FCC Exam Question: 3-67J1

What is the effective radiated power of a repeater with 50 watts transmitter power output, 4 dB feedline loss, 3 dB duplexer and circulator loss, and 6 dB antenna gain?

A. 158 watts.
B. 39.7 watts.
C. 251 watts.
D. 69.9 watts.
Correct Answer: B

Explanation: Effective Radiated Power (ERP) is the power delivered to the antenna multiplied by the antenna's gain in a specific direction, relative to a half-wave dipole, after accounting for all system losses. To calculate ERP, first sum all gains and losses in dB: 1. **Total System Loss:** 4 dB (feedline) + 3 dB (duplexer/circulator) = 7 dB. 2. **Net dB Change:** Antenna gain - Total System Loss = 6 dB - 7 dB = -1 dB. This indicates a net loss of 1 dB for the system. Next, convert this net dB change into a power multiplication factor: Power Ratio = 10 ^ (dB / 10) = 10 ^ (-1 / 10) = 10 ^ (-0.1) ≈ 0.794. Finally, multiply the transmitter power output by this factor: ERP = 50 watts * 0.794 ≈ 39.7 watts. Therefore, the effective radiated power is approximately 39.7 watts. Options A, C, and D are incorrect as they do not properly account for the combined effects of gains and losses on the transmitted power.

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Includes Elements 1, 3, 6, 7R, 8, and 9.