A trust region-based approach to the solution of nonlinear circuits

Problem in DC nonlinear circuits and steady state solutions demonstrate slow convergence using Newton-Raphson (NR) methods. This paper presents a technique for dealing with the convergence problems that the NR methods encounter. This technique is simple and practical for finding the solution of nonlinear circuits. It is based on a trust region concept and a hyperplane as used in the predictor-corrector algorithm. The proposed algorithm can avoid the "reversion" phenomenon of the curve-tracing problem. Issues related to the implementation of the algorithm are analyzed and discussed. This algorithm is then compared to the NR based solver currently used in some circuit simulators. Using various examples, the comparisons show that this method can find the global solution of equations and avoid the divergence behavior encounter in the NR methods.