An ellipsoid-based approach to the solution of nonlinear circuits

A problem in DC nonlinear circuits with steady state solutions demonstrates slow convergence using Newton-Raphson (NR) methods. The 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 uses ellipsoids instead of hyperplanes as used in the predictor-corrector algorithm. The proposed algorithm can avoid potential dangers: it forms a loop path, it attaches to different solution curves. Also, the “reversion” phenomenon of the curve-tracing problem can be avoided. 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. The comparisons show that this algorithm can find the global solution of equations and avoid the divergence behavior encounter in the NR methods