*Question E9A06:
What is the effective radiated power (ERP) of a repeater station with 200 watts transmitter power output, 4 dB feed line loss, 3.2 dB duplexer loss, 0.8 dB circulator loss, and 10 dBd antenna gain?*  

*Correct Answer is  A: 317 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, losses in the system, and the antenna gain. Here's how you can calculate it:

1. **Convert dB values to linear scale**:  
   - Feed line loss: $4 \, \text{dB} = 10^{(4/10)} = 2.51$ (linear scale)
   - Duplexer loss: $3.2 \, \text{dB} = 10^{(3.2/10)} = 2.09$ (linear scale)
   - Circulator loss: $0.8 \, \text{dB} = 10^{(0.8/10)} = 1.20$ (linear scale)
   - Antenna gain: $10 \, \text{dBd} = 10^{(10/10)} = 10$ (linear scale)

2. **Calculate total system loss**:  
   Multiply the linear values of the losses:  
   $$\text{Total Loss} = 2.51 \times 2.09 \times 1.20 = 6.30$$

3. **Calculate the effective radiated power (ERP)**:  
   Use the formula:  
   $$ERP = \frac{P_T}{\text{Total Loss}} \times G_A$$  
   where:
   - $P_T = 200 \, \text{watts}$ (transmitter power)
   - $\text{Total Loss} = 6.30$
   - $G_A = 10$ (antenna gain)

   Plug in the values:  
   $$ERP = \frac{200}{6.30} \times 10 = 31.75 \times 10 = 317.5 \, \text{watts}$$

   Rounding to the nearest whole number gives us 317 watts.

**Why the correct answer is correct:**
- The correct answer is 317 watts because it accurately reflects the ERP after accounting for all system losses and antenna gain.

**Why the other choices are incorrect:**
- **Choice A (317 watts)** is correct.
- **Choice B (2,000 watts)** is incorrect because it does not account for the significant losses in the system.
- **Choice C (126 watts)** is incorrect because it underestimates the ERP by not properly calculating the effect of the antenna gain.
- **Choice D (300 watts)** is incorrect because it is a close approximation but does not precisely account for the calculated ERP.

By following these steps, you can accurately determine the ERP for any given setup.