Matrix-oriented methods for searching the topological conditions for the analysis of nonlinear resistive circuits

The paper presents two methods based on matrix techniques for finding the pair of conjugate trees and the pair of compatible i-v orientations in the circuit topology. The existence of both topological conditions are used to asses the uniqueness of the DC solution. The method resorts to matrix manipulations and it is based on the RE Algorithm (reduction to an Echelon matrix) and on the colored-branch algorithm. The method deals with circuits containing V-resistors, I-resistors, independent current and voltage sources, nullators and norators.