Variational analysis of dielectrically loaded multidepth corrugated waveguides

The propagation behavior in a multidepth corrugated waveguide is analyzed on the basis of the theory of nonstandard eigenvalues and variational methods. This method is tested for an empty dual-depth corrugated guide. The test results have been previously calculated in the literature by using surface impedance and space harmonic methods. These methods are summarized here. Space harmonic formulas are rederived in the form where the fundamental surface admittance component is separated from the higher order terms. It is found that, with elementary trial functions, very accurate dispersion relations can be obtained by the variational method. The method is then extended to a tridepth guide operating in three different frequency bands and to dielectrically loaded dual-depth and tridepth guides