*Question E4D12:
What is the link margin in a system with a transmit power level of 10 W (+40 dBm), a system antenna gain of 10 dBi, a cable loss of 3 dB, a path loss of 136 dB, a receiver minimum discernable signal of -103 dBm, and a required signal-to-noise ratio of 6 dB?*  

*Correct Answer is  C: +8dB*  

### AI Response: (may contain errors)  

To determine the link margin in the given system, we can use the following formula:

$$
\text{Link Margin} = P_T + G_A - L_c - L_p - (S + R)
$$

Where:
- $P_T$ = Transmit power in dBm
- $G_A$ = Antenna gain in dBi
- $L_c$ = Cable loss in dB
- $L_p$ = Path loss in dB
- $S$ = Receiver minimum discernible signal in dBm
- $R$ = Required signal-to-noise ratio in dB

### Given Values:
- $P_T = 40 \text{ dBm}$ (10 W)
- $G_A = 10 \text{ dBi}$
- $L_c = 3 \text{ dB}$
- $L_p = 136 \text{ dB}$
- $S = -103 \text{ dBm}$
- $R = 6 \text{ dB}$

### Step-by-Step Calculation:
1. **Calculate the total losses and required signal:**
   - Total losses = $L_c + L_p + S + R$
   - Total losses = $3 + 136 - 103 + 6 = 42 \text{ dB}$

2. **Calculate the link margin:**
   - Link Margin = $P_T + G_A - \text{Total losses}$
   - Link Margin = $40 + 10 - 42 = 8 \text{ dB}$

### Conclusion:
- The link margin is **+8 dB**, which indicates that the system has a sufficient margin above the minimum required signal level.

### Explanation of Choices:
- **Choice A: -8 dB**  
  This would imply that the system is below the required signal level, which is incorrect based on our calculations.

- **Choice B: -14 dB**  
  This also suggests a negative margin, indicating insufficient signal strength, which does not match our result.

- **Choice C: +8 dB**  
  This is the correct answer, as calculated.

- **Choice D: +14 dB**  
  This suggests an even higher margin than calculated, which is not supported by the given parameters.

### Summary:
The link margin of +8 dB indicates that the system can operate effectively above the minimum requirements, ensuring reliable communication. Understanding how to calculate link margin is crucial for evaluating the performance of radio systems.