Calculation of noise figure for cascaded amplifier

For a three stage cascade amplifier, calculate the overall noise figure when each stage has a gain of 12 DB and noise figure of 8dB.

Options:

a) 12
b) 24
c) 13.55
d) 8

Correct Answer: c) 13.55

Explanation :

As the signal passes through various stages of an amplifier, the output has the original signal and some noise that gets amplified at different stages of amplifiers. So the final noise figure of the cascaded amplifier is obtained by

F_N = F₁ + (F₂- 1)/ G₁+ (F₃- 1)/ G₁G₂+…..+(F_N- 1)/ G₁G₂G₃… G_N
F₁, F₂, F₃….. F_N, G₁,G₂, G₃.... G_N are the noise figures and the gains respectively of the amplifiers at different stages.
F₁= 12, F₂= 12, F₃= 12
G₁= 8, G₂= 8, G₃= 8
F_N = 12 + (12- 1)/ 8+ (12- 1)/ 8*8
= 12+ 11/8+11/64
= 13.55