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GATE 2016 EC (EC3) – Question 64

Electromagnetics · Antennas and Antenna Arrays · 2 marks · Numerical answer

A 5 GHz radar uses one antenna for transmitting and receiving. The antenna gain is 150 and points at a target 1 km away with radar cross-section $3\ \mathrm{m^2}$. With transmitted power 100 kW, the received power in μW is ________.

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Correct answer: 0.01 to 0.02

Explanation

For a monostatic radar,
$$P_r=\frac{P_tG^2\lambda^2\sigma}{(4\pi)^3R^4}.$$
The wavelength is c/f=0.06 m. Insert Pt=$10^5$ W, G=150, σ=3 m² and R=1000 m. The result is approximately $1.2246\times10^{-8}$ W.

Convert watts to microwatts by multiplying by $10^6$: **0.01225 μW**, within 0.01–0.02 μW.

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