*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 the repeater station, we need to account for the transmitter power, feed line loss, duplexer loss, and antenna gain. The formula for ERP is:

$$
ERP = P_T \times G_A - L
$$

where:
- $P_T$ = transmitter power in watts
- $G_A$ = antenna gain in linear scale
- $L$ = total losses in watts

### Step-by-step Calculation:

1. **Convert Antenna Gain from dBd to Linear Scale**:
   The antenna gain in dBd (decibels relative to a dipole) can be converted to a linear scale using the formula:

   $$
   G_A = 10^{(G_{dBd}/10)}
   $$

   For $G_{dBd} = 7$ dBd:

   $$
   G_A = 10^{(7/10)} \approx 5.012
   $$

2. **Calculate Total Losses**:
   The total losses include feed line loss and duplexer loss, both in dB. We can convert these losses to a linear scale as well:

   - Feed line loss = 2 dB
   - Duplexer loss = 2.2 dB

   Total loss in dB:

   $$
   L_{dB} = 2 + 2.2 = 4.2 \text{ dB}
   $$

   Convert to linear scale:

   $$
   L = 10^{(L_{dB}/10)} = 10^{(4.2/10)} \approx 2.630
   $$

3. **Calculate ERP**:
   Now we can plug in the values into the ERP formula:

   - $P_T = 150$ watts
   - $G_A \approx 5.012$
   - $L \approx 2.630$

   Thus,

   $$
   ERP = 150 \times 5.012 - 2.630 \approx 150 \times 5.012 \approx 751.8 \text{ watts}
   $$

   However, we need to account for the losses:

   $$
   ERP = \frac{150 \times 5.012}{2.630} \approx 286 \text{ watts}
   $$

### Why the Correct Answer is Correct:
The correct answer is 286 watts because it accurately reflects the effective radiated power after accounting for the transmitter power, antenna gain, and total losses.

### Why the Other Choices are Incorrect:
- **A: 469 watts**: This value does not account for the losses correctly.
- **B: 78.7 watts**: This is too low and likely results from miscalculating the losses or gain.
- **C: 420 watts**: This value is also incorrect as it does not properly factor in the losses.

### Summary of Useful Formulas:
- **ERP Calculation**: 
  $$
  ERP = P_T \times G_A - L
  $$
- **Antenna Gain Conversion**: 
  $$
  G_A = 10^{(G_{dBd}/10)}
  $$
- **Loss Conversion**: 
  $$
  L = 10^{(L_{dB}/10)}
  $$

Understanding these calculations and conversions is crucial for accurately determining ERP in various scenarios.