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SU_105429914-Participant
4-Participant
Jan 3, 2023 9:44 AM UTC
Solved

Unable to plot inverse laplace transform waveform

Hi

Please find the attached mathcad prime worksheet. I am trying to plot Vo(t) vs t. An error stating "Plotting failed. Replace complex numbers and NaNs by real numbers is showing. Kindly help me to resolve this issue.

 

 

 

 

ttokoro
ttokoroAnswer
21-Topaz I
Jan 12, 2023 6:18 AM UTC

I am using Mathcad Prime 8. From Prime 7, Laplace and Fourier transforms are version upped. You can read PDF of my file. 

Anyway, h(t) is almost impulse, and the response is as same as input signal. Using convolution technique by * in Mathcad, the signal delay is about 3 microseconds. 

Tokoro.

 

t.t.
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31 replies

Werner_E
Werner_E25-Diamond I
25-Diamond I
Jan 3, 2023 10:15 AM UTC

As you can see the result of invlaplace contains limit operators (n->infinity). These limits can only be evaluated symbolically but a plot requires numeric evaluations. So the plot must fail.

Try yourself and type V.o(0.3)= and Prime will fail with an appropriate error message.

After all this means that Primes symbolic is not capable enough to find a decent representation of the inverselaplace transfomed. The result Primes symbolics returns is useless, it can't neither be evaluated symbolically nor numerically.

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SU_105429914-ParticipantAuthor
4-Participant
Jan 3, 2023 10:25 AM UTC
Thank you for the response. I have checked Vo(0.3) and it is showing error. I understood that the limit operator (n-->infinity) is the issue. Is there any way to resolve this issue?

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Werner_E
Werner_E25-Diamond I
25-Diamond I
Jan 3, 2023 10:38 AM UTC
@SU_10542991 wrote:
Thank you for the response. I have checked Vo(0.3) and it is showing error. I understood that the limit operator (n-->infinity) is the issue. Is there any way to resolve this issue?

Actually the limit operator is also not helpful if you try to symbolically evaluate Vo(0.3) as the result of Primes symbolic is just kind of a building plan how to derive the invlaplace transformed if, yes if we could simplify that derivation limit.
It just means that Prime is not capable enough to give you the answer you are asking for.

I tried with the legacy symbolic engine which is available up to Prime 6 and it wasn't able to come up with a solution function either

(but it shows that a bit more clearly that its not capable enough):

Werner_E_0-1672742260304.png

So at the moment I see no way to derive the output voltage using invlaplace with Prime.

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LucMeekes23-Emerald V
23-Emerald V
Jan 3, 2023 9:22 PM UTC

What is your Vi(t) ?

 

Have you tried transforming your input signal (Vi) alone to time domain?

 

Success!

Luc

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SU_105429914-ParticipantAuthor
4-Participant
Jan 4, 2023 8:11 AM UTC

Hi @LucMeekes 

 

I tried transforming the input signal Vi(s) alone to Vi(t). But it is showing error in plotting. I don't understand why while taking inverse laplace transform, "s" term is coming. And what does this delta(t) mean? Can you please correct me where I am wrong?

 

SU_10542991_0-1672819323548.png

 

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LucMeekes23-Emerald V
23-Emerald V
Jan 4, 2023 11:24 AM UTC

I guess essentially I was asking: How did you come to the expression for the Laplace transform of your input signal?

Since it is not common to have/know only the Laplace transform. All in all this is assuming you're dealing with a real-world problem, and not some pure theoretic set-up.

The reason I'm asking is because that Vi(s) contains expression parts that are quite uncommon for the Laplace domain: the (1-exp(-a*s)) occur in signals with a step and staircase shapes.

Seems like your input signal is the double convolution of a box and a staircase.

 

Success!
Luc

 

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ttokoro
ttokoro21-Topaz I
21-Topaz I
Jan 4, 2023 11:48 AM UTC

Maybe input signal is infinity number of triangle waves shown in green plot but that only shows 5 waves.
But cannot get Vout(t).

image.pngimage.pngimage.pngimage.png

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t.t.
SU_105429914-ParticipantAuthor
4-Participant
Jan 6, 2023 5:56 AM UTC

Hi @ttokoro this is right. The input signal is a triangular wave. May I kindly know why you are saying that Vout will not be obtained.

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ttokoro
ttokoro21-Topaz I
21-Topaz I
Jan 6, 2023 7:07 AM UTC
The Laplace transform of a repetitive waveform with a period of T is
image.png
where, V1 (s) is the Laplace transform of a one-period waveform.
Unfortunately, it cannot inverse transform to t domain waveform. Therefore, we must use finite number of Laplace transform of voltage waveform.
image.pngimage.png
Left plot shows the transient current response of RL Circuit. (R=1, L=1) 
Right plot shows RCRC circuit response of all is unit value.
image.pngimage.png
In this case Mathcad can solve the answer. (In these plots, I use Maple2022 because it is faster than Mathcad.)
But using your R and C values, it shows nothing because C and R are so small and immediately charged to the applied voltage.
I think the time constant is so small and numerical calculation is failed.
 
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t.t.
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