Advanced Computational Method for Analysis of the Circular Waveguide, Loaded with an Azimuthally Magnetized Ferrite Toroid and a Dielectric Cylinder

摘要

A sophisticated method is developed for investigation of the dependence of the phase constant of the normal TE₀₁ mode, supported by a circular waveguide, containing an azimuthally magnetized ferrite toroid and a dielectric cylinder on its geometry and material parameters, and the frequency. The debate is focused on the case in which the relative permittivity of the isotropic region is smaller than that of the anisotropic one. This necessitates the employment of three forms of the structure's characteristic equation, written with the help of complex Kummer and Tricomi confluent hypergeometric Φ(a, c; x) and Ψ(a, c; x) and real ordinary or modified Bessel functions J₀(y) and J₁(y) and I₁(u) and I₀(u), resp. Each of them is responsible for the calculation of a definite portion of the phase portrait of transmission line. The propagation problem needs to use in the equation referred to the logarithmic representation of Ψ(a, c; x) functions. This calls for in addition elaboration of special schemes for numerical evaluation of the involved in the power series, defining them complex Euler gamma function Γ(a)and logarithmic derivative of the latter of complex ψ(a)and of integer variable ψ(n). Procedures for reckoning up Φ(a, c; x), J₀(y), J₁(y), I₀(u) and I₁(u), and for ferreting out the purely imaginary roots of the equation spoken of in the independent variable of Tricomi functions, worked out, constitute an integral part of the method, being the object of the study, as well. A sample of the results obtained for selected parameters is presented in numerical form. The analysis shows that the area of wave propagation is restricted. A numerical technique for tracing its upper border is brought forward. It requires the introduction and tabulation of certain real positive numbers (L̃_4±), proportional to some roots of the aforesaid equation.