Higher-Order Modes in Circular Eccentric Waveguides

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

“…Without modifying the dimension of conductors, the characteristic impedance of a coaxial cable is adjustable by laterally changing the offset of the inner conductor. This technique can be used to realize a quarter-wave matching element that forms one of the sections in a multisection quarter-wave transformer for broadband-matching applications [1]. Besides, the analysis of cavities excited by thin probes can be simplified using eccentric circular metallic waveguide structures with a small ratio of inner-to-outer conductor dimensions [2].…”

“…Despite of these interesting applications, the shape of boundaries severely limits the possibility for analytical solutions of eccentric circular metallic waveguide configurations [3,4]. The investigations of this type of waveguide have initiated interest of researchers for a long time [1][2][3][4][5][6][7][8][9][10][11][12][13][14][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].…”

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.…”