Im having a hard time figuring out how to write transfer functions. I need the transfer function for this notch filter. Any help would be great.

Picture is attached

 

You've posted this in the homework help forum, where you're supposed to show what work you've already done to solve the problem.

What method of attack have you tried already?

 

I eliminated the op amps assuming ideal op amps and reduced the circuit to just resistors and capacitors. Then I attempted node voltage but got all nodes to equal 0. I just dont know how to go about writing a transfer function with op amps. Work is attached

 

I can't see how you can eliminate "legaly" the OpAmps. I 've never seen anybody doing such a thing.

You must imperatively use either Kirchoff's Laws along with the ideal OpAmps equations to do a nodal or mesh analysis, or use an algorithmic method (ie network analysis for electric circuits) that actually incorporates these aforementioned equations. I 'm afraid I don't know any english literature to direct you to, so Kirchoff will be your best friend for now.

 

You can't ignore the opamps. Notice that after the first opamp, the second simply adds the output of the first opamp to the input and inverts, so the only difficulty at all is deriving the transfer function of the first opamp.

Have a look at the image I've attached. I've numbered the nodes, and changed some of the designators for the passive components.

You'll notice that if you only derive the transfer function for the first opamp, you only need to use the first 3 nodes. Node 4 is dealt with by using the relation V4 = A*V3, where A is the opamp open loop voltage gain.

Write 3 equations is the same manner you've done so far, including V4, but replacing V4 with A*V3.

You should end up with 3 equations in 3 unknowns, solve and calculate the ratio V4/V1; that will be your transfer function for the first opamp. Then you can add V1 to that expression, negate and you'll have the overall transfer function.

Give it a try, post your work, and if you have any problems I'll help you out.