[ S/N \text{ (dB)} = 10 \cdot \log_{10}\left(\frac{S}{N}\right) \]

Calculating the S/N ratio in dB:

\[ S/N \text{ (dB)} = 10 \cdot \log_{10}(100) = 10 \cdot 2 = 20 , \text{dB} \]

Therefore, the Signal-to-Noise ratio is 100 and the S/N ratio in decibels is 20 dB.

Based on this calculation, the answer is:

100, 20 dB