Numerical Determination of Possible Multiple DC Solutions of Nonlinear Circuits

TLDR

The method offers efficient analysis of medium‑size nonlinear resistive circuits built from common microelectronic components, though it does not guarantee finding all solutions. This paper proposes an approach to find possible multiple solutions of nonlinear resistive circuits. The approach partitions the circuit into subcircuits, builds an oriented dependency graph whose loops indicate multiple operating points, and removes a minimal set of nodes to open these loops. The study shows that the nodes whose removal opens loops form a very small subset of the circuit, highlighting a key strategy for locating multiple solutions.

Abstract

This paper proposes an approach to find possible multiple solutions of nonlinear resistive circuits. The approach does not guarantee to find all the solutions; its main features are efficiency, the ability to deal with circuits composed of elements described by the most common models employed in microelectronics, such as DIODEs, bipolar junction transistors, MOSFETs and the capability to simulate medium size circuits composed of, but not limited to, some thousand transistors. The proposed approach is based on the partitioning of the original circuit in subcircuits and on the construction of an oriented dependency graph that defines a suitable ordering in the solution of the subcircuits. The oriented dependency graph can have oriented loops and loops can be sources of multiple operating points. These loops can be opened by removing a minimal number of circuit nodes. In general these circuit nodes constitute a very small subset with respect to the nodes of the original circuit and as shown in the paper represent a peculiar aspect to search for multiple solutions of a nonlinear circuit.