Complex gyrator circuit of three-port circulators using gyromagnetic resonators with six-fold symmetry

An important planar resonator for use in the design of commercial three-port circulators consists of a radial gyromagnetic region symmetrically loaded by six uniform or radial transmission lines. One possible model for this sort of junction is, in general, a six-port network with three-fold symmetry with three coupled ports and three short- or open-circuited ones. The development of the open-circuited parameters and the complex gyrator circuit or this arrangement is made particularly simple by taking advantage of the symmetry of the problem region. Its tracking solution is given special attention.