Simplified modeling of RR(ring resonator) using magnetization with broader negative permeability bandwidth

In this work, the ring resonator (RR), the original form of the split ring resonator (SRR), is simply modeled using the concept of magnetization and one convenient expression for its effective permeability is presented. An equivalent circuit for the ring resonator is also provided with closed-form expressions for all circuit elements. A method of achieving a wider negative permeability by decreasing the Q value is provided. The ring resonator with its resonant frequency of 13.56 MHz was designed and its characteristics were examined in terms of S-parameters, effective permeability, loss rate, bandwidth, etc. The theoretical, circuit-, and EM-simulated results are shown to be in an excellent agreement.