E9A02

ANTENNAS AND TRANSMISSION LINES · Basic antenna parameters: radiation resistance, gain, beamwidth, efficiency; effective radiated power (ERP) and effective isotropic radiated power (EIRP)

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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?

A469 watts
B78.7 watts
C420 watts
D286 watts

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.

HamSandwich explanation, first draft. The question and answers are the NCVEC text.

E9A02

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