Noise factor in cascaded amplifiers

Q11. The Noise Factor for cascaded amplifiers (F_N) is given by (F₁, F₂, F₃….. F_N, G₁,G₂, G₃....G_N are the noise factors and the gains of the amplifiers at different stages ):

Options:

a) F_N = F₁ + F₂/ G₁+ F₃/ G₁G₂+…..+ F_N/ G₁G₂G₃… G_N
b) F_N = F₁ + (F₂- 1)/ G₁+ (F₃- 1)/ (G1+G2)+…..+(F_N- 1)/ (G1+G2+G3+… +G_N)
c) F_N = F₁ + F₂/ G₁+ F₃/ (G1+G2)+…..+ F_N/ (G1+G2+G3+… +G_N)
d) F_N = F₁ + (F₂- 1)/ G₁+ (F₃- 1)/ G₁G₂+…..+(F_N- 1)/ G₁G₂G₃… G_N

Correct Answer: d) F_N = F₁ + (F₂- 1)/ G₁+ (F₃- 1)/ G₁G₂+…..+(F_N- 1)/ G₁G₂G₃… G_N

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 factor of the cascaded amplifier is obtained by
F_N = F₁ + (F₂- 1)/ G₁+ (F₃- 1)/ G₁G₂+…..+(F_N- 1)/ G₁G₂G₃… G_N