A variational calculation of TE and TM cutoff wavenumbers in circular eccentric guides by conformal mapping

Abstract

The cutoff wavenumbers of higher order modes in circular eccentric guides are computed with the variational analysis combined with a conformal mapping. A conformal mapping is applied to the variational formulation, and the variational equation is solved by the finite‐element method. Numerical results for TE and TM cutoff wavenumbers are presented for different distances between the centers and ratio of the radii. Comparisons with numerical results found in the literature validate the presented method. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 31: 381–384, 2001.

Analytical solution of higher order modes of a dielectric-lined eccentric coaxial cable

“…The investigations of this type of waveguide have initiated interest of researchers for a long time [1–15]. Various techniques have been used to obtain numerical results: point-matching [5], conformal transformation [6], related addition theorem [7], a combination of the conformal mapping of the cross-section with the intermediate problems method to obtain the lower bounds for the cutoff frequencies and the Rayleigh–Ritz method for the upper bounds [8], perturbation techniques [2], transforming eccentric coaxial into coaxial configuration using bilinear transformation [9], a combination of the polynomial approximation and quadratic functions with the Rayleigh–Ritz [10], a combination of conformal mapping with the finite-element [11], a combination of conformal mapping with the finite-difference [1, 12, 13], a combination of the fundamental solutions and particular solutions methods [14], a combination of the perturbation method with the separation of variables' technique followed by the well-known cosine and sine laws [3], and the separation of variables' technique in bipolar coordinate systems (BCSs) [15]. All these investigations have been concentrated on the evaluation of the higher-order modes and their cutoff frequencies without any dielectric support between the inner and outer conductors.…”

Cutoff wavenumbers of eccentric circular metallic waveguides

“…The shape of the boundaries severely limits the possibility for analytical solutions of these problems. Various techniques [1–11] have been used in order to obtain numerical results.…”

“…In [8], the polynomial approximation and quadratic functions have been used in the Rayleigh–Ritz procedure, whereas in [9] the eigenfrequencies are determined using a meshless numerical method. The method of conformal transformation combined with the method of finite difference and the finite element method have been used in [10, 11], respectively, in order to evaluate the cutoff wavenumbers of higher order modes. The case of an inner cylinder with small radius has been studied in [12].…”

Semi-Analytical Methods for the Electromagnetic Propagation Analysis of Inhomogeneous Anisotropic Waveguides of Arbitrary Cross-Section by Using Cylindrical Harmonics

“…We can find in literature several works that have employed transformation optics principles [29,39] to simplify the eccentric problem. In [40], the eigenvalue problem of an eccentric coaxial waveguide was solved via a conformal mapping combined with the finite-element method, while in [41] the conformal mapping was combined with a finite-difference method. In [42], the eccentric waveguide was analyzed by using a conformal transformation, and approximated formulas were obtained for expressing the field solutions in terms of cylindrical harmonics in the mapped (concentric) space.…”