TRB 2006 - Question 1

An amplifier A has $6$ dB gain and $50$ ohm input and output impedance. The noise figure of this amplifier is $3$ dB

A cascade of two such amplifiers will have noise figure of 

a) $6$ dB 

b) $8$ dB

c) $12$ dB

d) none of these

Correct Answer: Option D

Solution:

Gain of A = $6\;dB$ 

$10\;log_{10}(G)=6\;dB$ 

$G=10^{6/10}=10^{0.6}$ 

$G=3.98$ 

Noise figure = $3\;dB$ 

$10\;log_{10}(G)=3\;dB$ 

$F=10^{3/10}=10^{0.3}$ 

$F=1.995$ 

Equivalent noise figure of cascaded amplifiers, $$F_{cas}=F_1+\frac{F_2-1}{G_1}+\frac{F_3-1}{G_1\;G_2}+...$$ $$F_{cas}=1.995+\frac{1.995-1}{3.98}$$ $$F_{cas}=1.995+\frac{0.995}{3.98}$$ $$F_{cas}=1.995+0.25$$ $$F_{cas}=2.245$$ $$F_{cas}(dB)=10\;log_{10}(2.245)$$ $$F_{cas}(dB)=3.512\;dB$$