Mathematical foundations of the TC-method for computing multiple DC-operating points

Issue title: ISTET '01

Article type: Research Article

Authors: Reibiger, A.^{a; *} | Mathis, W.^b | Nähring, T.^c | Trajković, Lj.^d

Affiliations: [a] EE Department of the Technical University of Dresden, Mommsenstr. 13, D-01062 Dresden, Germany. E-mail: [email protected] | [b] EE Department, University Hannover, Appelstr. 9A, 30167 Hannover, Germany. E-mail: [email protected] | [c] EE Department of the Technical University of Dresden, Mommsenstr. 13, D-01062 Dresden, Germany. E-mail: [email protected] | [d] Simon Frazer University, Burnaby, BC V5A 1S6, ASB 9811, Canada. E-mail: [email protected]

Correspondence: [*] Corresponding author.

Abstract: In this paper, we present a detailed mathematical analysis of nonlinear resistive networks with multiple dc-operating points. In our approach, we use elementary set theoretical principles of network theory. We propose two new approaches: the TC-method (transfer-characteristic method) and the DPC-method (driving-point characteristic method). We use the TC-method to reduce the computation of dc-operating points of a given nonlinear resistive network to the computation of crossing points between transfer characteristics of associated modified resistive networks with a straight line. It can be proved that at least one operating point of the given network corresponds to each such crossing point. We show that the proposed approaches lead to continuation methods for the finding dc-operating points of resistive networks. These continuation methods can be readily used in standard SPICE-like circuit simulators.

DOI: 10.3233/JAE-2003-256

Journal: International Journal of Applied Electromagnetics and Mechanics, vol. 17, no. 1-3, pp. 169-191, 2003