Hi there, I'm having problems in being able to derive this expression - I don't understand why rpi/(rpi+rb) is multiplied by the other expression

Breaking the left part of the circuit down into something that looks like this:

then... using the voltage divider rule

Vout = Vs(rpi+rb||R1||r1)/(rpi+rb||R1||R2 + Rs)

But of course we want the voltage over Rpi.. which is where I'm stuck.

Sorry if this seems trivial...

 

Take Vout as an input voltage to the voltage divider formed by Rb and Rpi and use the voltage divider formula to find Vpi

Vpi=(Vout*Rpi)/(Rpi+Rb)

 

Hmm, I think I might have figured it out.. is this correct?

Since I need to find the voltage going through Rpi+Rb, this is actually my Vout and therefore to express the voltage over rpi =

rpi/(rpi+rb) * Vout
= rpi/(rpi+rb) * Vs(rpi+rb||R1||r1)/(rpi+rb||R1||R2 + Rs)

 

Ah was typing it while you posted.. thanks mik3

 

You are right, i have just posted the same answer!