Band pass filter


What is this bandpass filter transfer function derivation?

Best Answer

There are several mehods for calculating the closed-loop gain function of an opamp with feedback. I think, for the shown circuit the most simple way is as follows:

From H. Blacks famous formula - assuming ideal opamps with an open-loop gain of infinity - we know that the closed-loop gain can be written as


with (applying the superposition rule):

Hf (forward function)=Vn/Vi if Vout=0, and

Hr(return function, feedback factor)=Vn/Vout if Vi=0.

(Vn:voltage at the negative input terminal),

Both functions Hf and Hr can be found by applying the well-known voltage divider rule.