Effect of the Permittivity of Isotropic Load on the Area of Phase Shifter Operation of a Circular Ferrite-Dielectric Waveguide with Azimuthal Magnetization: Analysis in Terms of the L3 ± Numbers

A circular waveguide, entirely filled with a coaxially positioned azimuthally magnetized ferrite cylinder and a dielectric toroid, which sustains normal $TE_{01}$ mode, is considered. If $\varepsilon_{d}$ and $\varepsilon_{r}$ are the relative permittivities of the isotropic and anisotropic medium, resp., the impact of $\varepsilon_{d}$ on the width of the area in which the structure provides differential phase shift is studied, on condition that $\varepsilon_{d}\gt \varepsilon_{r}$ and $\varepsilon_{d}$ grows, while $\varepsilon_{r}$ is kept unchanged. The approach employs the characteristic equation of the configuration, derived previously by means of complex Kummer confluent hypergeometric and real ordinary Bessel and Neumann functions. In it the permittivities of the two strata participate through their ratio $\overline{\bar{\varepsilon}}=\varepsilon_{d}/\varepsilon_{r}$. That’s why it is chosen as a parameter in the investigation with a value, larger than 1 $(\overline{\bar{\varepsilon}}\gt 1)$, which increases, rather than $\varepsilon_{d}$ and $\varepsilon_{r}$. Using the definite purely imaginary roots of the equation mentioned in its independent variable, and certain new real positive numbers ($\overline{\bar{L}}_{3\pm}$ numbers), introduced by the authors earlier, the lower and upper cut-off frequencies of transmission line are computed. They allow to deduce the criterion, whose fulfillment guarantees its work as a phase shifter, and to reckon the width of the area in that this is observed. The dielectric region is assumed thin. Calculations are performed for several equidistant values of the off-diagonal ferrite Polder permeability tensor element, corresponding to strong anisotropy. The results are debated in detail.