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?

To calculate the Effective Isotropic Radiated Power (EIRP), first determine the net system gain or loss. Add the total system losses: 2 dB (feed line) + 2.8 dB (duplexer) + 1.2 dB (circulator) = 6 dB of total loss. Subtract this from the antenna gain: 7 dBi (antenna gain) - 6 dB (loss) = a net system gain of +1 dB. Convert this net +1 dB gain into a power multiplier using the formula 10^(dB/10). This gives 10^(1/10) or 10^0.1, which equals approximately 1.2589. Multiply the initial 200 watts by 1.2589 to find the EIRP: 200 watts * 1.2589 = 251.78 watts, which rounds to 252 watts. EIRP is calculated relative to an isotropic radiator (dBi), correctly matching the unit provided in the question.