*Question E9A02:
What is the effective radiated power (ERP) of a repeater station with 150 watts transmitter power output, 2 dB feed line loss, 2.2 dB duplexer loss, and 7 dBd antenna gain?*  

*Correct Answer is  D: 286 watts*  

### AI Response: (may contain errors)  

To calculate the effective radiated power (ERP) of a repeater station, we need to consider the transmitter power, feed line loss, duplexer loss, and antenna gain. The formula for ERP is:

$$
ERP = P_T \times 10^{\left(\frac{G_A - L_F - L_D}{10}\right)}
$$

where:
- $P_T$ = transmitter power in watts (150 watts)
- $G_A$ = antenna gain in dBd (7 dBd)
- $L_F$ = feed line loss in dB (2 dB)
- $L_D$ = duplexer loss in dB (2.2 dB)

**Step-by-step Calculation:**

1. **Calculate the total system gain/loss:**

   The total gain/loss is the antenna gain minus the feed line loss and duplexer loss:

   $$ G_{\text{total}} = G_A - L_F - L_D = 7 - 2 - 2.2 = 2.8 \, \text{dB} $$

2. **Convert the total gain/loss from dB to a linear scale:**

   To convert dB to a linear scale, use the formula:

   $$ \text{Linear Gain} = 10^{\left(\frac{G_{\text{total}}}{10}\right)} = 10^{\left(\frac{2.8}{10}\right)} \approx 1.905 $$

3. **Calculate the ERP:**

   Multiply the transmitter power by the linear gain:

   $$ ERP = 150 \times 1.905 \approx 285.75 \, \text{watts} $$

   Rounding to the nearest whole number gives approximately 286 watts.

**Why the Correct Answer is Correct:**

- **D: 286 watts** is correct because it matches the calculated ERP using the given parameters.

**Why the Other Choices are Incorrect:**

- **A: 469 watts** is incorrect because it overestimates the ERP, likely due to not accounting for all losses correctly.
- **B: 78.7 watts** is incorrect because it underestimates the ERP, possibly due to miscalculating the gain or losses.
- **C: 420 watts** is incorrect because it also overestimates the ERP, similar to choice A.

By following the steps and using the formula, you can accurately determine the ERP for the given setup.