Four Abstract Reference Frames of an Electric Network

Electrical engineers often treat their stationary networks, rotating machines, and microwave electronic devices as a collection of impedance elements Z without decomposing Z into its RLC components. It is shown here that a lumped or distributed impedance network, surrounded by its own electromagnetic field, is actually the sum of four different types of multidimensional networks: 1) the well-studied 1-network of branches in which the currents flow, 2) a 0-network forned by all the point generators, 3) a 2-network of equipotential surfaces that pass through the generators perpendicularly to the branches, and 4) a 3-network composed of three-dimensional impedance blocks surrounding the branches. Thus the topological structure of a stationary or rotating, electric or electronic network is neither a graph nor a polyhedron, but a so- called fiber bundle over a non-Riemannian manifold.