Mathematical aspects of electrical network connections

Abstract

In this paper, we survey the role of mathematics in electrical network connections. We discuss the behavior of current flows, voltages and impedances, mainly for series-parallel networks. In both one-port and multiport electrical networks, currents are governed by Maxwell’s power principle. The joint impedances of the networks, given in terms of series and parallel sums, satisfy the series-parallel inequality. An abstract idea can be formulated in functional analysis in which any network connection is viewed as a binary operation for positive operators satisfying certain algebraic, order and topological properties.