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A switchable circulator may be realised by internally or externally switching or latching a suitable ferrite resonator at the junction of three transmission lines or waveguides. This study investigates the split frequencies and therefore the quality factor of a geometry consisting of a half-wave-long cylindrical cavity and another which consists of a tri-toroidal structure. The model adopted in this study divides the surface of the resonator into up and down uniformly magnetised but unequal regions. The boundary, between the two regions, which is taken as the location of a single or a pair of switching wires, and the split counter-rotating frequencies of a typical resonator is theoretically obtained. This is done by investigating the split cut-off numbers of the related planar circuit with top and bottom electric walls and a magnetic sidewall. The magnetostatic model adopted in this study assumes equal fluxes in the up and down magnetised regions but unequal flux densities.