Azimuthally Magnetized Circular Ferrite-Dielectric Waveguide: Condition for Phase Shifter Operation

Abstract

The condition under that the circular waveguide, loaded with a co-axial dielectric cylinder and a latching ferrite toroid, magnetized azimuthally, exhibits properties of a nonreciprocal digital phase shifter for the normal $\boldsymbol{TE}_{01}$ mode, is derived. A numerical approach is developed and applied to study the dependence of the width of the area in which the structure regarded produces differential phase shift on its material and geometry parameters. It makes use of a specific set of roots of the characteristic equation of configuration, deduced earlier by complex Kummer and Tricomi or by Tricomi and its complex conjugate confluent hypergeometric functions, and by real zeroth and first order Bessel ones, and by the real positive $\overline{\boldsymbol{L}}_{4\pm}$ numbers, linked with another set of roots of the equation said. Results are given for a chosen value of the off-diagonal ferrite permeability tensor element and a changing dielectric cylinder to transmission line radius ratio. It is accepted that the relative permittivities of the two media are the same.