Network Properties of Circulators Based on the Scattering Concept

By treating the scattering matrix as an operator, it is possible to relate the properties of circulators to the cyclic substitutions of group theory and the oriented, 1-circuits of topology. The body of knowledge made available by these two branches of mathematics is shown to yield precise definitions of circulator performance. Useful results in treating the symmetries, interconnections, and cascade combinations of circulators are found by further application of group theory and topology.