Trying to get Vout/Vin here. (Transfer function)

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This probably isn't that tough, but I'm stumped. This is actually for a control systems class, so I'm supposed to start in the time domain and then take the Laplace transform. Once I have done that, I'm supposed to solve for the transfer function, but I can't seem to come up with enough equations because of the two supernodes connected at the bottom there.

Any supergeniuses out there willing to help little ol' me? I probably just need a little push.

Oh, forgot to mention: Top resistor is R2, bottom resistor is R1. Both capacitors are identical.

-Jason

 

The brute force approach is to realize that this network has 4 nodes and 4 branches and can be viewed as a three terminal device or a two port with one terminal common to the input and output ports. The excitation you describe is an ideal voltage source across the input port and the response is the open circuit voltage across the output port. The transfer function you are looking for is the "21" element in the hybrid g matrix. Set up the KCL equations for the 4 nodes and the KVL equations for the three loops. Finally set up the equation which defines the output voltage in terms of the branch voltages. Solve that mess and you have vout as proportional to vin.

Or

at s=0 open circuit the caps , what is vout/vin?

as s goes to infinity short circuit the caps, what is vout/vin?

at s where |Zc|= R1 what is vout/vin?

at s where |Zc| = R2 what is vout/vin?

Plot the four points and visualize the full curve.

If you replace the caps with inductors what do you think the dual looks like?

Next try the twin T network.