A method for automatically finding multiple operating points in nonlinear circuits

Abstract

A new algorithm based on a SPICE-like simulator that searches for multiple operating points automatically, with no user intervention required, is presented. This algorithm, which exploits the asymmetrical properties of nonlinear mappings that describe multistable circuits, has been implemented into a program which automatically finds multiple (in most cases, all) operating points of a circuit. In addition to finding multiple operating points, this method offers another feature: it is capable of detecting the stability of a particular operating point. Another useful feature of this method is that it allows the user to gauge how close a particular circuit is to possessing multiple operating points. For circuits known to possess multiple operating points, this method allows the user to specify which operating point is encountered first. Unlike other continuation methods, circuit element models are not modified; only augmenting resistors are required. Hence, this approach lends itself well as an "add-on" to existing circuit simulators. A number of circuit examples are given.