Globally convergent algorithms for dc operating point analysis of nonlinear circuits

Abstract

An important objective in the analysis of an electronic circuit is to find its quiescent or DC operating point. This is the starting point for performing other types of circuit analysis. The most common method for finding the DC operating point of a nonlinear electronic circuit is the Newton-Raphson method (NR), a gradient search technique. There are known convergence issues with this method. NR is sensitive to starting conditions. Hence, it is not globally convergent and can diverge or oscillate between solutions. Furthermore, NR can only find one solution of a set of equations at a time. This paper discusses and evaluates a new approach to DC operating point analysis based on evolutionary computing. Evolutionary algorithms are globally convergent and can find multiple solutions to a problem by using a parallel search. At the operating point(s) of a circuit, the equations describing the current at each node are consistent and the overall error has a minimum value. Therefore, we can use an evolutionary algorithm to search the solution space to find these minima. We discuss the development of an analysis tool based on this approach. The principles of computer-aided circuit analysis are briefly discussed, together with the Newton-Raphson method and some of its variants. Various evolutionary algorithms are described. Several such algorithms have been implemented in a full circuit analysis tool. The performance and accuracy of the evolutionary algorithms are compared with each other and with NR. Evolutionary algorithms are shown to be robust and to have an accuracy comparable to that of NR. The performance is, at best, two-orders of magnitude worse than NR, although it should be noted that time-consuming setting of initial conditions is avoided.

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ORCID for Mark Zwolinski: orcid.org/0000-0002-2230-625X

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