Answer to Question #3718 in Electric Circuits for zubair khan

Question

A three-stage amplifier has a second stage power gain of 5 dB and noise figure of 4.5 dB.
The third stage has a power gain of 3 dB and a noise figure of 5.5 dB. The overall power
gain is 12 dB and the signal to noise ratio at the input of the first stage is 10 dB.
Calculate the power gain and noise figure of the first stage required to give a signal to
noise ratio at the output of the third stage of 4 dB

Answer 1

Total Gain (dB) = Gain₁ + Gain₂ + Gain₃
therefore
Gain₁=12-5-3=4


Total NF (dB) = 4-10 = -6 and
Total NF (dB) = 10*log₁₀(nf₁ + (nf₂-1)/gain₁ + (nf₃-1)/(gain₁*gain₂)=10*log₁₀(nf₁+(4.5-1)/4+(5.5-)/(4*5))
= 10*log₁₀(nf₁+1.1)= -6


Hence nf₁ = -0.8488