Electrical – Transfer Function Of Multiple Feedback Bandpass Filter

band passtransfer function

I am trying to figure out the transfer function for this bandpass filter (images below).
I am sorry for badly drawn circuit. The operational amplifier is an ideal op amp.

I'd like to know if I correctly analyzed the circuit. I don't think so because when I try to simplify the transfer function into bandpass filter transfer function, something seems to be off.

enter image description here

enter image description here

Best Answer

By nodal analysis, using \$\large\Sigma\$(currents away from node) = 0:

Let \$\small V\$ be the voltage at the \$\small R_1,\: R_2,\: C_3,\: C_4\$ node, then:


And, at the summing junction node:


Eliminating \$\small V\$: