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# Transforming Relative Branch Networks to Physical Counterparts

IP.com Disclosure Number: IPCOM000121028D
Original Publication Date: 1991-Jul-01
Included in the Prior Art Database: 2005-Apr-03
Document File: 2 page(s) / 58K

IBM

Raver, N: AUTHOR

## Abstract

In package analysis, inductance matrices are simplified by transformation using network theory algorithms [*]. For example, Fig. 1 shows a general inductance network, and Fig. 2 shows the simplified and transformed result, which is always in relative branch form. This transformed result almost does not correspond to the original physical metal. For example, the analysis might require study of the current from node N1 to node N2. A general method is described to transform the resultant relative branch network to one specified by the user.

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Transforming Relative Branch Networks to Physical Counterparts

In package analysis, inductance matrices are simplified
by transformation using network theory algorithms [*].  For example,
Fig. 1 shows a general inductance network, and Fig. 2 shows the
simplified and transformed result, which is always in relative branch
form.  This transformed result almost does not correspond to the
original physical metal. For example, the analysis might require
study of the current from node N1 to node N2.  A general method is
described to transform the resultant relative branch network to one
specified by the user.

In the following discussion, inductance networks will appear in
two forms, branch network and relative branch network.  Fig. 1 shows
a general branch network, for which branch voltages are measured
across each branch.  Fig. 2 shows a relative branch network, for
which all branch voltages are measured from any node to the reference
node.

Assume we have a general branch network for which we can
specify the following matrices:
(A)is the incidence matrix
(AT)is the transpose of the incidence matrix
(MBG)is the inductance matrix
(MBG)1 is the inverted inductance matrix

It can be shown that we can transform to a relative branch
network with the calculation:
(1) [LMRB] = [[A][LMBG]-1[AT]-1]-1

Now suppose we want to transform the re...