Uniqueness of solutions of networks with two terminal piecewise linear resistors

For networks containing resistors, independent-sources, gyrators, ideal transformers, diodes and other saturating monotone piecewise linear resistors, a new condition is proposed to guarantee uniqueness of solutions. This is both necessary and sufficient and is easy to test. It requires that the characteristics should satisfy a condition with the null vectors of the matrix of the linear part of the network whenever it is singular. Diodes with infinite reverse resistance are also allowed in the formulation