Analyze this opamp active filter circuit

[ace130]

Hello, so this the circuit of an IdeaI OPAMP.

The Question is to find the function Vs/Ve .
I tried to make some sum ups to simplify it but I still unable to find a solution, so I tried to NOT sum up any component and found this:
E-S=iZ+i₂(Z+R)
E=iZ+i₃R
S=i₂R
so the idea is to find E=f(i₂) , This is the final Result but I'm not sure if it's correct :

 

[berkeman]

Hello, so this the circuit of an IdeaI OPAMP.
View attachment 219618
The Question is to find the function Vs/Ve .
I tried to make some sum ups to simplify it but I still unable to find a solution, so I tried to NOT sum up any component and found this:
E-S=iZ+i₂(Z+R)
E=iZ+i₃R
S=i₂R
so the idea is to find E=f(i₂) , This is the final Result but I'm not sure if it's correct :
View attachment 219619

I'm not quite sure what you are doing with your equations, but are you familiar with how to solve circuit problems using the Kirchhoff Current Law (KCL) equations? I would write the KCL equations for the two nodes in the middle (the - input of the opamp and the middle connection point between the 3 capacitors), and solve those simultaneous equations for the gain of the circuit s(t)/e(t).

Also, are you supposed to be solving this with phasors or differential equations?

 

[ace130]

Yes i know the KCL , also this should be solved in complex .
I don't know if I should sum up those Rs and Cs or just write KCL that will take more time

 

[berkeman]

Yes i know the KCL , also this should be solved in complex .
I don't know if I should sum up those Rs and Cs or just write KCL that will take more time

I don't know of a technique to "sum up" the Rs and Cs, but there may be one. Why not do it both ways to check your answer?

Can you show us the two KCL equations that I mentioned? Then show how you would solve them simultaneously...

 

[ace130]

this is the KCL and loops

and this is the final result:

Edit : the final line it should be Zc not 1/Zc .

 

[lewando]

Your equation (2) is not right. It suffers from a sign convention error.