Electrical – Finding the Transfer Function and Simplifying it to Standard Form

circuit analysistransfer function

enter image description here

Hello, forgive my formatting- I am new and am trying to learn the ropes.
When I tried to find H(s)=Vo/Vi, I derived:

[R2 || 1/(sC2)] / [(R1 || 1/(sC1) + (R2 || 1/(sC2)].

However, when trying to simplify the function into the form,

H(s) = K(1 + sTz)/(1 + sTp)

I am stumped. This might be as trivial as simple algebra, but perhaps I don't understand transfer functions that well. The closest I have gotten is:

1 / [((1/R2) + sC2) / ((1/R1) + sC1) + 1]

That was obtained from just dividing the top and bottom by the same expression 1 or 2 times.

I would like a hint or a push in the right direction. Thank you for your time.

Best Answer

It's actually nothing more than simple algebra. For this reason I usually use some kind of software to avoid mistakes.

In this case the result looks like this enter image description here

You find the constant K by setting s to zero, which should be obvious from doing the same to the standard form.

To factor this expression out, you would have to divide the numerator by R2 and the denominator by R1 + R2.