*Question E4D13:
What is the received signal level with a transmit power of 10 W (+40 dBm), a transmit antenna gain of 6 dBi, a receive antenna gain of 3 dBi, and a path loss of 100 dB?*  

*Correct Answer is  A: -51 dBm*  

### AI Response: (may contain errors)  

To find the received signal level, we can use the following formula:

$$
P_R = P_T + G_T + G_R - L
$$

where:
- $P_R$ = received power in dBm
- $P_T$ = transmit power in dBm
- $G_T$ = transmit antenna gain in dBi
- $G_R$ = receive antenna gain in dBi
- $L$ = path loss in dB

Given values:
- $P_T = 10 \text{ W} = +40 \text{ dBm}$
- $G_T = 6 \text{ dBi}$
- $G_R = 3 \text{ dBi}$
- $L = 100 \text{ dB}$

Now, substituting the values into the formula:

$$
P_R = 40 \text{ dBm} + 6 \text{ dBi} + 3 \text{ dBi} - 100 \text{ dB}
$$

Calculating step-by-step:

1. Add the transmit power and antenna gains:
   $$ 
   40 + 6 + 3 = 49 \text{ dBm} 
   $$

2. Subtract the path loss:
   $$ 
   49 - 100 = -51 \text{ dBm} 
   $$

Thus, the received signal level is $-51 \text{ dBm}$, which is the correct answer.

### Explanation of Choices:
- **Choice A: -51 dBm** (Correct)
  - This is the calculated received signal level based on the provided parameters.

- **Choice B: -54 dBm**
  - This value could result from an incorrect calculation, possibly by miscalculating the sum of gains or not properly accounting for the path loss.

- **Choice C: -57 dBm**
  - Similar to choice B, this value suggests a larger path loss or a smaller gain than what was provided, leading to an underestimation of the received power.

- **Choice D: -60 dBm**
  - This value is even further from the correct calculation, indicating a significant error in the application of the formula or misunderstanding of the gains and losses involved.

### Summary:
- The formula for received power combines transmit power, antenna gains, and subtracts path loss.
- The correct answer is derived directly from the values given, ensuring that all components are accurately accounted for.