# Finding the transfer function for this circuit

• Engineering
• jisbon
In summary, KVL can be used to find the current I1 and I3 for the two resistors in a transformed circuit. However, it is more work to use KCL.
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

#### Attachments

• 1590994839519.png
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jisbon said:
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:

#### Attachments

• 1591021907701.png
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Last edited:
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##.

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##.

Last edited:
jisbon and ammarb32
Thanks for all the replies :)
I do actually solved it after redrawing the circuit more clearly :)

ammarb32

## What is a transfer function?

A transfer function is a mathematical representation of the relationship between the input and output of a system. In the context of circuit analysis, it describes how the input voltage affects the output voltage of the circuit.

## Why is finding the transfer function important?

Finding the transfer function allows us to understand and analyze the behavior of a circuit. It helps us determine how the circuit will respond to different input signals, and allows us to design and optimize the circuit for specific applications.

## How do you find the transfer function for a circuit?

The transfer function for a circuit can be found by using circuit analysis techniques such as Kirchhoff's laws, Ohm's law, and the voltage and current divider rules. These techniques involve solving for the voltage and current values at different points in the circuit and then using them to calculate the transfer function.

## What information do you need to find the transfer function?

To find the transfer function for a circuit, you will need the circuit diagram, the values of all the components in the circuit (resistors, capacitors, inductors), and the input and output signals.

## Can the transfer function change for different input signals?

Yes, the transfer function can change for different input signals. This is because the behavior of a circuit can vary depending on the frequency, amplitude, and type of input signal. Therefore, the transfer function will be different for different input signals.

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