# [SI-LIST] Re: How to calculate the resistance and inductance of vias

• From: Steve Corey <steven.corey@xxxxxxxxxxxxxx>
• To: si-list <si-list@xxxxxxxxxxxxx>
• Date: Mon, 06 Jan 2003 13:39:24 -0800
```Hi Robert -- your statement below could imply that circuit theory is
only useful on electrically small objects such as vias.  A more rigorous
statement is that a second-order lumped element circuit (one R, one L,
one G, one C) can in general only be used to model an object which is
electrically small.  This statement falls directly out of the
quasistatic field approximation which you have mentioned below.

General circuit theory is far more broad than this, and higher order
circuits can accurately model electrically large structures.  For
example, the last decade's work on model order reduction has been based
on this premise.

Another example would be quasi-TEM transmission line models such as the
HSpice W element.  It is nodal and it is based on voltage and current,
so it falls neatly into the purview of circuit theory, yet it can be
used to represent electrically long transmission lines.

-- Steve

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

email: steven.corey@xxxxxxxxxxxxxx
phone: (503) 246-2272
fax:   (503) 246-2282
-------------------------------------------

Robert Friedman wrote:

>
> With all that there is a rule when circuit theory is used in regards to the
> wavelength of a field.  Circuit theory holds for dimensions much smaller
> that the electromagnetic wavelength of the frequency of the signal.  So if
> the highest frequency considered is 50 Mhz, the wavelength is 6 meters.  The
> dimensions of a printed circuit board is typically smaller than a tenth of a
> wavelength which is is 60 cm.  Since the field strengths across the via are
> constant at any one time, one can use a quasi-static approximation with very
> good accuracy.
>

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