Help with proving a transfer function?

[Chandasouk]

http://img195.imageshack.us/i/89020004.jpg/

I cannot get the Z2Z3 to appear in the bottom.

I'm saying Zout = Z2 || Z3 so that gives Z2Z3/Z2+Z3 and Zg = Z1

Then H(s) = Zout/Zg = Z2Z3/Z1Z2+Z1Z3

What am I doing wrong?

 

[Ecthelion]

You can attack this problem using voltage division. You can get the equivalent impedence across Vo and then divide it by the total impedence seen by the source, Vg.

So:

The voltage seen by Vo:
Zo = (Z3)(Z2)/(Z3+Z2)

The voltage seen by Vg:
Zi = Zo + Z1

So when you divide Zo/Zi and simplify you get the correct answer. Hope that helps! Let me know if you need further explanation.

 

[Chandasouk]

Can you explain why Zi = Zo + Z1? I always thought voltage division was

V_n = V_total(R_n/R_total)

Where V is voltage and R is resistance. In our case, we would just replace the R's with Z's for impedances but I'm still not sure how you got Zi = Zo + Z1 from that