ACCEPTED SOLUTION
Accepted Solutions
Here's an example, first your triangle:
Don't try to use the repetitive signal, due to the mod() function, the Laplace transform will not carry through:
Now we need G(s), to calculate X(s). As an example we take a simple Low-pass filter:
From here, apply the inverse Laplace transform to obtain x(t):
(Yes, it's a big expression)
And plot f(t) and x(t):
Success!
Luc
Very first check: see if the Laplace transform likes an 'if'-statement. I know it deals with the Heaviside step function OK, but have my doubts about if...
Success!
Luc
And even if you succeed in finding the Laplace transform of a triangular waveform, which, according to Spiegel "Laplace transforms":
for a triangle with amplitude A and period T and no offset, will be something like:
Then on trying to apply the inverse Laplace, you (may) get:
which means that the inverse Laplace isn't known.
Success!
Luc
Sometimes...
I found another method to define a (symmetrical) triangular waveform:
Unfortunately the Laplace transform isn't found by Mathcad:
Luc
Shouldn't you replace t.3 in your definition of f(t) by T. After all t.3 seems to be a duration, not a time stamp.
As Luc already wrote, the symbolic "laplace" does not work with conditionals (if's).
I am also not sure about trunc and/or mod (which you would use to make a periodic signal) and the used units. After all the symbolics does not know anything about units and treats them as unknown variables.
Using Fourier would require you to trunc the row and would just be an approximation.
EDIT: I just gave it a try and redefined f(t) using the Heaviside function as suggested by Luc.
We can laplace transform f(t), but as soon as we use "floor" to make it periodic, the symbolic is not able to transform it in a usable way - you see the calls to a (non-existent in Prime) laplace-function in the result.
I haven't tried, but I guess that different ways to make the signal periodic (using the "mod"-function e.g.) will have no success, too and you will have to resort to other methods to solve your task. Maybe the pdfs of @-MFra- , posted by @Derbigdog will be of help.
So this makes really fun, I must admit.
The pdf´s attached above are great, but unfortunately does not help...
See my attachment below, I have played and tried out a lot.
The solution is actually in the F1-mathcad-help-menu. Mathcad will not return any useful solution without the further command "assume, ALL>0"!
I also cleared all defintions, unfortunately clear(ALL) does not work ... Nevermind.
Completly symbolic it looks like this:
...
Tomorrow will follow more ... 🙂
Best Regards
You shouldn't "upgrade" to Prime 6 or any upcoming version.
Sooner or later the "legacy" symbolic (Mupad) will not be integrated anymore and the newly introduced symbolic isn't really ... competitive.
Remark: In Prime 6 you still have the option to switch between the two symbolic engines.
Number of input signal can change by as same as Werner_E posted.
If we have a impulse response, g(t), Mathcad can show the output signal waveform by using convolution even we can't write the equation of input function. (Just use the A/D signal data for input x(t).)
If we can write the both equations, convolution integral can show the output signal waveform.
Here's an example, first your triangle:
Don't try to use the repetitive signal, due to the mod() function, the Laplace transform will not carry through:
Now we need G(s), to calculate X(s). As an example we take a simple Low-pass filter:
From here, apply the inverse Laplace transform to obtain x(t):
(Yes, it's a big expression)
And plot f(t) and x(t):
Success!
Luc
We might not be able to Laplace-transform the periodic made signal, but at least we can repeat it a couple of times using a simple summation which the laplace command accepts.
But I guess that less simple filters might be a problem for invlaplace
Found another way to build a triangle. But it's neither symbolic-proof, nor fast:
Success!
Luc
In case you could not see the worksheet of the OP, as far as I understood it and depending on the sheet which was posted, the signal should look like this:
If I made no mistake then:
The Laplace transform of the triangular signal y starts with:
Your filter is:
And with the actual component values the Laplace transform of the response is:
Transformed back to time domain we get x3(t) that starts with:
And the time-plot is:
Success!
Luc
Unfortunately: no.
I do not have a Prime license, so I'm limited to Express (= No symbolics).
But I can show you what happens after more excitation signal:
Success!
Luc
As you can see in the next picture it looks like the symbolic laplace operator fails because of the units. So you may give your sheet a try by stripping the units. Take care of the labeling! Both "t", the function argument and the argument of the laplace operator must have the exact same label (either both (-) or both "variable").
I have not tried but I could imagine that MC15 sufffers from the same problem as it uses the same symbolic engine as Prime 3 (and the versions up to P6).
But it looks like it got worse.
The new symbolic engine introduced in P6 (and its the only one available in P7) is even more critical as it needs to be told that t is greater than zero to be able to laplace transform the simple Heaviside step.
Thats also the reason why I did not succeed in laplace transforming a simple rectangle (at the right hand side you see the results given by the legacy symbolic Mupad).
So far I could not be bothered downloading and test driving Prime 7, so I don't know if the problem still is present there. After all they promised an improved symbolic, didn't they.
In case you don't know - Luc uses MC11 and this version used Maple as its symbolic engine which of course is (even though its a rather old and stripped down version) still far superior to the engines now used. So what he shows often does not work in newer versions.
Both Mathsoft (former owners of Mathcad) and Mathworks(ownern of MatLab) changed their symbolic engine from Maple to Mupad around 2006 (Maplesoft probably did not extend the license). Mathcad was bought by PTC soon after. The difference was, that MatLab bought muPad and so Mathsoft/PTC had to license the symbolic module from them. Thats also the reason PTC was eager to get rid of muPad and implement its own thing based on a free engine.
Hello guys,
although it was solved I dont want to create a new topic.
With a simple RC-lowpass is was possible to obtain a solution.
Now I try to multiply Iout(s) * G(s) to obtain Vout(s), but with a far more complex filter.
When i do it on the symbolic way, then Mathcad is calculating for a long time with a result "too large to display" ...
Well, I tried it then with functions instead of symbolic math and maybe I have found a solution here, but:
- Please check if i did it correctly
- I cannot plot the final function
- My goal is to obtain a voltage ripple on the output of the filter (peak-to-peak) ...
I attached the sheet. The first part of the sheet is the older topic where the current by itself was plotted.
For the new issue please scroll below to page 13 ++
Best regards!
