To calculate the Signal-to-Noise Ratio (SNR), we use the following formulas:

A) Numerical Format

The SNR in numerical format is calculated as:

$\text{SNR} = \frac{P_s}{P_n}$

where:

• $P_s = 10 \, \text{mW} = 0.01 \, \text{W}$ (since $1 \, \text{mW} = 0.001 \, \text{W}$)
• $P_n = 0.0001 \, \text{W}$

Substituting the values:

$\text{SNR} = \frac{0.01}{0.0001} = 100$

B) SNR in dB

To express the SNR in decibels (dB), we use the formula:

$\text{SNR (dB)} = 10 \log_{10}\left(\frac{P_s}{P_n}\right)$

Substituting the SNR value:

$\text{SNR (dB)} = 10 \log_{10}(100) = 10 \times 2 = 20 \, \text{dB}$

Summary

• A) SNR in numerical format: 100
• B) SNR in dB: 20 dB

Do you want more details or have any questions? Here are some related questions you might consider:

1. What factors can affect the signal-to-noise ratio in a communication system?
2. How is the SNR related to the quality of a received signal?
3. What are the implications of a low signal-to-noise ratio?
4. How can one improve the signal-to-noise ratio in a practical scenario?
5. What are other common units used to express signal quality?

Tip: Understanding SNR is crucial for optimizing communication systems and ensuring reliable data transmission.