Electromagnetic modes in conical transmission lines with application to the linearly tapered slot antenna

A transmission line analysis of bow-tie antenna and linearly tapered slot a ntenna (LTSA) is presented. These structures belong to the class of conical transmission lines defined here in terms of conical coordinates. A complet e set of solutions of Helmholtz equation is obtained exhibiting TE and TM m odes. Modal fields are expressed by Lame and Bessel-Schelkunoff functions. TE and TM eigenmode analysis is particularized to the bow-tie structure. Bo w-tie antenna and LTSA are shown to be dual conical transmission lines by t he image method and Babinet's principle, The modes of LTSA are calculated o n the basis of the results obtained for the bow-tie structure. The radiatio n pattern of LTSA is computed as the integral of a closed-form expression o f the dyadic Green's function weighted by the modal electric field distribu tion over the slot aperture. The obtained dominant mode radiation patterns are validated by measurements from the literature. The radiation patterns o f the first two-order modes are calculated and compared.