Noise

Noise has always been a confusing topic. The treatment of noise at the systems level and circuits level seems to be disjointed. The systems level treatment doesn't care about the particular details of the connections between each block. One assumption is that the blocks are all 50 ohms input and output. What happens to the noise when the blocks are not matched to each other? What if the port impedances are complex or pure imaginary?

At the circuits level, I understand the concept of equivalent input voltage and current noise sources. Doing the algebra to get the expression for Vn, In is tough, especially if the frequency response of the circuit is also factored into the analysis. I don't understand how to get the op-amp's equivalent input Vn, In and how those noise sources are affected by the feedback network.

Definition of noise factor

F = total noise power at input of network, including the source / source noise power

If source is a resistor Rs, then F = (4kTRs + Vn^2 + (In*Rs)^2)/ 4kTRs

F = 1 + (Vn^2+(In*Rs)^2)/4kTRs

NF=10 log 10 (F)

perfect noiseless amp
F = 1 , NF=0 dB
noise added by amp is equal to that contributed by Rs
F = 2, NF = 3 dB


Notice In interacts with the source Rs.
Also note that Vn and In are assumed to be uncorrelated. This is a simplifying assumption. The proper, full blown way is to also include a correlation term like (In*Rcorr)^2 in the numerator. If correlation is ignored, then the worst possible NF error is 3 dB. (I think)