Electromagnetic Topology: An Additional Interaction Sequence Diagram for Transmission Line Network Analysis

The electromagnetic analysis of complex transmission line networks requires sophisticated modeling tools. Although the existing ones are useful, handling real-scale networks is still a challenge, hence requiring additional analysis tools. A new interaction sequence diagram called the coupling order graph (COG), which is able to quantify further approximations in complex situations, is presented. Its construction is based on the conventional interaction sequence diagram of electromagnetic topology (EMT). In this diagram, vertices are physical wires, and edges account for the interactions between them. This is an oriented graph that describes a source-victim interaction sequence. Introducing a weak coupling approximation, this interaction sequence appears as a set of parallel paths. Prior to any calculation, each of these paths may be analyzed in terms of bounded topological S parameters and its number of associated edges. An approximate answer is then obtained through the aggregation of predominant paths only. We illustrate the COG advantages through an arbitrarily chosen example. It is shown that approximate evaluations can be obtained from the subnetworks that are far simpler than the original one. In addition, we provide an example of a criterion that quantifies this approximation