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?

To find the Effective Radiated Power (ERP), you must first calculate the net system gain or loss in decibels (dB). Sum the losses: 4 dB (feed line) + 3.2 dB (duplexer) + 0.8 dB (circulator) = 8 dB of total loss. Subtract this loss from the antenna gain: 10 dBd (antenna gain) - 8 dB (loss) = a net gain of +2 dB. Next, convert the net gain in dB to a power multiplier using the formula 10^(dB/10). For a 2 dB gain, the multiplier is 10^(2/10) or 10^0.2, which is approximately 1.585. Finally, multiply the transmitter power output by this factor: 200 watts * 1.585 = 317 watts. Note that ERP is calculated relative to a half-wave dipole (dBd), which matches the given antenna gain unit.