We have the task of finding the transfer function, cutoff frequencies and the resonant frequency of the active filter that I have attached. We tried to acquire it via voltage division but it became too complicated. We could conclude that it is a bandpass filter but we couldn't come up with a general transfer function nor a calculated one. Any help would be appreciated.

 

That’s not an active filter. That’s a Schmitt trigger, unless you have the op-amp inputs reversed.
Is this homework?

 

I do not know if the present version of the circuit is the corrected one (after the two comments above).
However, now the circut diagram is OK - it is an inverting MFB-bandpass with Q-enhancement as proposed by Deliyannis (pos. feedback).
EDIT: But the values of the 6.8k resistor is wrong - it must be 8.6k

 

Yes, this is a homework and the circuit diagram was given with the figure description "Circuit diagram of a band-pass filter". I did not change anything about the circuit design. I am not equipped enough to determine whether the values are correct or not to achieve a bandpass filter but the LTSpice simulation results in a bandpass form when we choose an appropriate frequency range. All I actually need is the transfer function in terms of Ri and Ci, I will handle the calculation later on. Thanks for all the replies.

 

Watch my correction (EDIT): 8.6k (instead of 6.8k)

 

Watch my correction (EDIT): 8.6k (instead of 6.8k)

I cannot make a change to the circuit. This is given as an assignment and I'm asked to obtain the transfer function. I will let the instructors know about your correction.

 

Start by trying nodal analysis.

 

Found it, thanks everyone.

 

If you have posted the circuit exactly as it appeared, then it's a trick question.
The circuit will not work as a filter.

 

If you have posted the circuit exactly as it appeared, then it's a trick question.
The circuit will not work as a filter.

It is a little different than the common Multiple Feedback Bandpass Filter but it works in my simulation:

 

If you have posted the circuit exactly as it appeared, then it's a trick question.
The circuit will not work as a filter.

Why not? With 8.6k instead of 6.8k it realizes one of the well-known bandpass topologies (MFB with Deliyannis modification).

 

If you have posted the circuit exactly as it appeared, then it's a trick question.
The circuit will not work as a filter.

Hi,

What makes you say that?

 

Why not? With 8.6k instead of 6.8k it realizes one of the well-known bandpass topologies (MFB with Deliyannis modification).

Hi,

I noticed that the difference is the 8.6k variation produces a sharper response, while the 6.8k version produces a wider bandwidth response with roughly one-sixth the midband gain.