Generalized Network Formulation: Application to Flange-Mounted Radiating Waveguides

Electromagnetic linear field problems can be rigor- ously 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 the- orem provides the basis for expressing field at interfaces in a consis- tent way. The eigenfunction expansion of the Green’s function pro- vides a resonant-type equivalent circuit useful for expressing the field inside a sub-domain; while the Green’s function direct solu- tion emphasizes a transmission line network; in particular a spher- ical transmission line provides the network representation of radi- ation problems. In this paper, the generalized network formulation is applied to the problem of radiation from flange-mounted waveg- uides. 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 par- ticular 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 net- work representations.