Application of the extended Kuroda transform to the mixed lumped and distributed network model for the spherical modes

A comparison is made between the mixed lumped and distributed equivalent two-port networks for spherical modes, as derived by Thal, and the mixed lumped and distributed equivalent networks for certain classes of nonuniform transmission lines, as derived by Kobayashi. The extended Kuroda transform is used to derive a model for dipolar (radial index of 2) spherical mode propagation consisting of a nonuniform (but dispersionless) transmission line, a single lumped inductor, and an ideal transformer. Four different two-port models for dipolar spherical mode propagation are then compared, including: (1) Thal´s mixed lumped and distributed model; (2) a model containing a parabolic nonuniform dispersionless transmission line derived using the extended Kuroda transform; (3) a model containing a second-order binomial form nonuniform dispersionless transmission line also derived using the extended Kuroda transform; and (4) the dispersive nonuniform transmission line model originally given by Marcuvitz. Finally, some motivation for the study of equivalent models is presented.