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GATE 2017 EC – Question 35

Electromagnetics · Antennas and Antenna Arrays · 1 mark · Multiple choice

Consider a wireless communication link between a transmitter and a receiver located in free space, with finite and strictly positive capacity. If the effective areas of the transmitter and the receiver antennas, and the distance between them are all doubled, and everything else remains unchanged, the maximum capacity of the wireless link

  1. increases by a factor of 2
  2. decreases by a factor of 2
  3. remains unchanged
  4. decreases by a factor of $\sqrt{2}$

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Correct answer: (C) remains unchanged

Explanation

By the Friis formula the received power is proportional to $\frac{A_t A_r}{d^2}$. Doubling both areas multiplies it by 4, and doubling the distance divides it by 4, so the received power is unchanged. The capacity depends on the received power, so it also stays the same.