Cutoff wavenumbers of eccentric circular metallic waveguides

Abstract

Cutoff wavenumbers knm are determined analytically for an eccentric circular metallic waveguide. Separation of variables technique is used for the solution. For small eccentricities kd, where d is the distance between the axes of the cylinders, cosine and sine laws are used instead of the translational addition theorem, in order to satisfy the boundary conditions at the surface of the outer cylinder. Keeping terms up to the order (kd)2 exact, analytical expressions of the form knm(d) = knm(0)[1 + gnm(knmd)2 + O(knmd)4] are obtained for the cutoff wavenumbers of the waveguides, where knm(0) corresponds to the coaxial geometry, with d = 0. Both transverse magnetic and transverse electric modes are considered. Numerical results are given for all types of modes and for various values of the parameters. The method used here is an alternative of the one using the translational addition theorem, in the case of small eccentricities.

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

“…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].…”

“…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].…”

Efficient and Accurate Calculation of the Cutoff Wavenumbers of Coaxial Elliptical-Circular and Circular-Elliptical Metallic Waveguides

“…In [9], the authors derived closed-form expressions for the cutoff wavelengths of the single elliptical metallic waveguide, while in [10] closed-form expressions for the cutoff wavenumbers of elliptical dielectric waveguides were obtained. In [11], closed-form expressions were obtained for the simpler geometry of an eccentric circular metallic waveguide. Apart from the problem of the calculation of the cutoff wavenumbers, closed-form methods were also applied in the solution of scattering problems like the scattering by 0018-9480 © 2014 IEEE.…”

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

“…Equations (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12) and (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) are Helmholtz differential equations in cylindrical coordinates for the axial fields E z and H z in an uniaxial medium described by the tensors (2-2). The variable separation method [26][27][28] will now be used to seek the solutions.…”

“…Among them, we can mention the work in [5], where cylindrical harmonic functions were combined with the Graf's addition theorem for describing the effect of small eccentricities. In [6], specialized formulas to small eccentricities were also obtained from an eigenfunction expansion of cylindrical harmonics, but using a series of approximations to satisfy boundary conditions of the problem based on trigonometric formulae rather than the translational addition theorem. Very recently, the cutoff wavenumbers of eccentric coaxial waveguides were analyzed using a bipolar coordinate system and the corresponding Helmholtz equation solved via the method of separation of variables with proper approximations made for small eccentricities in [7,8].…”