Finding the transfer function for this circuit

[jisbon]

Homework Statement

As shown below.

Relevant Equations

-

Transformed circuit:

Using KVL,

Now, I am unsure about the current to use KVL in this case.
As far as equation goes:
Vi(s) =(I1*R)+(I3*R)+Vc(s), where Vc(s) = V0(s)/u as shown in the circuit.
How am I supposed to find the current I1 and I3 for the two resistors in this case?
Thanks

 

[ammarb32]

Homework Statement:: As shown below.
Relevant Equations:: -

View attachment 263864
Transformed circuit:
View attachment 263869
Using KVL,

Now, I am unsure about the current to use KVL in this case.
As far as equation goes:
Vi(s) =(I1*R)+(I3*R)+Vc(s), where Vc(s) = V0(s)/u as shown in the circuit.
How am I supposed to find the current I1 and I3 for the two resistors in this case?
Thanks

Would you be able to send a more clear picture of the circuit? Or atleast answer these questions about the problem statement so that I can get a better idea:

• Is that the greek letter "μ" next to the voltage-controlled voltage source (Please see screenshot below with red circle)? Are we given a value for μ or any other values?
• Do we have to put the transfer function in terms of Vc and Vi? Or do we have to put everything in terms of R , s and C? This will make a difference when we are re-arranging the terms in the system of equations to solve for Vo/Vi.
• Do we have any other voltage or current values across any other component in the circuit? Do we assume any voltage or current values across any other components in the circuit?
• Where is the ground symbol in the circuit? That will make a huge difference if you were to use the node-voltage method to solve for the Vo/Vi relationship.

Once you confirm all the information and the drawing from the problem statement, I'll be able to have a proper attempt at this problem.
So far, this is my drawing:

 

[The Electrician]

This should be helpful: https://en.wikipedia.org/wiki/Sallen–Key_topology

 

[Jody]

Are you okay with KCL or KVL? The approach here is you'll want to solve for $v_c$. Once you get that, then you know that $v_o$ is dependent on it and you'll be done.

KVL you can do this with two current loops. Some people might call it a mesh analysis (they're really the same). You'll have to bookkeep what sinks and sources and the total voltage of that loop has to sum to zero.

I don't like bookkeeping and so, even though it's little bit more work, I'll opt for KCL here. Here's the next step I would take.

It doesn't matter which direction you draw the arrows if you draw them all in or all out. This is because if you multiple both sides by $-1$ this flips the arrow, but $(-1)(0)$ is still $0$. I drew them all inwards in this case. Do whatever makes you feel more comfortable. I simply apply Ohm's law to each arrow so you can see on the left side the voltage across $R$ is $v_i - v_x$ and Ohm's law says the current through that resistor is $v/R$. I repeated it for each current for the entire equation.

Now you're working a very basic algebra problem and you have two unknowns: $v_x$ which I made up and $v_c$. You can come up with an equation for $v_x$ that is dependent on $v_c$.

Spoiler

Hint: Do Ohm's law across the resistor and the capacitor for $v_x$. In the equation above I only did it across the resistor, but the current going through $R$ and $C$ is the same.

Once you've eliminated $v_x$ so that the only unknown is $v_c$, then you can isolate $v_c$ for its solution. Just as said earlier: If you know $v_c$, then you know $v_o$.

 

[jisbon]

Thanks for all the replies :)
I do actually solved it after redrawing the circuit more clearly :)