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

Abstract

This study provides an analytic method for the calculation of the cutoff frequencies and waveguide modes of a partially filled eccentric coaxial cable. The method is based on the expressions of the involved electromagnetic fields in bipolar coordinate systems and the validity range of the solution is discussed. It is shown how the waveguide geometry and dielectric parameters may be selected to engineer the lined waveguide's spectral response. Numerical results are included which show good agreement with the corresponding results from full-wave simulations by commercial software.

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.…”

“…The variable separation method [26][27][28] will now be used to seek the solutions. By assuming a z-variation in the form of exp(ik z z), we can write (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) in a compact form as follows:…”

“…, and k z is axial wavenumber. We can write G = {E z , H z } as the product of three functions that depend on (ρ, φ, z), namely, (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16) where Φ(nφ) and Z(k z z) are harmonic functions and B n (β e,h ρ) is a linear combination of solutions to the Bessel differential equation of integer order n = {0, ±1, ±2, . .…”

“…}, i.e. 1 B n (β e,h ρ) = A n H n (β e,h ρ) + B n J n (β e,h ρ), (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17) where H n and J n are the first kind Hankel and Bessel functions of order n,…”

“…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].…”