*Question E9A07:
What is the effective isotropic radiated power (EIRP) of a repeater station with 200 watts transmitter power output, 2 dB feed line loss, 2.8 dB duplexer loss, 1.2 dB circulator loss, and 7 dBi antenna gain?*  

*Correct Answer is  B: 252 watts*  

### AI Response: (may contain errors)  

To calculate the Effective Isotropic Radiated Power (EIRP) for the repeater station, we can use the following formula:

$$
EIRP = P_T - L + G_A
$$

where:
- $P_T$ = transmitter power output in dBm
- $L$ = total losses in dB (including feed line, duplexer, and circulator losses)
- $G_A$ = antenna gain in dBi

### Step-by-step Calculation:

1. **Convert Transmitter Power to dBm**:
   The transmitter power output is given as 200 watts. To convert this to dBm, we use the formula:

   $$
   P_T \text{(dBm)} = 10 \times \log_{10}(P_T \text{(watts)} \times 1000)
   $$

   Substituting $P_T = 200$ watts:

   $$
   P_T \text{(dBm)} = 10 \times \log_{10}(200 \times 1000) = 10 \times \log_{10}(200000) \approx 10 \times 5.301 = 53.01 \text{ dBm}
   $$

2. **Calculate Total Losses**:
   The total losses ($L$) are the sum of the feed line loss, duplexer loss, and circulator loss:

   $$
   L = 2 \text{ dB} + 2.8 \text{ dB} + 1.2 \text{ dB} = 6 \text{ dB}
   $$

3. **Antenna Gain**:
   The antenna gain ($G_A$) is given as 7 dBi.

4. **Calculate EIRP**:
   Now we can substitute these values into the EIRP formula:

   $$
   EIRP = 53.01 \text{ dBm} - 6 \text{ dB} + 7 \text{ dBi}
   $$

   Simplifying this:

   $$
   EIRP = 53.01 - 6 + 7 = 54.01 \text{ dBm}
   $$

5. **Convert EIRP from dBm to Watts**:
   To convert back to watts, we use the formula:

   $$
   EIRP \text{(watts)} = 10^{(EIRP \text{(dBm)} - 30)/10}
   $$

   Substituting $EIRP = 54.01$ dBm:

   $$
   EIRP \text{(watts)} = 10^{(54.01 - 30)/10} = 10^{2.401} \approx 252 \text{ watts}
   $$

### Conclusion:
- The correct answer is **252 watts** because this is the calculated EIRP after accounting for all losses and gains.

### Why Other Choices Are Incorrect:
- **A: 159 watts**: This value is too low and likely results from miscalculating losses or not converting correctly.
- **C: 632 watts**: This value is too high, possibly from incorrectly adding gains or not accounting for losses properly.
- **D: 63.2 watts**: This value is also too low and suggests a significant error in the calculations.

### Summary of Useful Formulas:
- EIRP calculation: 
  $$
  EIRP = P_T - L + G_A
  $$
- Power conversion to dBm:
  $$
  P_T \text{(dBm)} = 10 \times \log_{10}(P_T \text{(watts)} \times 1000)
  $$
- Conversion from dBm to watts:
  $$
  P \text{(watts)} = 10^{(P \text{(dBm)} - 30)/10}
  $$

This breakdown should help you understand how to approach similar questions on the Extra Class exam.