This paper examines various aspects of the electromagnetic responses of the ring resonator located in the transverse electromagnetic cell. In addition, an equivalent circuit for the ring resonator is proposed and analyzed based on the electromagnetic phenomenon of the resonator. The equivalent circuit was simply modeled based on the concept of magnetization. A method for achieving a wider operating bandwidth of the negative permeability 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 circuit and electromagnetic simulation results show an excellent agreement as well as that of theory.