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Laplace Transform of Discontinuous Loads

maximizer
1-Newbie

Laplace Transform of Discontinuous Loads

How do I attack a problem that has a periodic discontinous loading function? Example: I have an electrical circuit involving a voltage source, a series resistor followed by a capacitor for energy storage, followed by a series switch with a load impedance at the switch's output. The switch is closed for time t1 with period T, where the switch is open between t1 and T. Can this problem be solved using Laplace transforms? What would be the aproach?

Kind regards,

-Max

9 REPLIES 9

Max Edelhauser wrote:

How do I attack a problem that has a periodic discontinous loading function? Example: I have an electrical circuit involving a voltage source, a series resistor followed by a capacitor for energy storage, followed by a series switch with a load impedance at the switch's output. The switch is closed for time t1 with period T, where the switch is open between t1 and T. Can this problem be solved using Laplace transforms? What would be the aproach?

Kind regards,

-Max

I can't Laplace, or even a numeric solver to work, but

Hi Fred,

wow! I need to digest this first. The result looks like is what I am looking for. This is a helpful answer. Does this mean there is no solution using Laplace or is Laplace here simple not useful?

Kind Regards,

Max

Hi Fred,

wow! I need to digest this first. The result looks like is what I am looking for. This is a helpful answer. Does this mean there is no solution using Laplace or is Laplace here simple not useful?

Kind Regards,

Max

Hi Fred,

wow! I need to digest this first. The result looks like is what I am looking for. This is a helpful answer. Does this mean there is no solution using Laplace or is Laplace here simple not useful?

Kind Regards,

Max

Hi Fred,

wow! I need to digest this first. The result looks like is what I am looking for. This is a helpful answer. Does this mean there is no solution using Laplace or is Laplace here simple not useful?

Kind Regards,

Max

Max Edelhauser wrote:

Hi Fred,

wow! I need to digest this first. The result looks like is what I am looking for. This is a helpful answer. Does this mean there is no solution using Laplace or is Laplace here simple not useful?

Kind Regards,

Max

Max;

Sorry it took me so long, I'm not terribly electrical so it took a while for me tosort out the problem.

I tried to work a Laplace solution. I could do a "basic charging" capacitor, and a charging with steady load. Those worked okay.

I found a laplace transform for a square wave on Wikipedia; but Mathcad can't do an inverse laplace transform of that, and it won't do an inverse solution when it's put into the basic equation.

So I tried a numeric solver, rkfixed, Rkadapt, etc. ATTACHED IS THE SHEET WITH Odesolve and rkfixed working. They give a different answer than the brute force method.

When all else fails I revert to the old "small time steps" walk through the problem. Brute force still works.

Is there a Laplace solution? Well, you have an expression for the Laplace transform. If you can invert it (Mathcad appears to choke on tanh()) there sould be a solution assuming Wikipedia is right about the transform of a square wave. I'm a bit out of my depth, taking on water!

Fred

Message was edited by: Fred Kohlhepp

Perhaps there's a lifeline in the attached Fred!

Alan

Interesting.

The version I have at work (14.0000) stalls on laplace-->

I've got 15.05 at home; let me see if that's any better. I'm impressed that you got an output!!

I used 15.0 (haven't bothered to install the upgrade).

It works ok in 14 M020, but in 13 it needs all instances of laplace to be replaced by laplace,t and all instances of invlaplace to be replaced by invlaplace,s. This might work for 14.000

Alan

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