Subelement J: Antennas— Topic 67: Effective Radiated Power
Question 3-67J1
Element 3 (GROL)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?
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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