GATE EC 2017 Set 1 — Question 25
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Communications → Antennas → Channel Capacity Theorem
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Question
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
Correct answer
(C) remains unchanged
Solution
The received power in a free-space link is given by the Friis transmission equation:where is the transmitted power, and are the effective areas of the transmitter and receiver antennas, is the wavelength, and is the distance between them.If , , and are all doubled:
The new received power is:Since the received power remains unchanged and all other factors (bandwidth, noise power) are unchanged, the Signal-to-Noise Ratio (SNR) remains the same. Consequently, the maximum capacity remains unchanged.
The new received power is:Since the received power remains unchanged and all other factors (bandwidth, noise power) are unchanged, the Signal-to-Noise Ratio (SNR) remains the same. Consequently, the maximum capacity remains unchanged.
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