[SI-LIST] Transmission Line Causality
- From: Sam Sam <si.rules@xxxxxxxx>
- To: si-list@xxxxxxxxxxxxx, si-list-bounce@xxxxxxxxxxxxx
- Date: Tue, 24 Apr 2007 21:26:06 -0400 (EDT)
Hi,
I would like to raise a discussion on testing causality of a frequency
dependent lossy transmission line model. I have two concerns. One is regarding
visually checking causality and the other mathematically checking the
self-consistency of matrix data. Visually testing causality means applying an
input pulse, you get a non-zero signal before the minimum propagation time of
the line. But what is the minimum propagation time. Is it d/c where d is length
of line and c equal to speed of light/sqrt(Er). I also found that there is
another way of visually testing using pulse and impulse response.
1. Apply a unit step function to input of the line.
2 Record the time required for the output pulse to reach 10% of the final
value compared to the reference time determined by the time of the launched
step ?this time is the minimum propagation time
3. Measure the magnitude of the impulse response at the minimum propagation
time calculated. If the value at this time or at any preceding time exceeds 5%
of the final value (unity) it is not causal.
But I really dont see how this method works. When i use the same edge rate
for pulse and impulse responses, they seem to rise at same time. Or may be i am
not seeing something here.
Secondly, to mathematically verify all i am doing is using hilbert
transforms. Reconstructing the imaginary part of Z from the real part of Z
where Z = R+j*w*L.And then trying to match the original L data versus freq and
the reconstructed L datawith freq. The error was more than 6% and hence i
concluded non-causal whcih is also verified by my visual test 1 ( i dnt
understand visual test2). However when i used the reconstructed L data to
perform my simulation, the result is crappy. it still isnt causal, i am
puzzled...
What is the efficient way to enforce causality on RLGC data obtained from
field solvers. I notice one thing that the G matrix is exactly linear with
frequency and C is almost constant which is beacuse permitvitty is not
following frequency dependence and Hilbert realtions. What is the proper way to
correct the data without changing other information in result.
Sam
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