# Finding Thevenin Equivalent Circuit

• Engineering
• Lancelot59
In summary, In the first part of the question, the S domain transfer function was found without any issues. Now, in order to find the thevenin equivalent at the point V2(t), a short circuit must be created across the nodes. This was easily done by following the steps for finding the equivalent circuit.
Lancelot59
I'm given the circuit in the attached image (I just quickly re-created the circuit in LTSpice to save on drawing time).

In the first part of the question I managed to find the S domain transfer function without any issue. I found the transfer function as some function of the resistors, capacitors, and S.

Now however I need to find the thevenin equivalent at the point V2(t), and I'm not quite sure how to get started with this working in the S domain.

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Simon Bridge said:
But there is a short circuit across those nodes!

Anyway - do you know how to find impedences in the s-domain?
Try: http://www.engr.mun.ca/~egill/index_files/unit5382106.pdf p22
(diagrams didn;t come out for me - but you can see the method without them)
Maybe: http://www.stanford.edu/~boyd/ee102/laplace_ckts.pdf

Oops, I left a connection in by accident. Ignore the short. Finding the impedances was easy enough, and like I said I found the transfer function.

A thought occurred to me. Isn't this going to wind up being the equivalent series impedance, in series with a voltage source that is the the transfer function?

You can find ##V_{AB}## - a bit more care is needed for the input impedance.
Just go through the normal steps for finding the equivalent circuit. You should be able to satisfy yourself about the validity if you keep in mind what the various bits of math mean.

I would approach this problem by first understanding the concept of Thevenin equivalent circuit. Thevenin's theorem states that any linear electrical network can be replaced by an equivalent circuit consisting of a voltage source in series with a resistor, called the Thevenin voltage and resistance respectively.

To find the Thevenin equivalent circuit at the point V2(t), we need to determine the Thevenin voltage and resistance. This can be done by considering the open circuit voltage and the short circuit current at the point V2(t).

To find the open circuit voltage, we can set V2(t) to be an open circuit and apply a test voltage at the terminals. By using Kirchoff's voltage law, we can determine the voltage across V2(t) which will be the Thevenin voltage.

Next, to find the short circuit current, we can short the terminals of V2(t) and apply a test current. By using Kirchoff's current law, we can determine the current flowing through the shorted terminals. This will be the Thevenin resistance.

Once we have determined the Thevenin voltage and resistance, we can construct the Thevenin equivalent circuit by placing a voltage source with the Thevenin voltage in series with a resistor with the Thevenin resistance.

To work in the S domain, we can use the Laplace transform to convert the circuit into an equivalent circuit in the S domain. We can then apply the same steps as mentioned above to determine the Thevenin voltage and resistance in the S domain.

In summary, finding the Thevenin equivalent circuit involves understanding the concept of Thevenin's theorem and applying it to determine the Thevenin voltage and resistance. Working in the S domain involves using the Laplace transform to convert the circuit into an equivalent circuit in the S domain.

## 1. What is Thevenin's theorem?

Thevenin's theorem is a fundamental concept in circuit analysis that states that any linear circuit can be represented by an equivalent circuit with a single voltage source and a single resistance. This equivalent circuit is known as the Thevenin equivalent circuit.

## 2. How do you find the Thevenin equivalent circuit?

To find the Thevenin equivalent circuit, you need to follow these steps:1. Remove the load resistor from the original circuit.2. Calculate the open-circuit voltage (Voc) across the terminals where the load resistor was connected.3. Calculate the total resistance (Rt) seen from those terminals.4. The Thevenin equivalent circuit will have a voltage source with a value equal to Voc and a resistor with a value equal to Rt.

## 3. Can Thevenin's theorem be applied to non-linear circuits?

No, Thevenin's theorem only applies to linear circuits, where the relationship between current and voltage is linear. In non-linear circuits, the relationship between current and voltage is non-linear, and thus Thevenin's theorem cannot be used to find an equivalent circuit.

## 4. What is the purpose of finding the Thevenin equivalent circuit?

The purpose of finding the Thevenin equivalent circuit is to simplify the analysis of a complex circuit. It allows us to replace a complicated circuit with a simpler one, which can make calculations and analysis much easier. The Thevenin equivalent circuit is especially useful in circuit design and troubleshooting.

## 5. Can Thevenin's theorem be used in AC circuits?

Yes, Thevenin's theorem can be used in AC circuits as long as the circuit is linear. However, the calculations for the Thevenin equivalent circuit will involve complex numbers and phasors instead of just real numbers. The process for finding the Thevenin equivalent circuit in AC circuits is the same as in DC circuits.

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