Generalized Network Formulation: Application to Flange—Mounted Radiating Waveguides

Electromagnetic linear field problems can be rigorously and systematically formulated in terms of linear networks. Use of the equivalence theorem permits the decomposition of the computational domain into sub-domains with common interfaces. In each sub-domain the basic building blocks for a linear network representation are provided by Tellegen's theorem and by the two alternative representations of the Green's function. Tellegen's theorem provides the basis for expressing field at interfaces in a consistent way. The eigenfunction expansion of the Green's function provides a resonant-type equivalent circuit useful for expressing the field inside a sub-domain; while the Green's function direct solution emphasizes a transmission line network; in particular a spherical transmission line provides the network representation of radiation problems. In this paper, the generalized network formulation is applied to the problem of radiation from flange-mounted waveguides. While this problem has been already solved with a variety of approaches, the advantage of the generalized network formulation is that, while comprising the previously developed approaches, it also allows rigorous derivation of network representations. In particular it is shown that, by expressing the field in the half-space in terms of spherical waves, the physically matched solutions provide, in some cases, advantages for numerical computations and for network representations.