What is the effective radiated power of a repeater with 100 watts transmitter power output, 4 dB feedline loss, 3 dB duplexer and circulator loss, and 7 dB antenna gain?

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Multiple Choice

What is the effective radiated power of a repeater with 100 watts transmitter power output, 4 dB feedline loss, 3 dB duplexer and circulator loss, and 7 dB antenna gain?

The key idea is that effective radiated power (ERP) reflects what power actually leaves the antenna in the direction of interest, taking into account both losses before the antenna and the antenna’s gain. First, combine the losses from the feedline and the duplexer/circulator. A total of 7 dB loss means the power reaching the antenna input is P_t times a linear factor of 10^(-7/10) ≈ 0.1995. With a transmitter output of 100 W, that leaves about 19.95 W at the antenna input. Then apply the antenna’s gain. A 7 dB gain corresponds to a linear factor of 10^(7/10) ≈ 5.0119. Multiplying the 19.95 W by this gain factor gives about 100 W radiated in the direction of interest. So the 7 dB of losses is exactly offset by 7 dB of antenna gain, leaving the effective radiated power essentially equal to the original transmitter power: 100 W. If the numbers weren’t balanced this way, ERP would be higher or lower accordingly.

The key idea is that effective radiated power (ERP) reflects what power actually leaves the antenna in the direction of interest, taking into account both losses before the antenna and the antenna’s gain.

First, combine the losses from the feedline and the duplexer/circulator. A total of 7 dB loss means the power reaching the antenna input is P_t times a linear factor of 10^(-7/10) ≈ 0.1995. With a transmitter output of 100 W, that leaves about 19.95 W at the antenna input.

Then apply the antenna’s gain. A 7 dB gain corresponds to a linear factor of 10^(7/10) ≈ 5.0119. Multiplying the 19.95 W by this gain factor gives about 100 W radiated in the direction of interest.

So the 7 dB of losses is exactly offset by 7 dB of antenna gain, leaving the effective radiated power essentially equal to the original transmitter power: 100 W. If the numbers weren’t balanced this way, ERP would be higher or lower accordingly.

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