What is the effective radiated power (ERP) of a repeater station with 150 watts transmitter power output, 2 dB feed line loss, 2.2 dB duplexer loss, and 7 dBd antenna gain?
Why ERP is transmitter power multiplied by the net system gain, where gain is in dBd (referenced to a dipole). Add the gains and subtract the losses in decibels first: 7 dBd - 2 dB - 2.2 dB = 2.8 dB net gain. Then convert: 150 W x 10^(2.8/10) = 150 x 1.905, which is about 286 watts.
Watch out The 469 watt answer comes from using only the 7 dBi/dBd gain (or ignoring one of the losses); you must subtract both the feed line and duplexer losses before converting.
Do all the dB math first, then one power conversion: P x 10^(dB/10). Net +3 dB roughly doubles the power.
Net gain 7 - 2 - 2.2 = 2.8 dB, a hair under 3 dB, so a hair under double 150 W: 286, not 300-something.