Circulators Using Planar Triangular Resonators

This paper gives the theoretical description of 3-port circulators using planar triangular resonators. The standing-wave solution for this circulator is obtained by taking a linear combination of two TM/sub 1,0,-1/ standing waves with one of them rotated through 120/spl deg/. The loaded Q factor for this junction is derived by forming the ratio of the energy stored in the circuit to that dissipated in the termination. The bandwidth of circulators using apex-coupled triangular resonators is three times that of circulators using conventional disk resonators. In the case of circulators using side-coupled triangular resonators, the bandwidth is one-third of that of the conventional arrangement.