Perturbation for Open Analysis and Design Equations and Closed-Ring Microstrip Resonators

Simple closed-form expressions for the resonant frequency and electromagnetic field distribution for various modes of the open- and closed-ring microstrip resonators are derived by utilizing the perturbation analysis of the equivalent curved waveguide model. These results are shown to be in good agreement with the exactly computed values obtained by the solution of the eigenvalue equation for the equivalent waveguide model and the experimental data. The effect of gap capacitance on the eigenvalues of the open-ring resonator is also examined.