[SI-LIST] Transmission Line Causality

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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