Synthesis of wide-band planar circulators using narrow coupling angles and undersized disk resonators

Circulators using radial/lumped-element resonators with narrow coupling angles that result in gyrator circuits that are as good as, if not better than, those obtained with the classic approach are presented. The form of the lumped element variable is not unique and can be realized by making use of the fringing capacitance at the interface between a dielectric resonator and a substrate with a higher relative dielectric constant than that of the resonator. The topology requires the adjustment of electromagnetic, electrostatic, and network conditions with common parameters, so that a solution that relies on fringing effects only is not generally ensured. The synthesis of octave-band circulators using two quarter-wave-long impedance transformers is reported. A 1-2-GHz circulator based on one such solution with an insertion loss of no more than 0.35 dB between any two ports and typical return loss of 20 dB is described