Geometric characterization of series-parallel variable resistor networks

The authors describe an efficient method for computing exact bounds on the operating conditions of series-parallel networks. The range of operating conditions for a series-parallel network of variable linear resistors, voltage sources, and current sources can be represented as a convex polygon in a Thevenin or Norton half plane. For a network with k variable elements, these polygons have at most 2k vertices. By introducing a class of infinite points, circuits with potentially infinite Thevenin resistance or Norton conductance can also be represented.<<ETX>>