An Algorithm for Solving Nonlinear Resistor Networks
JACOB KATZENELSON · Bell System Technical Journal · 1965
This article describes an algorithm for solving electrical networks which consist of linear and nonlinear resistors and independent sources, and where the characteristics of each of the resistors is described by a function Gk(.), i &equal; Gk(v), where Gk(.) is continuous, monotonically increasing, piece-wise linear, and one-to-one from (− ∞, ∞) onto (− ∞, ∞), and where k is an index which spans all the resistors in the network. The solution is found by solving successively equivalent linear networks which represent the nonlinear network locally and which correspond to a “solution curve.” Essential to the efficiency of the computation process is the method of modifying matrices which enables the process to find the inverse of a conductance matrix by modifying another matrix rather than by matrix inversion. The algorithm provides a fast computation method for both of the following two cases: (1.) the network contains both linear and nonlinear resistors and (2.) the sources are functions of time and the solution is required for successive values of time. In the latter case the algorithm computes each solution from the previous one rather than solving each case independently.