## [SI-LIST] Re: SSO pushout, ground bounce definition

• From: Steve Corey <steve@xxxxxxxxxxxxxx>
• Date: Wed, 24 Apr 2002 09:43:28 -0700

```Mark -- I would like to propose a nomenclature change as well.  Circuit
theory is little more than techniques for analyzing ordinary
differential equations, and as such is a complete subject.  (Of course,
distributed as well as lumped techniques, so they supersede this more
common definition.)  In the same sense, E/M theory consists to a large
degree of techniques for analyzing partial differential equations.
Based on your example, it seems like you are really pointing out the
perceived inability of lumped circuit elements to represent distributed
structures at "high" frequencies.  This is a modeling issue, and in my
opinion, experience, and research, lumped elements (R,L,C,K netlist) are
quite capable of representing a distributed structure up to an arbitrary
cutoff frequency.  I will explain below:

Lumped element representation is little more than the spatial
discretization of Maxwell's equations.  As Francis has implied, this
transforms the partial differential equations into ordinary differential
equations.  The finer your discretization, the higher the cutoff
frequency to which your results will be accurate.  Not surprisingly,
spatial discretization (i.e., meshing) is the starting point for a
typical 3-D field solver -- the first thing that it does is confine its
quantities of interest to certain basis structures and assume a
distribution on each structure.  In its discretization process, the
field solver has now also limited the accuracy of its results to below a
certain cutoff frequency.  So if a lumped-element discretization is
incapable of representing a structure, a field solver will suffer from
the same type of innacuracy.

Your example of using coupled inductors to represent connector pins is
essentially a first-order approximation, where zeroth order would be
simply using a single resistance.  Being a first-order approximation, it
is not surprising that it has limited bandwidth.  Again, not because
lumped elements are incapable of a higher bandwidth representation, but
because of the coarseness of the model.  Finer discretizations of the
problem space result in accuracy at higher frequencies, and yes, you can

I guess the point I want to make is that lumped-element representations
and distributed representations are far more similar than they are
different, for the same reason that linear ODE's are very similar to
linear PDE's.  Furthermore once Maxwell's equations are discretized
spatially, both approaches are mathematically equivalent.  I think the
perceived discrepancies result from a communication gap between the two
worlds (E/M vs. circuits).  Due to higher bandwidths in digital systems,
these two worlds are only recently starting to come into contact on any
sizable scale, and some miscommunication is to be expected.

I think it's important to point out where a pure distributed
representation has capabilities not available via a lumped-element
representation:  this is when we need an "exact" analytical solution
which is continuous in the spatial domain, no discretization allowed.  A
lumped circuit cannot provide us with this information for a general
structure, and not surprisingly, neither can a field solver.  But to be
honest, the last time I calculated the analytical field distribution on
a conducting wedge illuminated by a plane wave was in a graduate E/M course.

-- Steve

-------------------------------------------
Steven D. Corey, Ph.D.
Time Domain Analysis Systems, Inc.
"The Interconnect Modeling Company."
http://www.tdasystems.com

email: steve@xxxxxxxxxxxxxx
phone: (503) 246-2272
fax:   (503) 246-2282
-------------------------------------------

mark.gailus@xxxxxxxxxxxx wrote:

>
> Dear Francis,
>
> (1) I agree with your criticism of the use of the term "fluctuation" for
> this phenomenon.  It does have special meanings in other areas of physics,
> and for that reason should not be used in this case.  However, I still
> agree with Raymond Chen that "ground bounce" is a misleading and, I think,
> even a nonsensical term.  Perhaps "power/ground noise", "power/ground
> transients", or even "power/ground bounce" would be an improvement.  "SSO",
> etc, are also OK with me.  What do other SI-Listers have to say? The
> crucial point here, I feel, is that it is not an effect that is determined
> by the configuration of "ground" conductors or ground currents alone, but
> by the interaction of ground conductors with signal and power conductors
> and currents, etc.
>
> (2) With regard to uniqueness of voltages, you have encouraged me to
> clarify my thoughts -- thank you -- that is always a good thing -- and I
> agree that my terminology was imprecise.
>
> Let's see if I can be any clearer today:
>
> I agree that in an actual physical circuit, Electric and Magnetic Fields
> and Fluxes (as well as charges and currents) are uniquely determined.
>
> Where I think there are pitfalls, is in the "mapping" of a transient
> electromagnetic problem such as SSO, into the more restricted types of
> descriptions allowed by circuit theory.
>
> In electromagnetics we can separate an arbitrary electric field into
> conservative (i.e, curl free) and purely nonconservative components, and
> speak of the path integral of one as "potential difference" and the other
> as "voltage" or "electromotive force".
>
> (Typically, this electromotive force might involve something like a
> chemical battery, or something like a conductor placed in a region with a
> changing magnetic field, such as  the secondary of a transformer, or the
> various pins of a device package, connector, etc.  There is an nice short
> discussion of "voltage" or "electromotive force" versus "potential
> difference" at the start of Chapter 11-1 on Faraday's Law, in  the book
> "The Electromagnetic Field", by Albert Shadowitz, Dover Publications. )
>
> It is a common practice to model the set of conductive pins in a device
> package or a connector as coupled inductors.  Up to some frequency, a set
> of coupled inductors includes the effects of electromotive forces caused by
> changing currents in these same inductors, and if expanded into a lumped or
> distributed multiconductor transmission line model includes the effects of
> electromagnetic waves travelling "along" the intended transmission
> direction.  However, by itself, neither model includes the effects of
> electromotive forces in these same conductors associated with radiating
> fields from the whole set of conductors, or with "externally" incident
> fields on the outside of the set of conductors, or in other words, "common
> mode" effects. This omission can give rise to differences of certain
> predictions of these circuit theory models versus the real system.
> Accuracy of agreement depends upon whether these differences are important
> to the particular results being sought in the simulation. These common mode
> effects, by definition, may produce roughly the same electromotive force
> along all power, ground, and signal conductors in the "length" of the
> interconnection, and therefore substantially "cancel out" in calculation of
> "voltage differences" between various conductors at one or the other end of
> the interconnections.
>
> The result is that of the various voltages measureable in the simulation
> circuit, some accurately match the real world, and some do not.  As you
> said, it is a separate problem to determine which "voltages" we can
> measure.  Even here, I think, the ones we can most easily measure are
> exactly those which are more "automatically" in agreement between the
> circuit model and the real world.
>
> (You can tell -- I am still thinking.)
>
> Thanks and best egards,
>
> Mark Gailus
>
>
>
>
> "Kai, Francis" <francis.kai@xxxxxxxxx>@freelists.org on 04/19/2002 06:20:20
> PM
>
>
> Sent by:  si-list-bounce@xxxxxxxxxxxxx
>
>
> To:   "'mark.gailus@xxxxxxxxxxxx'" <mark.gailus@xxxxxxxxxxxx>,
>       chen@xxxxxxxxxxx
> cc:   si-list@xxxxxxxxxxxxx, "Kai, Francis" <francis.kai@xxxxxxxxx>
>
> Subject:  [SI-LIST] Re: SSO pushout, ground bounce definition
>
>
>
> Dear Gurus,
>
>      I do not agree with Mark on certain concepts listed below, however,
> any
>
>
> (1) "Fluctuation" has a quite different meaning if you agree with the
> concept
> in Statistical Mechanics or Thermodynamics. The "Fluctuation theory"
> phenomena
> do differ from the "ground bounce" effect occurred in signal integrity.
> Therefore, if we want
> to be consistent with physics (or physical concepts), the term
> "Power/ground
> fluctuation" will
> not be as nice as "ground bounce" in signal integrity.
>
> (2) I do not see the term "voltages" is not "uniquely defined". All those
> theorems,
> Ohms Law, Tellegen theorem, Maxwell Equations, do represent that voltages
> are well-defined uniquely in an Electrical System. These theorems satisfy
> the ODE (ordinary differential equations) and PDE (partial differential
> equations)
> and are well-posed. Therefore, "uniqueness" is guaranteed. There is no
> theorem
> to prevent voltages to be measurable, like Heisenberg's Uncertainty
> Principle in
> quantum mechanics. However, whether Mark or any other engineers/technicians
> can
> accurately measure those voltages is a different story.
>
> Best regards,
>
> Francis Kai
>
> -----Original Message-----
> From: mark.gailus@xxxxxxxxxxxx [mailto:mark.gailus@xxxxxxxxxxxx]
> Sent: Friday, April 19, 2002 2:06 PM
> To: chen@xxxxxxxxxxx
> Cc: si-list@xxxxxxxxxxxxx
> Subject: [SI-LIST] Re: SSO pushout, ground bounce definition
>
>
>
>
> Raymond,
>
> Thanks for a very clear presentation.  I agree with you on all points,
> especially the following:
>
> (1) "Power/ground fluctuation" is a much clearer term than "ground boun=
> ce",
> which is always misleading and should not be used.
>
> (2) In the real world and in EM theory, "voltages" (i.e., differences o=
> f
> electric potential) are frequently not uniquely defined or measurable,
> particularly between "distant" points or where radiation can take place=
> .
>
> (3) With respect to multiconductor transmission lines: "Voltage drop al=
> ong
> the ground conductor (except DC) is not well defined based on EM theory=
> ."
>
> I will add a couple of generic observations:
>
> Much confusion and mischief results when inappropriate oversimplified
> circuit-theory models are applied to electromagnetic problems.
>
> There is wisdom in the microwave engineers' dictum that "there is no su=
> ch
> thing as ground".
>
> Best regards,
>
> Mark Gailus
>
>
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