What is the effective radiated power of a repeater with 75 watts transmitter power output, 4 dB feedline loss, 3 dB duplexer and circulator loss, and 10 dB antenna gain?

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Multiple Choice

What is the effective radiated power of a repeater with 75 watts transmitter power output, 4 dB feedline loss, 3 dB duplexer and circulator loss, and 10 dB antenna gain?

Effective radiated power reflects the power that actually leaves toward the direction of maximum radiation after all losses, scaled by the antenna’s gain. First combine the in-line losses: 4 dB feedline loss plus 3 dB for the duplexer and circulator, totaling 7 dB of loss. Convert this to a linear factor: 10^(-7/10) ≈ 0.1995. So the power delivered to the antenna is 75 W × 0.1995 ≈ 14.96 W. The antenna provides 10 dB of gain, which is a linear factor of 10^(10/10) = 10. Multiply the delivered power by the gain: 14.96 W × 10 ≈ 149.6 W. Therefore, the effective radiated power is about 150 watts. (If you needed EIRP, you’d multiply ERP by 1.64, but this question asks for ERP.)

Effective radiated power reflects the power that actually leaves toward the direction of maximum radiation after all losses, scaled by the antenna’s gain.

First combine the in-line losses: 4 dB feedline loss plus 3 dB for the duplexer and circulator, totaling 7 dB of loss. Convert this to a linear factor: 10^(-7/10) ≈ 0.1995. So the power delivered to the antenna is 75 W × 0.1995 ≈ 14.96 W.

The antenna provides 10 dB of gain, which is a linear factor of 10^(10/10) = 10. Multiply the delivered power by the gain: 14.96 W × 10 ≈ 149.6 W.

Therefore, the effective radiated power is about 150 watts. (If you needed EIRP, you’d multiply ERP by 1.64, but this question asks for ERP.)

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