# [SI-LIST] : The impedance looking into the power/ground plane structure

From: Raymond Y. Chen ([email protected])
Date: Fri Jun 09 2000 - 13:12:18 PDT

Michael,

There are vias connected to the power/ground planes. When we measure the
"driving point impedance", we are measuring a structure consisting of planes
and vias. The impedance looking into an ideal infinite large power/ground
plane will be the characteristic impedance of a radial transmission line,
which can be analytically obtained as:

Z0(a)=(j*n*d)/(2*pi*a)*H02(ka)/H12(ka)

where n is the wave impedance of the medium between the power/ground planes,
a is the via radius, k is the wave number. H02 and H12 are the zeroth and
the first order Hankel's function of the second kind. Therefore your
"driving point impedance" depends on the via radius.

For a finite size power/ground plane structure, the input impedance looking
into a port(via location) depends upon plane size, via locations, via radii,
and other parameters. The impedance can only be found by numerically solving
Maxwell equations or by measurement.

For more information about the impedance looking into the power/ground plane
structure, please refer to
"Modeling of Power/Ground Plane Noise in High-Speed Digital Electronics
Packaging," IEEE 2nd EPEP Conference Proc., Oct. 20-22, 1993.
"Modeling of Delta-I Noise in Digital Electronics Packaging," 1994 IEEE
Multi-Chip Module Conference, Conference Proc., pp. 126-131, Mar.
15-17,1994.

Actually, three years ago, on SI-list there are discussions on power/ground
plane impedance, and I posted a message on "The Facts about the Input
Impedance of Power and Ground Planes", you can find it at the following

and other related information about power/ground modeling/measurement at
http://www.sigrity.com/support.htm

Raymond Y. Chen
Vice President, Products and Services
*-------------------------------------------------------
* Sigrity, Inc. Tel: 408.377.2180
* 2105 Hamilton Ave. Suite 310 Fax: 408.377.2565
* Santa Clara, CA 95125 Web: www.sigrity.com
*-------------------------------------------------------

>-----Original Message-----
>From: [email protected]
>[mailto:[email protected]]On Behalf Of Chan, Michael
>Sent: Friday, June 09, 2000 10:03 AM
>To: 'Doug'; [email protected]
>Subject: RE: [SI-LIST] : Upper limit of interplane capacitance
>
>
>I would like to point out that what would be the impedance look like when
>you looks at it from the center of the two plates viewing from the top? Can
>you still qualify it as a rectangular wave guide as the wave is spread out
>in
>360 degree other than in one particular direction. Instead of
>calling it the
>
>traditional "characteristic impedance" I would prefer to see it as
>" driving
>
>point impedance". Any comment from any guru ????
>
>
>Michael Chan
>
>
>-----Original Message-----
>From: Doug [mailto:[email protected]]
>Sent: Friday, June 09, 2000 11:36 AM
>To: [email protected]
>Subject: Re: [SI-LIST] : Upper limit of interplane capacitance
>
>
>> Larry Miller wrote:
>>
>> Dr Howie Johnson did an article on this sometime back.
>>
>> Here is an excerpt. See what you think:
>
>What would people expect the characteristic impedance
>to be of a 4" x 6" x 4mil FR-4 structure?
>
>Parallel plates are just two dimensional transmission
>lines with L and C being in units of H/area and F/area.
>The equations pop out pretty much the same as a one
>dimensional transmission line, i.e.
>
> vprop = 1/sqrt(LC)
> Z0 = sqrt(L/C)
>
>In fact, there's some pretty neat derivations
>for parallel plates such as
>
> Z0 = sqrt(mu/epsilon)*d/w
>
> d = distance of separation
> w = width
>
>ignoring fringing effects.
>
>Just was wondering if anyone has done any
>research into correlating pure theory
>versus reality.
>
>- Doug McKean
>
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