Numerical Determination of Possible Multiple DC Solutions of Nonlinear Circuits

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.