**From:** Larry Smith (*ldsmith@lisboa.eng.sun.com*)

**Date:** Thu Aug 17 2000 - 15:48:04 PDT

**Next message:**Istvan Novak - Board Design Technology: "RE: [SI-LIST] : Decoupling capacitors (again!)"**Previous message:**Todd Westerhoff: "[SI-LIST] : Free NetSeminar - "Closing the Loop Between System Timing and Signal Integrity Analysis""**Maybe in reply to:**Bob Perlman: "[SI-LIST] : Spreading Inductance?"

Mary - I'll probably have to take the credit or blame for coining the

phrase "spreading inductance" or inductance that comes of units of

"ohms per square". I began using that terminology in a paper at

the 1994 EPEP conference: "Decoupling Capacitor Calculations for CMOS

Circuits".

The phrase shows up again in a 1998 EPEP paper by Tanmoy Roy and

myself: "ESR and ESL of Ceramic Capacitor Applied to Decoupling

Applications". In that paper, we show the spreading inductance for

several power plane dielectric thicknesses and from several positions

on the power planes. From the center of the board the current has 4

ways to escape. It has 3 ways to escape from the edge and 2 ways to

escape from the corner. There is a measurable change in decoupling

pad mounting inductance depending on the position on the board. We

have good model to hardware correlation for this using our plane

simulator. The spreading inductance can vary from over 400 pH for a

corner position and 14 mils dielectric thickness, to less than 20 pH

for a center position on 2 mil dielectric planes. Quite a wide

variation. I have intended to write a paper on this but never got

around to it. So, here it is on si-list. I hate to keep plugging it,

but these papers are on Ray Andersons's web site at

http://www.qsl.net/wb6tpu/si_documents/docs.html

same site as the si-list archives.

Spreading inductance will show up again in a paper at EPEP 2000:

"Power Plane Spice Models for Frequency and Time Domains." We get most

of our data from simulation of these models. By stimulating the planes

at a point with a 1 amp current source, you see an inductive up-slope

with frequency. The slope has an equivalent inductance that is the

spreading inductance. Hopefully I will get a chance to do a follow-up

journal paper from the EPEP conference that will clearly document this

concept for critical review.

The spreading inductance is completely independent of the loop

inductance between two vias that access the planes. I think it makes

sense to define an inductive loop that includes the decoupling

capacitor pads and vias to the power planes. The loop is completed on

the top by an imaginary shorting bar across the surface of the pcb and

an imaginary shorting plane midway between the vdd and ground pcb

planes. That way, we do not miss or double count any of the inductance

on the pcb. BTW, there is also an inductance associated with the

capacitor height above the pcb surface.

For your example, vias spaced 10 cm apart would have a large loop

inductance. The inductance is very much related to the loop area which

is the via spacing and the via height. It would also be related to the

via barrel diameter.

Our vias are much closer than this, perhaps 50 mils apart and 10 mils

deep. We get via loop inductances less than 1 nH.

Got to go now, I've spent way too much time on email today...

regards,

Larry Smith

Sun Microsystems

*> X-Sent: 17 Aug 2000 21:38:44 GMT
*

*> From: "Mary" <mary@advocate.net>
*

*> To: <si-list@silab.eng.sun.com>
*

*> Subject: RE: [SI-LIST] : Spreading Inductance?
*

*> Date: Thu, 17 Aug 2000 16:38:44 -0500
*

*> MIME-Version: 1.0
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*> Content-Transfer-Encoding: 7bit
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*> X-Priority: 3 (Normal)
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*> X-MSMail-Priority: Normal
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*> Importance: Normal
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*> X-MimeOLE: Produced By Microsoft MimeOLE V5.50.4133.2400
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*>
*

*> Larry,
*

*>
*

*> I'm having a little trouble with the concept of "spreading inductance".
*

*> Do you have a reference you could provide that defines this concept a
*

*> little more precisely? How is spreading inductance calculated and how
*

*> does it relate to the total inductance of a loop formed with two vias
*

*> and two planes? For example, if I have two vias (0.1 mm dia.) spaced
*

*> 10 cm apart connecting two infinite planes spaced 0.1 mm apart, how do
*

*> I calculate the spreading inductance?
*

*>
*

*> Mary
*

*>
*

*> -----Original Message-----
*

*> From: owner-si-list@silab.eng.sun.com
*

*> [mailto:owner-si-list@silab.eng.sun.com]On Behalf Of Larry Smith
*

*> Sent: Thursday, August 17, 2000 11:30 AM
*

*> To: si-list@silab.eng.sun.com; bobperl@best.com
*

*> Subject: Re: [SI-LIST] : Spreading Inductance?
*

*>
*

*>
*

*> Bob - spreading inductance is something like spreading resistance for a
*

*> sheet of conductive material. Most of us are familiar with resistance
*

*> in ohms/square. If you have a strip (sheet) of conductive material
*

*> with a length and width, the resistance in the length direction is
*

*> simply L/W * Rs. L/W gives you the number of squares. Multiply that
*

*> by sheet resistance in ohms per square and you get the resistance in
*

*> Ohms. If we have a point source and a point sink with some diameter in
*

*> a sheet of material, the resistance between the two points can be found
*

*> by counting the number of curvilinear squares in series and parallel
*

*> and calculating the resistance. This is often called a spreading
*

*> resistance problem. The physics has a lot to do with current traveling
*

*> through a conductive material. Well, that is the concept.
*

*>
*

*> It turns out that we can do exactly the same thing for inductance of a
*

*> power plane pair and call it spreading inductance. The physics is no
*

*> longer related to conductivity but rather permeability. As current
*

*> spreads out on the voltage plane (and an opposite current "spreads in" on
*

*> the ground or return plane), it creates a magnetic B field between the
*

*> planes. Inductance is essentially a measurement of the energy stored
*

*> in this B field.
*

*>
*

*> Think of the power plane pair as a bunch of transmission lines with a
*

*> width and thickness, divided up into long narrow strips. It is easy to
*

*> think of capacitance per inch of these transmission line strips. There
*

*> is a velocity associated with the transmission lines strips that is
*

*> sqrt(L/C) where L is inductance per inch and C is capacitance per
*

*> inch. So if you know the velocity and capacitance, you know the
*

*> inductance. Extend these 1 dimensional transmission lines concepts to
*

*> two dimensional power planes and you get capacitance per square inch
*

*> and inductance per square (a lot like ohms per square). Inductance per
*

*> square is the spreading inductance. Attached is another email from
*

*> last march on the same subject.
*

*>
*

*> regards,
*

*> Larry Smith
*

*> Sun Microsystems
*

*>
*

*> > From: "Bob Perlman" <bobperl@best.com>
*

*> > To: si-list@silab.eng.sun.com
*

*> > Date: Wed, 16 Aug 2000 16:40:53 -0700
*

*> >
*

*> > Hi -
*

*> >
*

*> > I've seen the term "spreading inductance" used repeatedly here.
*

*> > Would someone be so kind as to define it?
*

*> >
*

*> > Thanks,
*

*> > Bob Perlman
*

*>
*

*>
*

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**Next message:**Istvan Novak - Board Design Technology: "RE: [SI-LIST] : Decoupling capacitors (again!)"**Previous message:**Todd Westerhoff: "[SI-LIST] : Free NetSeminar - "Closing the Loop Between System Timing and Signal Integrity Analysis""**Maybe in reply to:**Bob Perlman: "[SI-LIST] : Spreading Inductance?"

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