Accurate Model for Ring- and Disc-Type Microstrip Resonators

A novel and accurate model to frequency dependent characterization of ring and disc micros trip resonators, based on a parallel-ring radial waveguide model, is given. closed form expressions for the resonant frequencies associated with microstrip resonators of arbitrary conductor widths and radii are supplied for the use in microwave CAD programs. Experimental results from 1 to 12 GHz are shown to be in good agreement with the model. The accuracy of this model is within ± 0.4% for the resonant TM_n10-modes (n ⩾ 0) and within ±1.5% for the resonant TM_nm0-modes (n ⩾ 0,m > 1). Design curves for microstrip disc resonators on an alumina substrate are given. The construction of an x-junction micros trip circulator employing a ring resonator and the design of an annular microstrip radiator are taken as examples to demonstrate the high accuracy of the model and its application in a CAD.