A globally and quadratically convergent algorithm is presented for solving nonlinear resistive networks containing transistors modeled by the Gummel-Poon model or the Shichman-Hodges model. This algorithm is based on the Katzenelson algorithm that is globally convergent for a broad class of piecewise-linear resistive networks. An effective restart technique is introduced, by which the algorithm converges to the solutions of the nonlinear resistive networks quadratically. The quadratic convergence is proved and also verified by numerical examples.

An efficient algorithm is presented for solving nonlinear resistive networks. In this algorithm, the techniques of the piecewise-linear homotopy method are introduced to the Katzenelson algorithm, which is known to be globally convergent for a broad class of piecewise-linear resistive networks. The proposed algorithm has the following advantages over the original Katzenelson algorithm. First, it can be applied directly to nonlinear (not piecewise-linear) network equations. Secondly, it can find the accurate solutions of the nonlinear network equations with quadratic convergence. Therefore, accurate solutions can be computed efficiently without the piecewise-linear modeling process. The proposed algorithm is practically more advantageous than the piecewise-linear homotopy method because it is based on the Katzenelson algorithm that is very popular in circuit simulation and has been implemented on several circuit simulators.