What term describing total radiated power takes into account all gains and losses?
Why Effective radiated power is the transmitter output power adjusted by every gain and loss in the system: feedline loss, connector and duplexer or filter losses, and the antenna's gain referenced to a dipole. You convert everything to decibels, add the gains and subtract the losses, then apply that net dB figure to the transmitter power. ERP is what a half-wave dipole would need to be fed to produce the same signal in the antenna's favored direction; EIRP is the same idea referenced to an isotropic radiator, which is 2.15 dB higher.
Watch out Power factor and apparent power are AC power terms describing the phase relationship between voltage and current in a reactive circuit, and half-power bandwidth describes the width of a resonant response between its -3 dB points. None of them relate to radiated signal strength.
ERP = TX power + antenna gain - feedline and component losses, all in dB. EIRP is ERP plus 2.15 dB.