Transverse equivalent networks for slotted inhomogeneous circular waveguides

Transverse equivalent networks are determined for a circular waveguide of infinite extent possessing a narrow longitudinal slot in the waveguide wall. The waveguide contains a dielectric rod of circular cross-section located on the waveguide axis. It is shown that, provided that the ratio rod-radius/waveguide-radius does not approach unity too closely, a simple transverse representation is permissible. Azimuthally dependent hybrid fields in the waveguide are represented by a combination of radial-line modes of pure Htype and pure Etype. The discontinuity presented by the slot to each mode is determined for n = 0 and n = 1 azimuthally dependent fields, and, in the latter case, two angular positions of the slot are considered. The slot susceptances are evaluated by obtaining the solution of an integral equation for the aperture electric field, subject to quasistatic and small-aperture approximations. The slot conductances are obtained using a variational expression into which the aperture field is inserted.