# RE: [SI-LIST] : Spreading Inductance?

From: Mary ([email protected])
Date: Thu Aug 17 2000 - 14:38:44 PDT

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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