A new method for exact computation of the differential phase shift in the circular waveguide, loaded with an azimuthally magnetized ferrite cylinder and a dielectric toroid

摘要

A novel numerical technique for calculating the differential phase shift, brought forth by the circular waveguide, containing a ferrite cylinder of azimuthal magnetization and a dielectric toroid that supports normal TE0n modes, is worked out. It is based on the method of successive approximations and yields the roots α1 and α2 (|α1| ≤|α2)| of a biquadratic equation, connecting the off-diagonal ferrite Polder permeability tensor element α and the eigenvalue spectrum of the configuration. The spectrum depends on the relative permittivities of inner and outer medium εr and εd, resp., the factor ρ, determining the degree of filling of geometry with anisotropic material, the element α and the normalized regarding frequency and the constant εr guide radius r̅0. It is calculated by the roots of the structure's characteristic equation, derived formerly through complex Kummer confluent hypergeometric and real Bessel and Neumann functions. For chosen values of the quantities εr, εd, ρ, |α| and r0 the imaginary part of the complex first parameter of confluent functions is varied, until the modulus of counted root α1 (or α2) coincides with the selected numerical equivalent of the element α within the range of the prescribed accuracy. If |α| = |α1| (|α| = |α2|), for the normalized as pointed out above_phase constant β of the electromagnetic field it holds β̅ = β̅(1) (β̅= β̅(1)), where β̅1 = |α2| (β̅(2) = |αl|), (β̅(1) ≤ β̅(2)). For each set of the parameters mentioned the procedure is repeated twice for positive (counterclockwise) and negative (clockwise) direction of the magnetization of its anisotropic load towards that of the wave propagation. The difference between the two computed constants gives the phase shift sought. Numerical outcomes for three geometries are obtained in case of TE01 mode, assuming εr =εd. The approach is rather complicated, too cumbersome and very time consuming, but it provides extraordinarily high accuracy of the results (more than ten decimal places), comparable with the one, due to the recently developed for the same purpose method, invented also by the authors. The combined application of both schemes makes possible to disclose completely the entire picture of the phase shifting behaviour of transmission line considered.