*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, we need to calculate the received signal power at the receiver and compare it to the minimum discernable signal (MDS) plus the required signal-to-noise ratio (SNR).

### Step-by-step Calculation:

1. **Transmit Power (in dBm):**  
   The transmit power is given as 10 W. To convert this to dBm:  
   $$ P_{\text{dBm}} = 10 \times \log_{10}(P_{\text{W}}) + 30 $$  
   $$ P_{\text{dBm}} = 10 \times \log_{10}(10) + 30 = 40 \, \text{dBm} $$

2. **Effective Isotropic Radiated Power (EIRP):**  
   EIRP is calculated by adding the antenna gain and subtracting the cable loss from the transmit power:  
   $$ \text{EIRP} = P_{\text{dBm}} + G_{\text{antenna}} - L_{\text{cable}} $$  
   $$ \text{EIRP} = 40 \, \text{dBm} + 10 \, \text{dBi} - 3 \, \text{dB} = 47 \, \text{dBm} $$

3. **Received Signal Power (in dBm):**  
   The received signal power is the EIRP minus the path loss:  
   $$ P_{\text{received}} = \text{EIRP} - \text{Path Loss} $$  
   $$ P_{\text{received}} = 47 \, \text{dBm} - 136 \, \text{dB} = -89 \, \text{dBm} $$

4. **Required Signal Level:**  
   The required signal level at the receiver is the MDS plus the required SNR:  
   $$ P_{\text{required}} = \text{MDS} + \text{SNR} $$  
   $$ P_{\text{required}} = -103 \, \text{dBm} + 6 \, \text{dB} = -97 \, \text{dBm} $$

5. **Link Margin:**  
   The link margin is the difference between the received signal power and the required signal level:  
   $$ \text{Link Margin} = P_{\text{received}} - P_{\text{required}} $$  
   $$ \text{Link Margin} = -89 \, \text{dBm} - (-97 \, \text{dBm}) = 8 \, \text{dB} $$

### Conclusion:

- **Correct Answer: C: +8dB**  
  The link margin is +8 dB, indicating that the received signal is 8 dB stronger than the minimum required level.

- **Why Other Choices are Incorrect:**
  - **A: -8dB** and **B: -14dB**: These values suggest a negative link margin, which would mean the received signal is weaker than required. This is not the case here.
  - **D: +14dB**: This value overestimates the link margin, as the correct calculation shows a margin of +8 dB.

Understanding these calculations helps ensure that a communication link has sufficient margin to maintain reliable operation under varying conditions.