I remember in my comunications module at university they told us a formula for the SNR in cascaded amplifiers, when each amplifier has a different gain: I did a quick google search but could not find what i was looking for, anyone know this or could give me a link?
If you think about it, the first amplifier in the chain has the greatest effect on signal to noise. Each succeeding amp contributes noise which is effectively 1/(gain) of the preceeding amps because its noise is not amplified by all that gain.
Except for unusual cases, you can often simply take the first amp's signal to noise as the S/N for the whole mess with little error.