Numerical modeling of the area of phase shifter operation of the azimuthally magnetized circular ferrite waveguide

The borderlines of the area in which the circular waveguide, entirely filled with azimuthally magnetized ferrite, works as a phase shifter for the normal TE₀₁ mode, are determined. For the purpose the special features of the cut-off regime of the configuration and of its limiting one, observed at higher frequencies in which the propagation stops, provided the magnetic bias is negative, are used. For a fixed numerical equivalent of the normalized in an appropriate way guide radius, the off-diagonal ferrite permeability tensor element and the phase constant of the wave are counted by the roots of the structure´s characteristic equation, derived through the Kummer confluent hypergeometric function. This is done repeatedly for a varying negative (positive) value of the imaginary part of its complex first parameter. The process continues, until the computed value of the element coincides with that of the same, corresponding to the cut-off state for the radius chosen (to the limiting one, if the latter is greater than certain number) with a prescribed accuracy. The relevant calculated numerical equivalent of the phase constant is accepted as the one, searched for. The differential phase shift equals the constant mentioned in the first case, whereas in the second one, it is found from it by a simple arithmetic. Changing the normalized radius, the boundaries of the domain studied are traced. The outcomes are presented graphically in a normalized form.