Electromagnetic Topology: A Formal Approach to the Analysis and Design of Complex Electronic Systems

This paper summarizes several of the concepts included in the new and expanding subject of electromagnetic topology. Beginning with the elementary concepts of volumes and boundary surfaces, these entities are specialized to layers and shields, and sublayers and subshields, and also associated with equivalent graphs. Next one defines a set of indices associated with the various levels of topological decomposition. The general supermatrix equation describing electromagnetic propagation is partitioned according to these indices. The partitioned equation leads to useful approximate solutions which can be used to bound signals, relate the performance of the system to its parts, and allocate shielding to various subshields so that a system of interest can be protected against various electromagnetic environments.