# Question on Laplace Transform of a constant voltage source

Hello.

I am reviewing the use of the Laplace Transform to do circuit analysis and I am slightly confused about the transform of a constant voltage source.

For example, lets say we have a constant voltage source V1(t) applied to a circuit for a long time - lets say it reaches steady state. We then apply a step function voltage V2(t) some place else in the circuit while V1(t) is left on.

What is the S-domain equivalent of this circuit? How do you handle the constant voltage source V1(t)? It's not a step response - I have looked all over and I have found nothing on this.

Thanks

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Have you drawn a schematic of your considered situation? I recommend you do.

I can't see any problem with having a circuit with multiple voltage sources.. So i can't see what you are trying to ask.

By applying V2(t) after V1(t) is left on for a long time, you are simply left with a new circuit altogether, for which you can solve in the S-domain, and yield the output response.

donpacino
Gold Member
Hello.

I am reviewing the use of the Laplace Transform to do circuit analysis and I am slightly confused about the transform of a constant voltage source.

For example, lets say we have a constant voltage source V1(t) applied to a circuit for a long time - lets say it reaches steady state. We then apply a step function voltage V2(t) some place else in the circuit while V1(t) is left on.

What is the S-domain equivalent of this circuit? How do you handle the constant voltage source V1(t)? It's not a step response - I have looked all over and I have found nothing on this.

Thanks
There is not a clean way to do what you are asking.

You have two choices.

1.
have v1 as a step function at time=-1000 (scale this number appropriately)
then evaluate two step functions

2.
evaluate the step function of magnitude v2-v1

I am assuming you are talking about analyzing the frequency response of a transfer function.

remember that a transfer function looks at the relationship between 1 input and 1 output. If you wish to evaluate the effect a constant will have, you need to make it an input.