Finding DC Operating Points of Nonlinear Circuits Using Carleman Linearization

Abstract

In this paper, we present a procedure for approximating DC operating points of nonlinear circuits. The procedure is based on the Carleman linearization that transforms polynomial algebraic equations into an equivalent infinite dimensional linear system. Hence, we first perform a polynomial approximation of the nonlinear equations describing circuits. The infinite system of linear equations is then transformed into a finite system using a self-consistent technique. The presented procedure enables derivation of an approximation for all roots within a predefined interval. The initial interval is gradually divided into sub-intervals until all roots are identified. Contrary to usually applied methods, this approach does not depend on the domain of attraction of a root and may be also applied in cases of multiple solutions.