laplace representation of transmission line
laplace representation of transmission line
(OP)
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)
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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RE: laplace representation of transmission line
The delay F(s) should be [exp(-s*d)]/s
which corresponds to an f(t) = u(t-d)
RE: laplace representation of transmission line
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RE: laplace representation of transmission line
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RE: laplace representation of transmission line
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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RE: laplace representation of transmission line
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RE: laplace representation of transmission line
RE: laplace representation of transmission line
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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RE: laplace representation of transmission line
IL(s) = Is(s) * 2*Z0/(Z0+sL)*exp(-s*d)
where Is(s) = Vs(s) / z0
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RE: laplace representation of transmission line
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