[SI-LIST] Re: Transmission Line Causality

Vlad, great insight!!

Although I have used causality / passivity enforcement tools... (different
vendor than stated)...  They seem to work well... but  I still  tend to stay
away from them....  Maybe only use them when ball parking first run
answers....  It is possible to enforce one of these parameters and cause
violations in the other...   I have also run across data where enforcement
in one or both of the parameters is impossible...

It is always better to fix the source of the error(s) (either measurement or
the simulation... typically in the setups) then to start squeezing the tube
of tooth paste using mathematical assumptions that may or may not be
applicable to the data in question.

BR
Gus



-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of Gary Otonari
Sent: Wednesday, April 25, 2007 1:38 PM
To: vladimir_dmitriev-zdorov@xxxxxxxxxx; si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: Transmission Line Causality

FYI,

Agilent has put in a lot of work in ADS, to address these challenging =
issues pertaining to accurate simulation of lossy networks.  The latest
version = of the tool has new causality "enforcement" for both transmission
line = models and S-parm data.  There is also a new "passivity" correction
for = measured S-parms that exhibit non-physical behavior. =20

Agilent currently has an SI Seminar making the rounds, where you can = learn
about this stuff.  Eric Bogatin is presenting at some stops....

http://www.home.agilent.com/agilent/eventDetail.jspx?cc=3DUS&lc=3Deng&cke=
y=3D87378
7&nid=3D-536900532.536905430.08&id=3D873787

-- Gary Otonari -- GigaTest Labs
=20
** Disclaimer -- GigaTest is an Agilent Channel Partner



-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] =
On Behalf Of Dmitriev-Zdorov, Vladimir
Sent: Wednesday, April 25, 2007 9:22 AM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Transmission Line Causality

Hi Sam,

The issue you are rising is very important and I believe it is not receiving
enough attention. BTW, very similar problem exists for S-parameters data and
this of course converge in the fact that very often we use S-parameters to
describe same objects we represent as transmission (T-) lines.

I know two quick tests for T-lines causality.

1. Chopped line. You choose a certain type of lossy line and describe a long
segment of it (e.g. 1 meter with typical PCB PUL matrices). Perform
transient simulation by finding response to a step or square pulse.
Then, represent the same line as a series connection of N pieces each 1/N
meter long, with same parameters. Perform similar analysis, compare the
results. Ideally, they should be identical. Try the case of large dielectric
loss.

2. Comparison between transient and AC analysis. Apply sine input to the
lossy line, simulate long enough to see the magnitude settled. Repeat this
for different frequencies of the sine input. Then, run AC analysis and
compare the response magnitudes you see in AC to those you measured in
transient. The test may bring surprises especially for lines with
considerable dielectric losses (frequency dependent) and high enough
frequencies. Of course, when simulating in time domain, make sure the step
is small enough not to bring in LTE.

More general observation.
Model non-causality is a violation of cause-effect relations. Due to
sequential manner of time domain analysis algorithms, we can never see that
the model responds prior to receiving the input. However, this does not mean
that it corresponds to a causal representation in frequency domain. In most
cases, the core of lossy T-line model is its frequency response (not voltage
or current but characteristic admittance and delay-less propagation
operator). The models differ in how they (a) form those frequency-dependent
matrices and (b) how they convert those matrix operators into time domain
responses when performing transient analysis.

Hence, we first need to make sure that those internal frequency domain
responses are causal. Typically, we can output them (or others, closely
related to them) from AC analysis. After you get the responses in frequency
domain, they can be investigated for causality. Any causal response is a
complex function of frequency where real and imaginary parts obey Kronig
Kramers relations (derived from Hilbert transforms).
These relations are not easy to check though. One practical way to do so is
e.g. applying Vector Fitting, or transforming them into touchstone files and
applying ELDO simulation algorithms. The key point is that causal
dependences can be fitted VERY accurately, non-causal - cannot.
Of course, you can also right your own IFFT procedure to find the time
domain response and see if it has something at t<0. However, make sure that
your frequency response is not 'truncated' otherwise this IFFT will always
give you nonzero output for negative time.

> 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.

Agree. Any matrix-value function (like L,C, etc.) must be causal in order to
form causal PUL Z or Y matrices. If G is linear (real part!) then there
should also be defined some behavior for imaginary part, not just left zero,
otherwise the model is non-causal. The common error is that they provide
only real part that describes the changing with frequency inductance or
capacitance or conductance and forget about imaginary part.

A good transmission line algorithm must be able to analyze causality of the
tabulated matrix data and if necessary, restore causality, e.g. by restoring
missing imaginary parts.

Vladimir


Msg: #7 in digest
Date: Tue, 24 Apr 2007 21:26:06 -0400 (EDT)
From: Sam Sam <si.rules@xxxxxxxx>
Subject: [SI-LIST] Transmission Line Causality

Hi,
  =3D20
  =3D20
  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.=3D20
  =3D20
  =3D20
  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.
  =3D20
  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.=3D20
  =3D20
  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 =3D3D R+j*w*L.And then trying to match the original L data =3D
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...
  =3D20
  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.
  =3D20
  =3D20
  Sam

      =3D20

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