Capturing all the DC solutions of the PWL resistive circuits by means of the polyhedral components

An algorithm for finding all the DC solutions for piecewise-linear (PWL) resistive circuits is presented. Each PWL characteristic of a circuit is partitioned sequentially into smaller portions, until the single segments are reached. The circuits formed with these portions can be ordered in a genealogical tree, of which the original PWL circuit is the founder, while the terminal nodes represent the linear circuits associated to the linear regions. The analysis of the polyhedral circuits associated with the nodes of the tree yields the solutions for the PWL circuit. An example shows that the efficiency of the algorithm increases when the rank of the nonlinear components arises