Topological considerations on minimal sets of variables describing an LCR network

Abstract

In a linear resistive network, a maximal set, called a basis, of variables that are linearly independent with respect to coefficients that are rational functions in edge admittances is determined. It is shown that the basis is an important concept in linear network analysis in the sense that any network equation can uniquely and minimally be expressible in terms of the elements in a basis. In order to characterize the algebraic structure of the variables in connection with the basis, existence theorems on mappings from given variables to all the source currents and voltages are presented.