topic Re: Inverse Laplace Transforms in Mathcad

Inverse Laplace Transforms

ssato — Wed, 22 Dec 2021 07:29:31 GMT

Hello everyone,

I attached the work sheet by Prime7.

I want to draw the graph of i1(t).

But I can't draw the graph.

I tried without unit. But the result is same.

Please advise me.

Re: Inverse Laplace Transforms

LucMeekes — Wed, 22 Dec 2021 08:33:15 GMT

Apparently your Vin is a square wave...

Have you tried what Prime finds for the invlaplace of just:

tanh(s) ?

According to WolframAlpha it's:

I don't see how Prime got an infinit'th derivative in there, but that's what it tries to do apparently.

That said, I don't think you will be able to solve this problem in this generic way. Try to describe your input for just a few cycles of the square wave, instead of the general square wave. That gives you a better chance of performing the inverse laplace. I suggest you have alook here: https://community.ptc.com/t5/PTC-Mathcad/Square-Sine-and-PiceWise-Linear-Waves-Functions/m-p/718121#M194834

And, if you're only curious about the form of the resulting wave, use a circuit simulator (SPICE, LTspice, or the like).

Success!
Luc

Re: Inverse Laplace Transforms

-MFra- — Wed, 22 Dec 2021 18:09:22 GMT

Hi!
my solution with Mathcad 15:

Re: Inverse Laplace Transforms

ssato — Wed, 22 Dec 2021 23:25:29 GMT

Luc san,

The input voltage is continuous rectangular wave.

We get the laplace transofrm from a text book.

I agree the using circuit simulator.

Thanks

Re: Inverse Laplace Transforms

ssato — Wed, 22 Dec 2021 23:32:17 GMT

MFra san,

Your answer is too difficult for me.

I try to study your reply..

Thanks

Re: Inverse Laplace Transforms

-MFra- — Thu, 23 Dec 2021 06:14:21 GMT

Hello,

in the file you find at https://community.ptc.com/t5/PTC-Mathcad/3-LOW-PASS-I-order-DIGITAL-FILTERS-EQUIVALENT-TO-LINEAR-CLASSICS/mp/449024 # M176358, there is the study with the use of the Laplace transform, of the response of a linear and stationary system to different periodic signals.

Re: Inverse Laplace Transforms

ttokoro — Thu, 23 Dec 2021 10:07:52 GMT

Using E(s) instead of 1/s*tanh(s*T/4), you can get the answer. T and E must change the ones you use in your sheet.

Re: Inverse Laplace Transforms

-MFra- — Thu, 23 Dec 2021 11:55:21 GMT

Hello,

Re: Inverse Laplace Transforms

LucMeekes — Thu, 23 Dec 2021 16:17:06 GMT

If I'm not mistaken, this your circuit:

(L1 is quite a large inductor)

This is I1, the current in L2:

Appears to increase to a steady amplitude, but look further:

And in the long run, the first 20 ms:

And up to 200 ms.

Success!
Luc

Re: Inverse Laplace Transforms

ttokoro — Thu, 23 Dec 2021 23:32:53 GMT

Magnitude of i1(t) is different but the shape is almost same by Prime 7 for 25 cycles of applied voltage with +-both sign applied.

Re: Inverse Laplace Transforms

ssato — Fri, 24 Dec 2021 04:49:42 GMT

Hello Luc san, ttokoro san,

I attempt your method what is to describe my input wave form for just a few cycles of the square wave

I attached the work sheet. Almost is OK.

But I think the polarity of the only first cycle is reversed.

The polarity of waveform attached by ttokoro-san looks correct.

Is my wave form is correct , or do I have a mistake ?

Thanks

Re: Inverse Laplace Transforms

ttokoro — Fri, 24 Dec 2021 05:03:59 GMT

This is my Prime 7 answer of just 4 cycles. The value of each impedance has very small or large. So I without use float command and using all digits that Mathcad can.

Re: Inverse Laplace Transforms

ssato — Fri, 24 Dec 2021 05:15:09 GMT

ttokoro san

I checked the wave form without float.

The results is OK.

I understood that "float" affects the later calculated values.

Thanks

Re: Inverse Laplace Transforms

-MFra- — Fri, 24 Dec 2021 18:31:25 GMT

Hi!

Taking the cue from the circuit provided by LucMeekes and considering I1 as the current produced by the generator, I made this analysis of the circuit by inspection. The results are:

Re: Inverse Laplace Transforms

ttokoro — Fri, 24 Dec 2021 23:50:03 GMT

Using unipolar voltage signal the result is as same as by LucMeekes.

Re: Inverse Laplace Transforms

ttokoro — Sat, 25 Dec 2021 00:17:57 GMT

instead of 9.02*10^-12.

Re: Inverse Laplace Transforms

-MFra- — Sat, 25 Dec 2021 15:50:30 GMT

Improved solution:

Re: Inverse Laplace Transforms

ttokoro — Sat, 25 Dec 2021 12:14:32 GMT

Dear MFra,

Your last equation h(t) has no Unit step function, USF

I think step voltage responce must have USF for every switchuing time as at first Luc shows us.

Because this transient responce is a convolution of Voltage signal and the inpulce response of the system.

Re: Inverse Laplace Transforms

-MFra- — Sat, 25 Dec 2021 15:47:40 GMT

thank you very much, I corrected the original.

Re: Inverse Laplace Transforms

MSheykman — Sun, 02 Jan 2022 10:59:06 GMT

You get symbolic evaluation result that contains a limit and cannot be evaluated to real numbers neither symbolically, not numerically, that is why it also cannot be plotted.

Behind the scene plot just takes the input function and calculates it's values in some set of points. The function that you pass to plot cannot be evaluated in any of the points, that is why you see this error message and no trace.

We did some improvements related to integral transforms in Mathcad Prime 8, but they do not help in this particular case.

Please report this problem to tech support (https://www.ptc.com/support/case-logger) and we will check if it is possible to improve handling of such cases.