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

• From: Eric Bogatin <eric@xxxxxxxxxxxx>
• To: SI list <si-list@xxxxxxxxxxxxx>
• Date: Tue, 07 Jan 2003 11:20:54 -0600

```Andy, and others-

Inductance is one of the most confusing topics in signal
integrity because we more often than not use the term with
out a preface qualifier. One person says "inductance" and
really means loop self inductance, while another person says
"inductance" and really means partial mutual inductance. We
must get in the habit of using the correct qualifier and
there will be no ambiguity or confusion.

Here is my list of the various types of inductance, each of
which is precisely defined with no ambiguity.

The various "flavors" of inductance:

loop self inductance
loop mutual inductance

partial self inductance
partial mutual inductance

total, or net or effective inductance

To save space, I refer interested folks to read the various
papers I've written on inductance or attend our Fundamental
Principles Course (#122) where all the details are spelled
9, 29, 32, 33, 72, 80, 81, 83, 88, 94

--eric

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Msg: #4 in digest
Subject: [SI-LIST] Re: How to calculate the resistance and
inductance of vias
Date: Mon, 6 Jan 2003 10:41:11 -0500
From: "Ingraham, Andrew" <Andrew.Ingraham@xxxxxx>

Greg Edlund and Rich Peyton are 100% correct ... you must
look at the
whole current path as a loop ... include return paths in the
inductance
calculation.  These formulas are for the partial inductance.
The total
loop inductance could be much greater or much less.

As to where these formulas come from ... I believe there are
no closed
form solutions to all but the simplest of inductance
problems.  Thus,
almost all inductance formulas you see, are approximations,
derived

Any approximation has some region over which it fits the
actual data
reasonably well, and regions where it doesn't.  Sometimes
pairs of
formulas like this one, are meant to apply over two
different ranges of
values.  Sometimes one formula was an improvement over the
other.  And
occasionally a formula is just plain wrong, but it continues
to be

Off-hand, I know nothing about the origins of these two
formulas.  They
might be perfectly good approximations, given their
limitations.  They
are no good without knowing their limitations.

Regards,
Andy

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