# Circuit challenge to solve. Help appreciated. -Transfer function of capacitance multiplier

## Is this a difficult circuit to solve?

• ### No

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#### David82

Joined Jun 13, 2017
2
Hello fellow EEs! I've been struggling at work to come up with transfer function for the capacitor multiplier circuit attached. Getting the transfer function will help select the proper values for resistors to produce desired response (without doing trial and error approach). Seems like a simple task but there're some dependencies in the circuit that makes it hard to solve. On the circuit, the input voltage is a step function, DC. Output is depends on time to charge the cap and the dependent voltage source (op amp). If there're any experts on here that are willing to help.. I'll be very grateful!

My first take at this was to do a KCL approach: I = I1 + I2.
I = (Vin - Vi)/R1 I1=(Vi-Vc)/R3 I2 = (Vi-Vc)/R2
Vc=Vi( 1-e^(-1/R3*C) ) So Vi = Vc/( 1-e^(-1/R3*C) ) Substituting Vi and solving for Vc in terms of t and Vin produced below. With extremes of time (infinity and 0) it seems to make sense.

View attachment 128911
But plotting it does not look correct. I think the error is Vin is not fixed but time dependent.. This is where I'm stuck..

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