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?  

Choices:  
A: 317 watts  
B: 2,000 watts  
C: 126 watts  
D: 300 watts    

Correct Answer is  A: 317 watts  

To find ERP, add gains and losses in dB, then convert the net dB to a linear power ratio and multiply by the transmitter power.

Step-by-step:
- Total losses: $L = 4 + 3.2 + 0.8 = 8.0\ \text{dB}$
- Antenna gain (ERP uses dBd): $G = 10\ \text{dBd}$
- Net gain: $G_{\text{net}} = G - L = 10 - 8 = +2\ \text{dB}$
- Convert to linear: $10^{(+2/10)} \approx 1.585$
- ERP: $200 \times 1.585 \approx 317\ \text{W}$

Therefore, 317 W is correct (Choice A).

Why the other choices are incorrect:
- B: 2,000 W — This is what you get if you ignore the 8 dB losses and apply only the 10 dB antenna gain: $200 \times 10 = 2000$.
- C: 126 W — This results from flipping the sign on the net dB (using −2 dB instead of +2 dB): $200 \times 10^{-2/10} \approx 126$.
- D: 300 W — A rough rounding error treating +2 dB as a 1.5× multiplier instead of the correct 1.585×.

Useful formulas and tips:
- $$\text{ERP (W)} = P_T \times 10^{\frac{G_{\text{dBd}} - \sum L_{\text{dB}}}{10}}$$
- dB arithmetic: add/subtract gains and losses in dB; convert to linear with $10^{(\text{dB}/10)}$.
- ERP uses dBd; EIRP uses dBi. Convert with $G_{\text{dBd}} = G_{\text{dBi}} - 2.15$.
- Handy ratios: 3 dB ≈ ×2, 2 dB ≈ ×1.58, 1 dB ≈ ×1.26, 10 dB ≈ ×10.