I am the developer of the transmission-line simulation technology used
by several popular simulators including Hspice's W element. Recently, a
number of postings in this reflector pointed out a discrepancy between
the ac and transient responses of W elements with frequency-dependent
loss. Although I am no longer with Avant!, I would like to respond in
defense of my algorithm.
The answer may surprise you... It is supposed to be this way. And it
does not indicate accuracy problems with either ac or transient model.
This is a quite interesting phenomenon, and I would like to explain it
here.
It is caused by non-physical nature of the Sqrt(f)*Rs skin-effect and
f*Gd dielectric-loss equations. They are lacking imaginary parts, or
the corresponding frequency dependence of L and C. Real and imaginary
parts of any analytic complex function cannot be arbitrary but are
uniquely related by Riemann-Cauchy equations. This is not obvious, as
one may envision specifying arbitrary unrelated functions for the real
and imaginary parts (and have done so in this case). But there are laws
for everything.
As a result, transient responses of transmission lines with Sqrt(f)*Rs
and f*Gd loss are non-causal, i.e. the response starts before the
excitation is applied. If you take FFT of the W-element's ac waveforms,
you can observe signal traveling faster than the speed of light, but it
is a mathematically accurate frequency-domain solution.
To assure correctness and accuracy of the transient solution, I change
the frequency response as to restore the correct relationship between
the real and imaginary parts. This is why the frequency responses of ac
and transient models are different.
The corrective change depends on line length. This creates another side
effect, a slight difference between transient responses of segmented and
unsegmented lines. The difference is small, as the correction affects
primarily higher frequencies at which both transmission-line responses
and excitation spectrum are significantly attenuated.
The transient model is just as accurate for non-zero Rs and Gd as it is
for constant loss, but with respect to the corrected frequency
response. In fact, I use the same frequency-dependent algorithm for
both cases. The accuracy is not improved by segmenting the line or
changing .option RISETIME from it's actual value. It is important to
set this option, especially for longer lines with low loss.
Another popular skin-effect equation, Sqrt(j*2*f)*Rs, has correct
real/imaginary part relationship and does not require correction.
However, its inductive component is L(f)=Lo+Rs/(2*Pi*Sqrt(f)), which
produces infinite inductance at dc, and causes other interesting
phenomena for large Rs.
I do have the solution that eliminates above problems. But I believe
that present Hspice's implementation of my algorithm is still good as it
provides a robust way to achieve simulation results that are very close
to measurements with minimum number of model parameters.
This was verified by many users, I would recommend downloading IMAPS
presentation by Jim Foppiano. It was discussed recently in this
reflector and contains comprehensive comparison of time-domain
measurements and W-element simulations with non-zero Rs and Gd.
I hope you found these comments useful. I have been working hard for 6
years developing my simulation technology, and can say with confidence
that it is by far the most accurate and general transmission-line
simulation method.
Regards,
Dr. Dmitri Kuznetsov
Scott McMorrow wrote:
>
> One might be careful about comparing simulator accuracy to
> Hspice, especially the w-element transmission line model.
> It seems there are some issues with simulating frequency
> dependent loss effect. With the latest release 99.2 they have
> published an app note titled:
>
> "Boosting Accuracy of W Element for Transmission Lines
> with Nonzero Rs or Gd Values"
>
> It is a very interesting paper.
>
> Scott McMorrow
> SiQual
>
>
Mike Degerstrom wrote:
>
> John,
>
> Are you refering to the W-element model instead of the T-element model?
> If so then, WRT the W-element inaccuracies: did you try to adjust the
> .options RISETIME parameter? We've looked at the w-element
> model in some detail and we totally agree that the AC models
> give a very different response than that predicted with the
> transient w-element model. By adjusting the RISETIME parameter
> you can get the transient loss correct at one or two frequencies.
> In general, I think the w-element model can be used with
> good results for modeling of wide-band digital signals. The
> trick is knowing whether you are getting good results or not!
>
> However, this is getting way off the subject of the original
> posting. I suspect the original post was not concerned with losses.
> If that is the case then the w-element does a great job with
> multiple coupled conductors. We often run at least 3 coupled
> conductors together and run many randomly switching bits in
> the simulation. Then we view the resulting eye diagram to
> see the effects of the crosstalk, i.e., coupling modes. It took
> us some time to develop these capabilities. You can, of course,
> use the approach suggested by Dima which is to use convert
> the coupled lines to decoupled lines. In fact, it is probably
> best to start with Dima's approach so you better understand
> the theory instead of just trusting that some fully coupled
> EM result is correctly translated to a fully coupled transmission
> line model.
>
> Mike
>
> On Jul 16, 8:57am, John Williamson wrote:
> > Subject: RE: [SI-LIST] : even-odd mode influence
> > Folks,
> >
> > A comment on HSPICE lossy coupled T-line accuracy. Be careful when using the
> > W-element.
> > We've found that the time and frequency domains do not agree. For example, a
> > set of extracted
> > RLGC parameters resulted in a frequency domain attenuation of -25dB at
> > 10GHz. However when
> > the same model was used in the time domain driven by a 10GHz sine wave, the
> > attenuation was
> > only -8dB. We've found that this can be corrected by dividing the model up
> > into several shorter
> > ones. It's not computationally efficient, but it works fairly well.
> >
> > Regards,
> >
> > jw
> >
> > John M. Williamson, 0V30, Electromagnetic & interconnect technology
> > Nortel Networks
> > (613) 763 3198, ESN 393-3198 E-mail: williamj@nortel.ca
> >
>
>
Jim Foppiano wrote:
>
> Scott,
>
> I presented a workshop paper on simulating Fibre Channel Loss at the
> IMAPS High Speed seminar in January. The simulations were done using the
>
> W element model in HSPICE. I correlated modeled and measured
> results. I would be happy to send you a copy if you wish.
> It is a 10MB Power Point presentation that I have divided
> up into 5 files.
> Regards,
>
> Jim
<
> Jim Foppiano
> Senior Electrical Engineer II
> Microelectronics Technology Center
> Digital Signal Processing Systems
> <jim-foppiano@raytheon.com>
> P.O. Box 660246 M/S 261
> Dallas
> Texas
> 75266
> Pager: 972-597-2053
> Fax: 972-344-3287
> Work: 972-344-288
Tarek Ali - WGS Board Design Technology wrote:
>
> Hi,
>
> If anyone needs to download the imaps presentation please access
> my freedrive account at http://www.freedrive.com.
>
> login: tarek
> password: tarek
>
> And you can download the ppt file from the imaps folder.
> Most email systems will not permit files above 5 Meg, and this
> file is 10 Meg.
>
> Thanks,
>
> Tarek Ali
>
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