Simplified modeling of ring resonator (RR) and thin wire using magnetization and polarization with loss analysis

In this work, the ring resonator (RR) and thin wire are simply modeled using the concept of magnetization and polarization, respectively, with convenient expressions for its effective permeability and permittivity. Equivalent circuits for them are also provided with closed-form expressions for all circuit elements. The ring resonator and the thin wire were designed and their characteristics were examined in terms of S-parameters, effective permeability and permittivity, loss rate, bandwidth, etc. The theoretical, circuit-, and EM-simulated results are shown to be in an excellent agreement. Based on this modeling, loss analysis has been carried out.