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A radar operating at 3 GHz radiating power of 200 kW. Calculate the. power of the reflected signal at the radar with a $20 m^2$ target at 300 nautical miles. Take $A_e = 9 m^2$
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Given,

$f=3 GHz=3 x 10^9 Hz \\ P_t=200 kW=200 x 10^3 W \\ σ=20 m^2 \\ R=300 nm=300 x 1852 m=5.556 x 105 m \\ λ=\frac{c}{f}=\frac{3 x 10^8}{3 x 10^8 }=0.1 m \\ G=4π \frac{A_e}{λ^2} =G=4π x \frac{9}{(0.1)^2} =11.3 x 10^3$

The received power by antenna is given by

$P_r=\bigg[\frac{P_t G A_e σ}{(4π)^2 R^4}\bigg]$

$P_r=\frac{200 x 10^3 x 11.3 x 10^3 x 9 x 20}{(4π)^2 (5.556 x 10^5 )^4 }$

$P_r=27.034 x 10^{-15} W$

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