Subelement J: Antennas— Topic 67: Effective Radiated Power
Question 3-67J6
Element 3 (GROL)What is the effective radiated power of a repeater with 50 watts transmitter power output, 5 dB feedline loss, 4 dB duplexer and circulator loss, and 7 dB antenna gain?
Explanation
Effective Radiated Power (ERP) is the net power radiated by an antenna in a specific direction, relative to a half-wave dipole. To calculate ERP, you start with the transmitter power output and then account for all gains and losses in the system.
Gains and losses expressed in decibels (dB) are added algebraically:
* Feedline loss: -5 dB
* Duplexer and circulator loss: -4 dB
* Antenna gain: +7 dB
Total effective gain = -5 dB - 4 dB + 7 dB = -2 dB.
To convert this total dB gain back to a power ratio, use the formula $10^{(\text{dB}/10)}$.
For -2 dB, the power ratio is $10^{(-2/10)} = 10^{-0.2} \approx 0.63$.
Finally, multiply the transmitter power output by this ratio to find the ERP:
ERP = 50 watts * 0.63 = 31.5 watts.
Therefore, the effective radiated power of the repeater is 31.5 watts. Options A, B, and D are incorrect due to errors in combining the dB values or converting them to a power ratio.
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