From: Steve Corey (firstname.lastname@example.org)
Date: Fri Apr 13 2001 - 11:30:07 PDT
What Paul says is true, that skin effect always causes frequency-dependent
inductance. The finite conductance of the metal, which allows it to
support E-fields, which are modeled by skin effect resistance, also allows
it to support H fields internally, which are modeled by skin-effect
inductance. Any model or equation which does not contain both is
non-physical, since by ignoring existing magnetic fields internal to the
conductor, it causes the model to not conserve energy. In terms of
simulation algorithms, a model which is an energy source opens the door to
I can't speak directly for the HSpice W element, since Avant!
understandably doesn't publish the internals of its implementation.
However, in earlier threads on this list, some of the developers have
mentioned that in HSpice time-domain simulations using the sqrt(w)
equation, the results are actually tweaked as part of the algorithm in
order to ensure causality, which is why their results agree with
measurement. (This was also given as the reason why their frequency-domain
results (untweaked) would not transform exactly back to their (tweaked)
Regarding sqrt(w) vs. sqrt(w)*(1+j) to represent conductor internal
impedance, it is worth noting that according to Clayton R. Paul's "Analysis
of Multiconductor Transmission Lines", both are approximations, not exact
analytical derivations. There are only certain geometries for which
derivations of skin-effect dependencies actually result in closed form
expressions, and these are typically bessel or other transcendental
functional relationships. Most of them do not result in closed-form
expressions at all, but are instead approximated by the above square root
dependencies, or numerically extracted by a solver. So neither expression
is analytically "exact", but using sqrt(w) with no modification is
guaranteed to introduce phase error. In many narrow-band frequency-domain
simulations and designs, the phase error is usually small since the small,
decreasing internal inductance is swamped by the external inductance at
higher frequencies. (Given various frequencies and geometries, either
model may be more accurate than the other.) However, in inherently
broadband time-domain simulations, the phase error _will_ show up, and a
potentially non-causal model is considered unacceptable. Not only does it
disagree with the laws of physics, but it looks silly to the average
The bottom line for any model is how well it compares against data from the
actual system or range of systems it is meant to represent. Since any
non-trivial simulation model is actually just an approximation of the
physical system it represents, the only answer is to find the least painful
way to verify your models for the types of systems which you are
simulating. (This ranges from asking your friends to doing full
verification against measurement.) You will quickly find out which models
are sufficient for your purposes and which are not.
Steven D. Corey, Ph.D.
Time Domain Analysis Systems, Inc.
"The Interconnect Modeling Company."
phone: (503) 246-2272
fax: (503) 246-2282
"Degerstrom, Michael J." wrote:
> I've noticed that w-element eye-diagram simulations show
> very minimal jitter whereas your statements below suggest
> to me that there should be jitter due to the internal inductance
> effect. I haven't used the HSPICE w-element model for
> a year or so but I have a technique to extract RLCG as
> a function of frequency and the inductance was flat. I haven't
> tried this yet for the new HSPICE w-element model with tabulated
> RLCG vs. frequency.
> I haven't directly looked into the lossy line equations but
> in working with someone who has my impression was that the 1+j
> factor was needed to provide a causal response. Also I thought
> that the HSPICE w-element lossy line algorithm used the
> 1+j but it somehow does not affect the inductance versus frequency.
> Mike Degerstrom Email: email@example.com
> Mayo Clinic; 200 1st Street SW ; Rochester, MN 55905
> Phone: (507) 538-5462 FAX: (507) 284-9171
> WWW: http://www.mayo.edu/sppdg/sppdg_home_page.html
> > -----Original Message-----
> > From: Paul Levin [mailto:firstname.lastname@example.org]
> > Sent: Thursday, April 12, 2001 6:32 PM
> > To: email@example.com
> > Subject: [SI-LIST] : Attenuation and Delay on a PCB Trance
> > To all concerned,
> > Besides the attenuation effects on PCB traces, don't forget that the
> > propagation
> > delay is a function of frequency EVEN IF EPSILON-R IS CONSTANT.
> > Few people realize that skin effect resistance is only a
> > portion of the
> > skin effect
> > impedance. The Rs figure must really be multiplied by (1+j). This
> > inductive
> > reactance means that there is a bit more inductance
> > (diminishing as the
> > frequency
> > increases.) Because of this, lower frequencies propagate more slowly
> > than
> > higher frequencies.
> > This effect has nearly disappeared by the time one gets to 1
> > GHz, but 1
> > and 2
> > Gbps data signals have frequency components much lower than a GHz.
> > Consider
> > Fibre Channel's "alternating disparity K28.5 pattern." This 20 bit
> > pattern has
> > quite a bit of energy at 1/20th of the data rate. Some others
> > have told
> > me that
> > they have been able to create some (admittedly pathological) data
> > patterns
> > that resulted in even lower frequency content.
> > Some years ago I computed the Fourier transform of the entire pattern
> > and
> > ran the harmonics through both the attenuation and phase
> > characteristics
> > of
> > microstrip. It surprised people how well I could simulate the
> > asymmetrical
> > eye pattern. The analysis worked for shielded, twisted pair, too.
> > Paul Levin
> > Senior Principal Engineer
> > Logic Innovations, Inc.
> > A Xyratex Company
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