Engineering Write transfer function G(s) of circuit

[Maurizio]

Homework Statement

The problem ask me to write the transfert function of a electrical circuit witch include an operational amplifier. I've follow some instruction bur I cannot figure out from this problem.
Could you suggest me somethings?

I'd like to calculate G(S) = U(s) / Y(s)

where U(s) is Lasplace transform of u(t) and Y(s) is Lasplace transform of y(t)

The circuit, and solution is in attached file tf.pdf.

I start cualculating the equivalent impedance Z2.

I get: R + 1/SC

How can I write equivalent impedance for Z1.

I'd like to apply the formula:

G(s) = U(s)/Y(s) = -Z2/Z1

Thank you very much!

Homework Equations

The Attempt at a Solution

 

[The Electrician]

How can I write equivalent impedance for Z1.

I'd like to apply the formula:

G(s) = U(s)/Y(s) = -Z2/Z1

Keeping in mind that the minus input of the opamp is a virtual ground, you should calculate how much current will flow to ground from the right end of the Z1 network if you apply 1 volt at the input node u. Then take the ratio of the applied voltage (1 volt) and the output current in the rightmost resistor R of the Z1 network, if the right end of that resistor is grounded.

That ratio will be the equivalent impedance of the Z1 network.

 

[Maurizio]

Thank you for your answer. I've found that it's possible to solve this kind of problem in simple way applying: Y-Δ transform

The link of a page on wikipedia is the following:
http://en.wikipedia.org/wiki/Y-Δ_transform

I hope that someone could find this post helpful.

Thank you
Bye
Maurizio