Radiation and circuit model of a planar resonator element with shorting via

We propose the study of a planar quasi-lumped resonator element. It is composed of a shorting via, modelled as a parallel inductance and a very short open-ended microstrip line, modelled as a capacitance. We discuss the physical parameter influences of the resonator, which offer a path to control its radiation characteristic. A circuit model with closed-form expressions of the radiation resistance and the unloaded quality factor is presented. The discontinuity influences of the shorting via and the open-ended microstrip borders are discussed. The experimental and theoretical results verify the proposed circuit model. A radiation model based on the results of electromagnetic simulations has also been proposed.