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Equation Ordering Algorithm for Nonlinear Circuits

IP.com Disclosure Number: IPCOM000075536D
Original Publication Date: 1971-Oct-01
Included in the Prior Art Database: 2005-Feb-24
Document File: 3 page(s) / 37K

Publishing Venue

IBM

Related People

Cooper, DW: AUTHOR

Abstract

Application. Steady state flow problems of electronics, hydraulics, and magnetics frequently may be approximately modeled as lumped parameter nonlinear circuits. Such circuits may be represented mathematically by Kirkhoff's laws; a combination of flow balance equations and potential difference equations as illustrated above.

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Equation Ordering Algorithm for Nonlinear Circuits

Application.

Steady state flow problems of electronics, hydraulics, and magnetics frequently may be approximately modeled as lumped parameter nonlinear circuits. Such circuits may be represented mathematically by Kirkhoff's laws; a combination of flow balance equations and potential difference equations as illustrated above.

It is desirable to order the evaluation of the describing nonlinear equations so as to reduce the number of variables on which iteration is performed to obtain a solution. In principle for a class of ladder type networks, the equations may be ordered so as to allow iteration on one variable.

This algorithm will order the equations for any cascading type of ladder network for iteration on one variable, so long as the function fa can be represented by a polynomial of degree four or less. A cascading network is defined here as a ladder network where the potential is known at some node on one of the end loops (i.e., all nodes in the above ladder lie on end loops; a ladder with five or more rungs will have nodes which do not appear in end loops). One method of extension of the algorithm to more complex circuits is presented. Nomenclature (Fig. 1) P R phi Electronics Voltage Resistance Current Hydraulics Pressure Resistance Flow Magnetics Potential Reluctance Flux Flow balance equation at a node, Epsilon /phi/(i) = 0 Potential difference equation (see Fig. 2) Form a p(b) = f(a) (phi(i), p(a)) Form b phi(i) = f(b) (p(a),p(b)) A branching node is any node with more than two incident branches. The Algorithm A. To start the algorithm: 1) Mark all nodes of known potential. If only potential difference generators occur in the circuit, then arbitrarily set and mark the potential of a node adjacent to a generator, immediately set and mark the other adjacent node. All other potentials will be relative to the first set potential. 2) Select a branch which (a) is incident to a marked node in one of the end loops. (b) is incident to at least one nonbranching node which may be the node of (a). Estimate the flow in that branch and set the pointer FIRST to that branch. If one node to which that branch is incident is unmarked, use the potential equation (Form a) to find the potential at the unmarked node. Begin step B. B. Check each marked node for the number, k, of unmarked flows either to or from the node. If the node is adjacent to a potential generator and the node across the generator is unmarked, calculate the potential of the unmarked node in the obviou...