RE: [SI-LIST] : Spreading Inductance?

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From: Larry Smith ([email protected])
Date: Thu Aug 17 2000 - 15:48:04 PDT

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

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
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...

Larry Smith
Sun Microsystems

> X-Sent: 17 Aug 2000 21:38:44 GMT
> From: "Mary" <[email protected]>
> To: <[email protected]>
> Subject: RE: [SI-LIST] : Spreading Inductance?
> Date: Thu, 17 Aug 2000 16:38:44 -0500
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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: [email protected]
> [mailto:[email protected]]On Behalf Of Larry Smith
> Sent: Thursday, August 17, 2000 11:30 AM
> To: [email protected]; [email protected]
> 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" <[email protected]>
> > To: [email protected]
> > 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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