Finding all DC solutions of nonlinear resistive circuits by exploring both polyhedral and rectangular circuits

A new fast method for finding all the DC solutions of piecewise-linear (PWL) resistive circuits is presented. The structure of the algorithm is based on the exploration of a binary tree: each node represents a specific PWLsub circuit, derived from the original PWL circuit by truncating the original PWL characteristics. The terminal nodes of the tree represent the linear circuits related to single linear regions. The natural exponential growth of the tree is controlled by two different criteria. They are based on the investigation of the convex solution domains of the so-called polyhedral circuits or, alternatively, of the so-called rectangular circuits. The first criterion is more efficient but more CPU-time consuming than the second one. An appropriate combination of both allows the realisation of an overall algorithm faster than those based on a unique criterion.