Broadband equivalent circuit modelling of spiral resonators for printed circuit board applications

This study presents a new equivalent circuit modelling methodology for various-type spiral resonators in printed circuit board environment. The N-turn spiral resonator can be decomposed into an N Pi-equivalent circuit model, and each Pi-model is comprised of a series inductance, parallel capacitance, two shunt capacitors and the resistances of the conductor and dielectric. Both the inductance and capacitance of the equivalent circuit are calculated by the proposed formulas, which are based on the electromagnetic theory. It has been demonstrated that the proposed equivalent circuit model of the spiral resonator is well matched in S-parameters, Q-factor and inductance values as well as in self-resonance frequency values within 8% tolerance with measurement and full-wave electromagnetic field solver.