Application of perturbation theory to toroidal phase shifters

A perturbation treatment provides a quantitative solution for inhomogeneous ferrite waveguide structures. The results yield accurate values when the geometry and associated depolarizing and demagnetizing factors are properly accounted for. Since the fields are evaluated to higher order when the coupling of modes are calculated, the impedance of the waveguide can be obtained from the line integrals of equivalent voltages and currents from the total electric and magnetic fields using the voltage-current relations of from the Poynting vector. Theory and experiments for the differential phase shift in single and double toroidal phase shifters agree within 5% over a broad band. Treatment of higher order modes, impedances, and extension to other devices are outlined.<>