If the distance between transmitter and receiver doubles, by what factor does the received power change?

If the distance between transmitter and receiver doubles, by what factor does the received power change?

• A. 2
• B. 8
• C. 4
• D. 16

Answer: (C)

In free-space propagation, received power falls with the square of the distance — the inverse-square law. If the distance doubles, the received power becomes Pr_new = Pr_old / (2^2) = Pr_old / 4. So the power is reduced by a factor of 4 (it becomes one quarter of what it was). This holds assuming the transmitter and receiver antennas stay the same and there are no additional losses or fading.

In free-space propagation, received power falls with the square of the distance — the inverse-square law. If the distance doubles, the received power becomes Pr_new = Pr_old / (2^2) = Pr_old / 4. So the power is reduced by a factor of 4 (it becomes one quarter of what it was). This holds assuming the transmitter and receiver antennas stay the same and there are no additional losses or fading.