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An antenna pointing in a certain direction has a noise temperature of 50 K. The ambient temperature is 290 K. The antenna is connected to a pre-amplifier that has a noise figure of 2 dB and an available gain of 40 dB over an effective bandwidth of 12 MHz. The effective input noise temperature $T_e$ for the amplifier and the noise power $P_a$ at the output of the preamplifier, respectively, are

1. Te = 169.36 K and Pa = 3.73×10−11 W
2. Te = 170.8 K and Pa = 4.56×10−11 W
3. Te = 182.5 K and Pa = 3.85×10−11 W
4. Te = 168.62 K and Pa = 4.6×10−11 W

Correct answer: Te = 182.5 K and Pa = 3.85×10−11 W

Solution

Noise figure in linear scale is $F=10^{2/10}$. The equivalent input noise temperature is $T_e=(F-1)T_0\approx 182.5$ K. The output noise power is found from $k(T_{ant}+T_e)BG$ using the given bandwidth and gain, giving approximately $3.85\times10^{-11}$ W.

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