For a satellite circuit the carrier-to-noise ratios are
uplink 23 dB, downlink 20 dB, intermodulation 24 dB.
Calculate the overall carrier- to-noise ratio in decibels.


The overall carrier-to-noise ratio \( (C/N)_{\text{overall}} \) in a satellite circuit can be calculated using the reciprocal of the sum of the reciprocals of the individual \( C/N \) values for each link in the system. This relationship is derived from the nature of signal-to-noise ratios (SNR) in cascaded systems.

For the uplink, downlink, and intermodulation components, the overall \( C/N \) is given by:

\[
\frac{1}{(C/N)_{\text{overall}}} = \frac{1}{(C/N)_{\text{uplink}}} + \frac{1}{(C/N)_{\text{downlink}}} + \frac{1}{(C/N)_{\text{intermodulation}}}
\]

We are provided with the following values in dB:
- \( (C/N)_{\text{uplink}} = 23 \, \text{dB} \)
- \( (C/N)_{\text{downlink}} = 20 \, \text{dB} \)
- \( (C/N)_{\text{intermodulation}} = 24 \, \text{dB} \)

### Step 1: Convert dB values to linear scale
The \( C/N \) ratio in linear form is given by:

\[
C/N_{\text{linear}} = 10^{C/N_{\text{dB}}/10}
\]

Applying this to each value:
- \( (C/N)_{\text{uplink}} = 10^{23/10} = 199.53 \)
- \( (C/N)_{\text{downlink}} = 10^{20/10} = 100.00 \)
- \( (C/N)_{\text{intermodulation}} = 10^{24/10} = 251.19 \)

### Step 2: Use the reciprocal formula
Now, calculate the reciprocal sum of these values:

\[
\frac{1}{(C/N)_{\text{overall}}} = \frac{1}{199.53} + \frac{1}{100.00} + \frac{1}{251.19}
\]

\[
\frac{1}{(C/N)_{\text{overall}}} = 0.00501 + 0.01 + 0.00398 = 0.01899
\]

### Step 3: Invert to find the overall \( C/N \) in linear scale
\[
(C/N)_{\text{overall}} = \frac{1}{0.01899} = 52.64
\]

### Step 4: Convert back to decibels
\[
(C/N)_{\text{overall}} = 10 \cdot \log_{10}(52.64) \approx 17.21 \, \text{dB}
\]

### Final Answer:
The overall carrier-to-noise ratio is approximately **17.21 dB**.

Would you like more details or have any questions?

Here are five related questions:
1. How does intermodulation noise affect satellite communication systems?
2. Why are carrier-to-noise ratios often expressed in decibels?
3. How would the overall C/N ratio change if the uplink ratio decreased?
4. What are other common sources of noise in satellite communication systems?
5. How is \(C/N\) different from \(E_b/N_0\) in communication systems?

**Tip**: Always convert dB values to linear form when working with ratios like \( C/N \) before applying mathematical operations.

For a satellite circuit the carrier-to-noise ratios are uplink 23 dB, downlink 20 dB, intermodulation 24 dB. Calculate the overall carrier-to-noise ratio in decibels.

Learn how to calculate the overall carrier-to-noise ratio for a satellite circuit using given uplink, downlink, and intermodulation C/N values. This problem involves converting C/N ratios from dB to linear form and applying logarithmic functions to determine the overall ratio in decibels.

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