DC operating points of nonlinear circuits and generalized Carleman linearization

Abstract

Purpose

The purpose of this paper is to present a procedure for approximating DC operating points of nonlinear circuits. The presented approach can also be applied in case of multiple DC operating points.

Design/methodology/approach

A generalized Carleman linearization is used, which transforms an algebraic nonlinear equation into an equivalent infinite-dimensional linear system. In general, no close-form solution can be given for the infinite-dimensional linear system. Hence, the infinite-dimensional linear system is approximated by a finite one over a predefined interval using a self-consistent technique. The presented procedure allows to approximate all possible DC operating points within a predefined interval. To isolate all DC operating points, the initial interval is gradually divided into subintervals.

Findings

It is shown that the presented approach is not restricted to the polynomial case and allows to approximate all DC operating points. The presented approach can be applied in case of multiple DC operating points and does not depend on the domain of attraction of the DC operating points.

Originality/value

A new procedure for the approximation of DC operating points of nonlinear circuits based on a generalized Carleman linearization is presented. This approach can be applied in case of multiple DC operating points and is independent of the domain of attraction. Further, this generalized approach is not restricted to the polynomial case and can be applied to a variety of circuits.

Citation

Weber, H. and Mathis, W. (2023), "DC operating points of nonlinear circuits and generalized Carleman linearization", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 42 No. 3, pp. 787-803. https://doi.org/10.1108/COMPEL-09-2022-0302