I'm trying to understand how a particular equation works. The scenario is: there is a load of some resistance connected onto an amplifier with some noise figure.

The thermal noise of the load alone is: $$ \langle i_{th}^2 \rangle = 4kTB/R $$ but since there is an amplifier before it, the noise at the input of the amplifier is $$ \langle i_{th}^2 \rangle = 4kTBF/R. $$

I know that $$ F = \frac{SNR_{in}}{SNR_{out}} = \frac{S_i}{S_o} \frac{N_o}{N_i} = \frac{1}{G} \frac{N_o}{N_i} $$ and I'm not seeing why multiplying $4kTB/R$ by $F$ is going to find the noise at the input of the amplifier.

Advice much appreciated.

Thank you.

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    $\begingroup$ This question should probably be migrated to electronics.stackexchange.com. $\endgroup$ – Matt L. Nov 10 '14 at 9:45
  • $\begingroup$ @MattL. Ah okay, yes I wasn't sure where to post it. It's not really DSP, but it's also not really electronics, but at the same time, it's sort of both of them! --- I think the answer might be because when compared to an ideal amplifier (no noise added, just signal gain), the $G$ well end up cancelling and it'll turn out that the noise increase by a factor of $F$. $\endgroup$ – user968243 Nov 10 '14 at 13:11

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