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# Received power of half-wave dipole antennas

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Assume that two antennas are half-wave dipoles and each has a directive gain of 3dB. If the transmitted power is 1W and the two antennas are separated by a distance of 10 km, what is the received power? Assume that the antennas are aligned so that the directive gain numbers are correct and that the frequency used is 100 MHz.

a) 4 * 10^-17 W
b) 20 W
c) 2.27 * 10^-9 W
d) 16 W

#### Solution Preview

The received power of the system in dBW is given by the equation:

P_R (dBW) = P_T (dBW) + G_T (dB) + G_R (dB) - PL (dB)

or alternately in Watts:

P_R = P_T*G_T*G_R/PL

(always remember not to combine dB and linear units. This is a common mistake.)

where PL is the path loss. Since there is nothing specified, I'm assuming the path loss is free space path loss, which is given by:

PL = ...

#### Solution Summary

This solution helps with a question regarding calculations for received power if transmitted power is 1W and the assumption that antennas are aligned so that the directive gain numbers are correct and that the frequency used is 100 MHz.

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