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

• From: "Rich Peyton" <p2rich@xxxxxxxxxxxxx>
• To: <si-list@xxxxxxxxxxxxx>
• Date: Mon, 6 Jan 2003 09:47:49 -0500

```I believe it would be "partial Inductance" of the wire, where you are only
looking at one particular area for understanding of changes made.  In
reality that would not be the true self Inductance because you do need a
return path, which affects the value of self inductance other active
conductor paths will affect the self inductance of original also?

* Digital Signal Integrity by Brian Young, pg. 211 - "wires do not have
inductance --- closed loops have inductance."
* What Really is Inductance by Eric Bogatin - Good reading, I got out of PCB
Design Mag/ March 2000, you may be able to download from Gigatest.com.

Rich

-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx]On
Behalf Of Gregory R Edlund
Sent: Monday, January 06, 2003 8:52 AM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] How to calculate the resistance and inductance of vias

Zhangkun,

I have seen forumulas similar to the ones you quoted and have always
wondered how they were derived.  They give answers that are in the
ballpark, but do they really calculate inductance?  My electromagnetics
textbook, "Introduction to Electrodynamics," by David Griffiths, defines
inductance as a property of current LOOPS (page 263).  Self inductance is
the constant of proportionality between the magnetic flux through the loop
and the current.  Since you can't have magnetic flux (integral of B-dot-da)
unless you have a loop, can anyone on the list explain how you can define
the inductance of an isolated cylindrical conductor with no return path?
What assumptions does one have to make?

Greg Edlund
Senior Engineer
Signal Integrity
IBM Engineering and Technology Services
3605 Hwy. 52 N, Dept. HDC
Rochester, MN 55901
gedlund@xxxxxxxxxx

Msg: #1 in digest
Date: Mon, 06 Jan 2003 10:24:26 +0800
From: Zhangkun <zhang_kun@xxxxxxxxxx>
Subject: [SI-LIST] How to calculate the resistance and inductance of vias

Hi all:

Could anyone tell me how to calculate the resistance and inductance of
vias. The frequancy range is from DC to 50MHz.

I have seen two formulars to calculate the inductance of vias. They are
very differenct.
One is from High Speed Digital Design written by Howard Johnson:
L=5.08*h*(ln(4h/d)+1)
L:inductance of via, nH
h:length of via, inch
d:diameter of via, inch

The other is from one paper written by Mark Alexander:
L=5.08*h*(ln(4h/d)-0.75)
L:inductance of via, nH
h:length of via, inch
d:diameter of via, inch

These two formular are different.

Best Regards
Zhangkun
2003.01.06

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