Question 3-67J4

Effective Radiated Power (ERP) is the total power an antenna would need to radiate to achieve the same signal strength in a specific direction as a theoretical half-wave dipole antenna. It's calculated by taking the transmitter output power, subtracting system losses, and adding antenna gain. When working with decibels (dB), gains are added, and losses are subtracted. 1. **Transmitter Power:** 100 watts converts to 20 dBW (decibels relative to 1 Watt), as 10 * log10(100/1) = 20 dB. 2. **Total System Losses and Gains:** Summing the given values: * Antenna gain: +7 dB * Feedline loss: -4 dB * Duplexer/circulator loss: -3 dB * Total change: +7 dB - 4 dB - 3 dB = 0 dB. 3. **Calculate ERP in dBW:** Start with the transmitter power in dBW and add the total change: 20 dBW + 0 dB = 20 dBW. 4. **Convert ERP back to Watts:** 20 dBW converts back to 100 watts (10^(20/10) = 10^2 = 100). Since the total system gain and loss perfectly cancel out (0 dB change), the ERP remains the same as the transmitter output power. The other options are incorrect because they result from miscalculations of the dB values or incorrect conversion to watts.