# Scaling and Laplace transforms

#### jesse21

Joined Dec 13, 2016
4
Good afternoon, my question is can you use magnitude and frequency scaling then apply Laplace/Inverse Laplace circuit techniques to obtain the same answer as you would of doing the analysis directly.
This step seems like it could simplify many analysis problems, simply be making the inductors/ capacitors equal to 1.

#### MrAl

Joined Jun 17, 2014
8,157
Hi,

If your circuit can be scaled then there is no reason why you shouldnt be able to use a Laplace Transform because that is just an analysis technique like any other. A circuit example would be a good idea though.
In matrix forms, it is common to scale the matrix before trying to solve it and that does not change anything, for one example.

#### jesse21

Joined Dec 13, 2016
4
Hi,

If your circuit can be scaled then there is no reason why you shouldnt be able to use a Laplace Transform because that is just an analysis technique like any other. A circuit example would be a good idea though.
In matrix forms, it is common to scale the matrix before trying to solve it and that does not change anything, for one example.
Thanks for the response I've attached an example, but I can't seem to get the scaling method to work.

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#### MrAl

Joined Jun 17, 2014
8,157
Thanks for the response I've attached an example, but I can't seem to get the scaling method to work.
Hi again,

I am not sure what your end goal here is, but if we have the following values:
R1=20k
R2=10k
C=50uf

and the scaling factor is 50e-6, then we get:
R1'=1
R2'=0.5
C'=1

and so the end result is the same as before.

Just for reference for any values R1,R2,C we have time domain response:
-Vout/Vin=(R2/R1)*(1-e^(-t/(C*R2)))

However, is this really frequency scaling? That's why i ask what you are really after here.

Frequency scaling usually comes into play when we have a circuit that works in a particular way at a certain frequency and we want that same circuit to work at a different frequency. That allows us to create reference designs that have generic values that can later be changed to sute the application.

Doing what you seem to be doing is fine, but notice that we didnt really change the frequency at all because R2*C=R2'*C'.
Since R1 was also changed the amplitude stayed the same too: R2/R1=R2'/R1'.
That's fine if that's what you wanted to do though.

Note that if we actually did change the frequency of something then the circuit would behave the same as before, except with that new frequency and so we cant expect to get the same response with the old frequency then.

Try this again and see what you get.

#### jesse21

Joined Dec 13, 2016
4
Thanks for taking the time to look at this. This circuit is not meant to do anything useful, I was just trying to do magnitude scaling (which is why I left the frequency alone), to demonstrate that the response would be the same. However I got two different answers. Which is where my confusion comes in.

Shouldn't I get the same response if I just did a magnitude scaling? I understand how to do magnitude and frequency scaling on time domain circuits, but seem to be a little foggy on why I get different inverse Laplace transforms.

I've attached another pdf of some analysis. I'm trying to make circuit analysis easier in Laplace domain by using certian values (i.e. 1), but if I were to take the laplace transform and inverse transform of these two circuits I would get different answers, this is where I am confused.

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#### jesse21

Joined Dec 13, 2016
4
I reworked the problems and I made mistakes, for example in the first one I put R'2 = 5 instead of =.5 this fixed the problem and I got the same answers.

#### MrAl

Joined Jun 17, 2014
8,157
Thanks for taking the time to look at this. This circuit is not meant to do anything useful, I was just trying to do magnitude scaling (which is why I left the frequency alone), to demonstrate that the response would be the same. However I got two different answers. Which is where my confusion comes in.

Shouldn't I get the same response if I just did a magnitude scaling? I understand how to do magnitude and frequency scaling on time domain circuits, but seem to be a little foggy on why I get different inverse Laplace transforms.

I've attached another pdf of some analysis. I'm trying to make circuit analysis easier in Laplace domain by using certian values (i.e. 1), but if I were to take the laplace transform and inverse transform of these two circuits I would get different answers, this is where I am confused.