Finding Thevenin 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.

 

[Simon Bridge]

I need to find the thevenin equivalent at the point V2(t)

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

 

[Lancelot59]

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?

 

[Simon Bridge]

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.

 

[rezeew]

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.