The GATE Grind

GATE 2016 EC – Question 62

Communications · Analog Communications · 2 marks · Multiple choice

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 $P_{ao}$ at the output of the preamplifier, respectively, are

  1. $T_e = 169.36$ K and $P_{ao} = 3.73 \times 10^{-10}$ W
  2. $T_e = 170.8$ K and $P_{ao} = 4.56 \times 10^{-10}$ W
  3. $T_e = 182.5$ K and $P_{ao} = 3.85 \times 10^{-10}$ W
  4. $T_e = 160.62$ K and $P_{ao} = 4.6 \times 10^{-10}$ W

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) $T_e = 169.36$ K and $P_{ao} = 3.73 \times 10^{-10}$ W

Explanation

A noise figure of 2 dB is $F = 10^{0.2} = 1.585$, so the effective input noise temperature of the amplifier is $T_e = 290(F - 1) = 169.6$ K. The output noise power is $P_{ao} = kG(T_{ant} + T_e)B$ with $G = 10^4$, which gives $1.38 \times 10^{-23} \times 10^4 \times 219.6 \times 12 \times 10^6 \approx 3.6 \times 10^{-10}$ W. Option A is the closest on both values.