Noise factor in cascaded amplifiers

Q.  The Noise Factor for cascaded amplifiers (FN) is given by (F1, F2, F3 .. FN, G1, G2, G3....GN) are the noise factors and the gains of the amplifiers at different stages:
- Published on 15 Oct 15

a. FN = F1 + F2/ G1 + F3/ G1G2+ ..+ FN/ G1G2G3GN
b. FN = F1 + (F2 - 1)/ G1 + (F3 - 1)/ (G1+G2)+ ..+(FN - 1)/ (G1+G2+G3+...+GN)
c. FN = F1 + F2/ G1 + F3/ (G1+G2) +...+ FN/ (G1+G2+G3+...+GN)
d. FN = F1 + (F2 - 1)/ G1 + (F3 - 1)/ G1G2+...+(FN - 1)/ G1G2G3GN

ANSWER: FN = F1 + (F2 - 1)/ G1 + (F3 - 1)/ G1G2+...+(FN - 1)/ G1G2G3GN
 
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
FN = F1 + (F2 - 1)/ G1 + (F3 - 1)/ G1G2+...+(FN - 1)/ G1G2G3GN

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