An always-convergent method for finding the DC operating points of nonlinear circuits

The Newton-Raphson algorithm is the most widely used nonlinear solving method, yet it has the serious drawback that, depending on its initial point, it can easily fall into an infinite loop or diverge to infinity. This paper presents a simple yet precise algorithm based on the piecewise-linear method by which an approximate solution of the network equations can be calculated. When this solution is used as a starting point, the Newton-Raphson algorithm will always converge to the exact result.