Assume that the signals have 1.98 volts RMS (root mean square) and are being corrupted by 30 mV
RMS of noise. Compute the S/N ratio

The **Signal-to-Noise Ratio (S/N ratio)** is a measure of the strength of the signal relative to the noise affecting it. It can be calculated using the formula:

\[
S/N = \frac{V_{\text{signal}}}{V_{\text{noise}}}
\]

Where:

- \( V_{\text{signal}} \) is the RMS voltage of the signal (1.98 volts in this case).
- \( V_{\text{noise}} \) is the RMS voltage of the noise (30 mV or 0.03 volts in this case).

Now, let's compute the S/N ratio:

\[
S/N = \frac{1.98}{0.03} = 66
\]

The **Signal-to-Noise Ratio (S/N)** is 66, meaning the signal is 66 times stronger than the noise.

If you'd like the S/N ratio in **decibels (dB)**, it can be calculated using the formula:

\[
S/N_{\text{dB}} = 20 \cdot \log_{10} \left(\frac{V_{\text{signal}}}{V_{\text{noise}}}\right)
\]

Let's calculate that too:

\[
S/N_{\text{dB}} = 20 \cdot \log_{10} \left(\frac{1.98}{0.03}\right)
\]

\[
S/N_{\text{dB}} = 20 \cdot \log_{10}(66)
\]

I will compute the decibel value for you now.The Signal-to-Noise Ratio (S/N) in **decibels (dB)** is approximately **36.39 dB**.

Would you like any further details or have any other questions?

Here are some related questions you might find interesting:

1. How does the S/N ratio affect the quality of transmitted signals?
2. What are the methods to reduce noise in a signal?
3. How does the S/N ratio differ between analog and digital signals?
4. What are some real-world applications where a high S/N ratio is crucial?
5. Can signal processing techniques improve the S/N ratio?

**Tip:** Increasing the signal power or reducing noise levels can help improve the Signal-to-Noise Ratio.

Assume that the signals have 1.98 volts RMS (root mean square) and are being corrupted by 30 mV RMS of noise. Compute the S/N ratio.

Learn how to compute the Signal-to-Noise Ratio (S/N) given signal and noise RMS voltages. In this example, the signal has 1.98V RMS and the noise 30mV RMS. This step-by-step guide shows how to calculate S/N both in standard ratio and decibels (dB), ideal for undergraduate students in electrical engineering or physics.

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