1.      The signal received at a device has a power of 10 mW (milliWatts), the noise at the receiver is 0.0001 Watts. A) What is the signal to noise ratio in numerical format at the receiver? B) What is the signal to noise ratio expressed in dB at the receiver?

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.

The signal received at a device has a power of 10 mW (milliWatts), the noise at the receiver is 0.0001 Watts. A) What is the signal to noise ratio in numerical format at the receiver? B) What is the signal to noise ratio expressed in dB at the receiver?

Learn how to calculate the Signal to Noise Ratio (SNR) from a power of 10 mW and noise of 0.0001 W. This page provides step-by-step solutions, showing SNR in numerical format as 100 and in dB as 20 dB. Ideal for high school students studying signal processing.

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