15-Moonstone

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Inverse Laplace Transforms

Forum|Forum|4 years ago
December 22, 2021
6 replies
8442 views

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.

1_Inverse-Laplace-Transform-without-unit.zip

2_Inverse-Laplace-Transform.zip

Electrical_Engineering

Best answer by LucMeekes

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

Answer

23-Emerald IV

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

Author

15-Moonstone

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

21-Topaz I

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.

t.t.

21-Topaz II

Hi!
my solution with Mathcad 15:

answer to ssato.jpg

2_answer-to-ssato.zip

Author

15-Moonstone

MFra san,

Your answer is too difficult for me.

I try to study your reply..

Thanks

21-Topaz II

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.

23-Emerald IV

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

21-Topaz I

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.

t.t.

Author

15-Moonstone

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

1_Inverse-Laplace-Transform-without-unit.zip

21-Topaz II

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:

answer to ssato++.jpg

1_answer-to-ssato++.zip

21-Topaz I

instead of 9.02*10^-12.

t.t.

21-Topaz II

Improved solution:

answer to ssato W.jpg

21-Topaz I

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.

t.t.

21-Topaz II

thank you very much, I corrected the original.

5-Regular Member

5-Regular Member

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.