SUMMARYA new method for finding the set of all d.c. operating points of non-linear electronic circuits is suggested. it is applicable in the case where the circuit equations are written in the hybrid-representation form. In the general case, the non-linear elements involved may be described by non-monotone continuous characteristics.The method suggested is based on interval analysis techniques. Unlike other non-interval methods, this approach guarantees that all operating points will be found within prescribed accuracy in a finite number of steps.The computational efficiency of the present method is illustrated by a numerical example.
. INTRODUCTIONThe problem of finding the set of all d.c. operating points of non-linear electronic circuits is one of the most challenging problems in non-linear circuit theory. In view of its numerous applications, it has been investigated by many authors. '-* Until a few years ago this problem had only been solved in the case of piecewise-linear resistive circuits described by the known hybrid-representation form. ' The best available algorithm is an improved version of the well-known brute-force combinatorial algorithm. ' However, its computational efficiency is questionable when the circuit investigated contains an increased number of non-linear elements modelled sufficiently well by a large number of piecewise-linear segments. Various methods have been published over the past decade. which are capable of finding multiple solutions in the general case of non-linear resistive circuits described by the equation where F : I?" + IR" is a C'-function. The most effective algorithms4-' involve numerically integrating some associated system of non-linear ordinary differential equations along a solution curve. Although deflation techniques' could be used to uncover additional branches for the general case of multibranched solution curve, these algorithms all share the serious shortcoming that they cannot guarantee the attainment of all solutions.The problem of finding all operating points of non-linear resistive circuits described by (1) was first solved rigorously in Reference 9. The method proposed therein is based on interval analysis techniques and guarantees the attainment, within prescribed accuracy, of all real solutions to (1) contained in a bounded 'rectangular' region D C IR". Its computational efficiency, however, seems to be limited to circuits of low dimensionality since it involves recursive splitting of the initial region D into subregions X", and the number of X " and hence the computational effort needed to locate all the solutions to (1) tend to grow exponentially with the dimensionality n of the problem. In this paper a new interval method for finding the set of all operating points of non-linear resistive circuits is suggested. The presented method is applicable to circuits whose equations are written in the known hybrid-representation form. The non-linear elements involved may, in the general case, be described by non-monotone continuous characteristics. In Section 2...
