Question

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

Answer 1

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**