An advanced microstrip resonator design consisting of a ferrite substrate formed in a closed magnetic path (toroidal structure) is shown to produce substantially improved tunability over previous versions that operated in an external magnetic field. Magnetically tunable toroidal resonators with tunability approaching 10% in magnetic fields of 60 Oe have been demonstrated using conventional ferrite compositions. Calculations with a hysteresis-loop theory developed specifically for modeling the low-field magnetization of ferrites were successfully fitted to resonator frequencies measured as a function of magnetic field. Performance predictions for resonators with ferrites optimized for low-field magnetization properties suggest that tunability approaching 15% is possible at magnetic fields of less than 5 Oe.
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