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# Method for Modeling the Skin Effect in Inductance Calculation Programs

IP.com Disclosure Number: IPCOM000117026D
Original Publication Date: 1995-Dec-01
Included in the Prior Art Database: 2005-Mar-31
Document File: 4 page(s) / 104K

IBM

## Related People

Frech, R: AUTHOR [+4]

## Abstract

Disclosed is a method for modelling the skin effect in the IBM* inductance analysis program COSMIC/L3D:

This text was extracted from an ASCII text file.
This is the abbreviated version, containing approximately 52% of the total text.

Method for Modeling the Skin Effect in Inductance Calculation Programs

Disclosed is a method for modelling the skin effect in the IBM*
inductance analysis program COSMIC/L3D:

A single bar is substituted by 4 conductors, where the cross
section is defined by the skin depth.  In contrast to the implemented
algorithm, this method is numerically more stable for high
frequencies as will be demonstrated by some examples.  Here, an
accuracy improvement of up to 48 % could be achieved for the mutual
couplings.  This method is also applicable to arbitrary inductance
calculations programs, when being incorporated into the source code.

Description - Calculation of inductances from three-dimensional
conductor geometries is a crucial problem in VLSI packaging designs
to determine the system performance and the noise coupling.  In
general, this is done by integrating the Green's function
where L(ij) denotes the mutual inductance between conductor i and
conductor j, a(i) and a(j) are the cross section areas
perpendicular to the current direction, L(fij) is the filament
inductance, &mu.  is the permeability constant, r(ij) is the euclid
distance between point i and j, I(i) and I(j) are the normal
vectors to the current direction.  Equation (2) is only correct, if a
uniform current distribution is given.

For high frequencies it is well known that the current
distribution increases at the conductor's surfaces.  This is
expressed by the skin depth d given by

(3)
with the specific resistance &Rho.  of the material and the frequency
f.  Within the skin depth d the current has decreased by 63 %.  This
effect leads to significant deviations from the dc results of
equation (1) and (2).  The COSMIC program L3D, which calculates the
inductances from a three-dimensional geometry, implements the skin
effect by "subtracting" an innerconductor, whose geometries are
determined by the skin depth.  For a mutual inductance between two
conductors 1 and 2 this leads to
where a(10) and a(20) are the cross sections of the inner
conductors.

Four-Bar Substitution and Improvement Results

Equatio...