Solving Steady-State Nonlinear Networks of 'Monotone' Elements

Abstract

This paper treats the problem of finding the steadystate currents and voltage drops in an electrical network of twoterminal elements, each of which has the property that its current-vs-voltage-drop graph, or "characteristic," is a curve going upward and to the right. (Thus, "tunnel diodes" are excluded, but nonlinear resistances, current and voltage sources, rectifiers, etc. are permitted.) The construction methods are specifically designed for digital computation techniques (either automatic or manual). The principal tools are: 1) the application of theorems from graph theory ("network-topology"), and 2) quantization of the variables (permitting them to take on only a discrete set of values).