Impedance matching: microphone +input transformer +amplifier

impedance matching:
This is an old tired subject, but I would like to
be able to prove that impedance matching improves S/N]:

to show that a microphone +input transformer +low noise amplifier improves the S/N]power
whereas ignoring impedance matching always gives LESS S/N]power

Can anyone help?
Can anyone direct me to an Internet site, where such a proof can be found
(and which I have unsuccessfully looked for)

falconear

Re: Impedance matching: microphone +input transformer +ampli

As a start, instead of dealing with the complexity of a microphone feeding a transformer which feeds an amp, why not say that any complex network can be modeled with a voltage source and a series resistance?

If you say this, then you could analyze a simple voltage divider circuit, which is what power transfer is after all.

Next, if you want a proof, you'll need a means to measure noise, something that will show you a number for a noise floor.

Then, I guess, measure the signal and the noise at the input and form the ratio. Next measure the output of an R/R divider versus a R/NR divider and form those ratios. This should show you what happens between matched and unmatched impedances.

Granted, there may be some mathematical proof, but I don't know of it.

Added after 44 minutes:


For the record, I say impedance matching has zero influence on s/n.

Hi

I entirely agree with Euler's Identity, impedance matchin guarantees maximum power transfer from the source to the load. now if you model the source as signal + noise, the power of both wil be equatly transfered at the maximum value to the load

cheers

Sal