Wave losses in the metal-dielectric transmission line with wedge-shaped conductor

We study wave losses in a metal-dielectric wedge-shaped transmission line in the form of a wedge-shaped metal conductor with circular dielectric cap. A distinctive feature of such a line is that it supports one fundamental mode not having the frequency cutoff. It is shown that the longitudinal current of the fundamental mode has a singularity at the rib of a wedge-shaped conductor. This singularity is described analytically. An efficient way for calculating the integrals arising during the losses calculation is proposed. It is pointed out that the mentioned singularity is non-integrable during the losses calculation in the case where the wedge degenerates into an infinitely thin half-plane. Expressions for the wave decay coefficients in a wedge-shaped transmission line in the metal and the dielectric for an arbitrary opening angle of the wedge are found. Structural decay coefficients of the fundamental mode for different dielectric permittivities of the cap and wedge angles are calculated. The results of calculation of losses in the metal and the dielectric in nine of the lower-order modes in a rectangular-wedge line are presented.