The Method of Elementary Solvers in SPICE

Abstract

Circuit simulators are fundamentally used for solving electric circuit problems with different degrees of complexity in which node voltages and branch currents are the unknowns. This is fully understandable since they were originally created for this specific task. However, behind the curtains, powerful simulation engines based on a variety of numerical techniques operate so as to always comply with Kirchhoff’s current and voltage laws. In this paper, it is shown how a simple circuital configuration, referred to as the elementary solver, consistent in two behavioral current sources in series, can be used to solve mathematical problems that go beyond electronics. Of course, the intention is not to substitute mathematical packages with well-proven calculus capacity but to increase the scope of circuit simulators for their application in other areas of research or simply for educational purposes. It is worth mentioning that no special programming skills are required (except a basic knowledge of the available tools and language) and, furthermore, that the user can operate exclusively in a graphical environment. It is shown, throughout a series of selected examples, how the method of elementary solvers (MES) works, providing a new and practical dimension to the applicability of circuit simulators.