laplace representation of transmission line

[electricpete]

I just wanted to double-check something:

When doing transient analysis of circuits in Laplace Domain, the representations of r/l/c components are familiar:
Zr= r, Zl = sl, Zc = 1/(sc)

If we wanted to include a circuit element which captures the terminal characteristics of a lossless transmission line, could I simply use an element:
Z = Z0*exp(-s*d)
where Z0 =sqrt(L/C) (Z0 is real-valued like a resistance)
and d is delay/travel time

(note - the intent would only be to analyse the forward transient and neglect reflections)

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[magoo2]

It's been a while since I messed with Laplace, but I think you're missing a /s term.

The delay F(s) should be [exp(-s*d)]/s

which corresponds to an f(t) = u(t-d)

 

[electricpete]

I don't think that's right. It doesn't delay the current.

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[electricpete]

We typed at the same time. My comments (I don't think that's right) were referring to my own post!

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[electricpete]

Maybe I just need two separate elements in series.

The second element is Z0 = sqrt(L/C)

The first element is something like a delay element. I guess I can just draw it as a box and remember that the current and voltage to the right of it are equal to the current and voltage to the left of it muliplied by exp(-s*d).

Would that be the correct approach?

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[electricpete]

Magoo- Thanks for your comments. I'm thinking the right approach would be multiply by exp(-s*d) rather than exp(-s*d)/s because I want time domain convolution with dirac(t-d) rather than u(t-d).

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[jghrist]

Note that sqrt(L/C) is the surge impedance and is important in determining lightning surge voltages. It is also important in determining the stability limits (surge impedance loading or SIL).

 

[electricpete]

System 1
Ground ==vs(t) == LossessTransmLineZ0 == L == Ground
We want to find the source current is(t) and its transform Is(s)
(still assuming all backwards reflection from right to left ignored)

First impression would be
Is(s) = Vs(s) / (z0+ s*L)

But I think it really should be:
Is(s) = Vs(s) / z0
as well as:
IL(s) = exp(-s*d)*Is(s) = exp(-s*d)*Vs(s) / z0

Do you agree ?


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[electricpete]

Whoops. Change IL(s) to
IL(s) = Is(s) * 2*Z0/(Z0+sL)*exp(-s*d)
where Is(s) = Vs(s) / z0

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[7anoter4]

Hi electricpete
This is very interesting issue, indeed.
My knowledge in Laplace Transformation is rusty, a bit. But, if I well understood, the problem is to calculate the current in a circuitry as follows [i (t) from I(s):

Am I wrong?
Best Regards