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# Algorithm to Efficiently Reduce Inductive Networks to Simplified Equivalent Circuits

IP.com Disclosure Number: IPCOM000099366D
Original Publication Date: 1990-Jan-01
Included in the Prior Art Database: 2005-Mar-14
Document File: 1 page(s) / 36K

IBM

## Related People

Huang, CC: AUTHOR

## Abstract

An algorithm has been developed which reduces the running time of an earlier developed computer program.

This text was extracted from an ASCII text file.
This is the abbreviated version, containing approximately 77% of the total text.

Algorithm to Efficiently Reduce Inductive Networks to Simplified Equivalent Circuits

An algorithm has been developed which reduces the running
time of an earlier developed computer program.

Existing software, to simplify a large inductive network,
follows the following algorithms (*). If
(L)(IB) = (VB)                              (1)
(A)T(VN) = (VB)                             (2)
(A)(IB) = (IN)                              (3) then

(VN) =  (A)(L)-1(A)T -1(IN)                    (4) Here, L =
inductive matrix, IB = branch current, VB = branch voltage, A =
incidence matrix, IN = nodal current, VN = nodal voltage, AT =
transpose of A, and IB = derivative of IB .

The foregoing is very CPU time-consuming because it is
necessary to invert a fully-populated matrix, L, and then perform the
triple product AL-1AT .

The proposed algorithm solves the following equation for IB
first:

(L)(IB) = (A)T(VN)                           (5) then IB is
substituted into equation (3) to obtain IN .  If we let VN be an
identity matrix of order m, where m = number of nodes, then the
calculated IN is the same as AL-1AT .

The existing software inverts the whole matrix L that requires
n forward and backward substitutions, where n = number of elements.
With the proposed sche...