On the symbolic calculation of nonlinear circuits

With a few exceptions, applications of symbolic analysis techniques have been limited to the calculation of linear circuits. In fact, for circuits with nonlinear voltage-current relations straightforward symbolic analysis is generally impossible because no mathematical methods exist for solving arbitrary nonlinear (differential) equations symbolically. In this paper, two approaches to the above problem are discussed. The first approach is restricted to the DC analysis of nonlinear circuits. By approximating nonlinear element characteristics using polynomial functions advanced computer algebra techniques can be applied to symbolically compute DC operating-point and transfer characteristics even for extremely nonlinear circuits. The second and more general approach is based on the manipulation of the system of symbolic (differential) equations of a nonlinear circuit Using complete SPICE models for the nonlinear devices, dominant circuit behavior can be extracted from these equations by employing equation-based simplification strategies