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?  

Choices:  
A: 159 watts  
B: 252 watts  
C: 632 watts  
D: 63.2 watts    

Correct Answer is  B: 252 watts  

To find EIRP, sum all gains and losses in dB, then apply that net dB to the transmitter power.

Key formulas:
- $$EIRP = P_T \times 10^{\frac{G_{\text{dBi}} - L_{\text{dB}}}{10}}$$
- Or in dBm: $$EIRP_{\text{dBm}} = P_{T,\text{dBm}} + G_{\text{dBi}} - L_{\text{dB}}$$

Given:
- Transmitter power: $P_T = 200\ \text{W}$
- Losses: $2 + 2.8 + 1.2 = 6.0\ \text{dB}$
- Antenna gain: $7\ \text{dBi}$
- Net: $7 - 6 = +1\ \text{dB}$

Compute EIRP:
$$EIRP = 200 \times 10^{\frac{1}{10}} \approx 200 \times 1.2589 \approx 252\ \text{W}$$

Why B (252 W) is correct:
- The net system gain is +1 dB, and $+1\ \text{dB} \approx \times 1.26$, so $200 \times 1.26 \approx 252\ \text{W}$.

Why the others are incorrect:
- A (159 W): Corresponds to a net of about −1 dB, i.e., $200 \times 10^{-0.1} \approx 159\ \text{W}$; this would require more loss than gain, which is not the case here.
- C (632 W): Corresponds to about +5 dB, i.e., $200 \times 3.16 \approx 632\ \text{W}$; this happens if you only subtract 2 dB of loss (ignoring the duplexer and circulator) to get $7 - 2 = +5\ \text{dB}$.
- D (63.2 W): Corresponds to about −5 dB, i.e., $200 / 3.16 \approx 63.2\ \text{W}$; this would imply losses exceed gain by 5 dB, which is not true here.

Rules of thumb:
- Add/subtract gains and losses in dB before converting to linear.
- Common dB-to-linear factors: 1 dB ≈ ×1.26, 3 dB ≈ ×2, 5 dB ≈ ×3.16, 10 dB ≈ ×10.
- Quick dBm method: $200\ \text{W} = 53\ \text{dBm}$; then $53 - 6 + 7 = 54\ \text{dBm} \Rightarrow 10^{(54-30)/10} \approx 251.2\ \text{W}$.