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

• From: "Ken Cantrell" <Ken.Cantrell@xxxxxxxxxxx>
• To: <Andrew.Ingraham@xxxxxx>, "si-list" <si-list@xxxxxxxxxxxxx>
• Date: Mon, 6 Jan 2003 09:15:29 -0700

```Zhangkun,
As far as I know: Andy quote -"I believe there are no closed
form solutions to all but the simplest of inductance problems.", is the
correct answer.  The same goes for via capacitance, and more importantly,
via impedance.  If anyone else on the list comes up with an analytical
solution, I'd love to hear about it.
Ken

-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx
[mailto:si-list-bounce@xxxxxxxxxxxxx]On Behalf Of Ingraham, Andrew
Sent: Monday, January 06, 2003 8:41 AM
To: si-list
Subject: [SI-LIST] Re: How to calculate the resistance and inductance of
vias

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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