What is the input voltage for the second stage in a 2-stage amplifier?

[perplexabot]

Hello all. I am currently trying to find the gain of a 2 stage amp. According to some notes I have, it is:

A = A1 x A2 x (rin2 / (rin2 + ro1))
Where
A1 = gain of first stage
A2 = gain of second stage
rin2 = input resistance of second stage
ro1 = output resistance of first stage

Let p = (rin2 / (rin2 + ro1)) so that A = A1 x A2 x p

I understand conceptually why 'p' comes in. It is due to loading of the stages together (right?).
But I don't understand how to get that factor ('p') mathematically. Please explain. Thank you.

PS: If a schematic of the amplifier is needed please let me know.

 

[Jony130]

In electronic circuits, we always hooking the output of something (output of a amplifier, output of a voltage input source...) to the input of something else (load resistor, input stage of a next amplifier...).
After we draw this in a simplified schematics we see our old friend the voltage divider.

p = Voltage divider equation

So the second stage input voltage is not equal to

Vin2 = Vin x A1 because we have a voltage divider in the circuit, so the second stage input voltage is equal to.

Vin2 = Vin x A1 x Rin/(Rout + Rin)