Cutoff wave numbers of eccentric circular and concentric circularelliptic metallic wave guides
Abstract
The cutoff wave numbers k_{nm} and the field of twoconductor, perfectly conducting wave guides are determined analytically. Three types of wave guides are considered: Eccentric circular conductors of radii R_{1}, R_{2} and distance d between their axes, elliptic inner with circular outer conductor, and circular inner with elliptic outer conductor. The electromagnetic field is expressed in the first case in terms of circular cylindrical wave functions referred to both axes in combination with related addition theorems, while in the last two cases, both circular and elliptical cylindrical wave functions are used, which are further connected with one another by wellknown expansion formulas. When the solutions are specialized to small eccentricities, kd in the first case and h = ka/2 in the last two cases (where a is the interfocal distance of the elliptic conductor), exact, closedform expressions are obtained for the coefficients g_{nm} in the resulting relations k_{nm}(d) = k_{nm}(0)[1 + g_{nm}(k_{nm}d)^{2} + ···] and k_{nm}(h) = k_{nm}(0) [1 + g_{nm}h^{2} + ···] for the cutoff wave numbers of the corresponding wave guides. Similar expressions are obtained for the field. Numerical results for all types of modes, comparisons, and certain generalizations are also included.
 Publication:

Radio Science
 Pub Date:
 October 1980
 DOI:
 10.1029/RS015i005p00923
 Bibcode:
 1980RaSc...15..923R
 Keywords:

 Circular Cylinders;
 Concentric Cylinders;
 Electromagnetic Fields;
 Elliptical Cylinders;
 Propagation Modes;
 Waveguides;
 Boundary Value Problems;
 Dielectrics;
 Eccentricity;
 Electric Conductors;
 Metal Surfaces;
 Numerical Analysis;
 Transmission Efficiency;
 Wave Functions