Efficient Computer Algorithms for Piecewise-Linear Analysis of Resistive Nonlinear Networks

Two efficient computer algorithms are presented for finding the dc solutions of resistive nonlinear networks containing two-terminal linear and nonlinear resistors, independent dc voltage and current sources, and linear controlled sources. The first algorithm is designed specifically for networks with multiple solutions, while the second algorithm is designed for networks with a unique solution. The first algorithm is based on the sign of the hybrid parameters associated with the linear n-port portion of the network. The second algorithm is a piecewise-linear version of the Newton-Raphson method, but it differs from the differentiable version in two important aspects. First, rather than diverging to
\pm \infty
, as in the usual case, the divergence phenomenon of the piecewise-linear algorithm takes the form of a cyclic repetition of two or more segment combinations. Second, the iteration formula depends not directly on the solution at the preceding iteration, but on the updated segment combination. These observations lead to an algorithm which assures that the piecewise-linear version of Newton-Raphson formula will always converge. Moreover, an important connection between the two algorithms is established on the basis that the iteration formula for the second algorithm is identical to the network equations associated with the first algorithm.