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I’ve been struggling with this circuit for over an hour I’m trying to find the transfer function, can anyone help me with that?enter image description here ![enter image description here] Here are my attempts on this: (https://i.stack.imgur.com/eMy2G.jpg)

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    \$\begingroup\$ On SE we do not answer question like this with at least an attempt from your side to solve it. What have you tried, how far did you get, where did you get stuck? \$\endgroup\$
    – Oldfart
    Apr 14 '18 at 12:40
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    \$\begingroup\$ You should add where are you having troubles, what have you tried. We will not do your homework, we will help if you show us you at least tried.. \$\endgroup\$
    – Andrés
    Apr 14 '18 at 12:40
  • \$\begingroup\$ I’m not asking you to do my homework, I want to actually understand and I did try I just don’t seem to be able to figure out the catch, how do I upload another picture? I’ll show you \$\endgroup\$ Apr 14 '18 at 13:55
  • \$\begingroup\$ There is a "edit" button on top of this comment \$\endgroup\$
    – Long Pham
    Apr 14 '18 at 14:01
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To determine this transfer function, you have several options: use the brute-force approach or the fast analytical circuits techniques (FACTs). The first option uses KVL or KCL (for instance) but I have selected superposition as shown below:

enter image description here

Now, good luck to develop this expression and factor it in a meaningful way without making mistakes. The FACTs, on the other hand, ask you to determine the time constants of this circuit for a zeroed excitation and a nulled response. This is described in the book I wrote in 2016. By breaking the circuit in small individual sketches, you will get the final result in a clear and ordered form without writing a line of algebra:

enter image description here

Simply remove an energy-storing element and "look" through its connecting terminals to express the resistance \$R\$ you see. The time constant is then \$\tau=RC\$. If you follow the steps, this is what you have:

enter image description here

The response between the brute-force expression and that of the FACTs are rigorously similar as shown below:

enter image description here

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I will try to use KVL over the three loops or Thevenin. Always working with impedance Zc and R. After finding the solution you can replace Zc with the respective w(omega) dependent function.

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