Simplified Modeling of Ring Resonators and Split Ring Resonators Using Magnetization

Abstract

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. This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/ by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. Ⅰ. IntroductionThe realization of media having negative permittivity and permeability, so called left-handed metamaterial, became feasible after 1991 when Pendry et al.[1] proposed a new method that used an array of thin wires and split ring resonators (SRRs). A number of approaches followed in many aspects in an effort to realize similar left-handed characteristics [2][3][4][5]. However, most of these showed high losses and narrow operating bandwidth (having a very sharp slope near the resonant frequency). In fact, the problem of SRRs has seldom been approached seriously from an engineering viewpoint, although many trials have been made. Basically, SRRs are similar to the ring resonator in their characteristics. In this paper, we model the ring resonator (SRRs) starting from the definition of a magnetic dipole moment and leading to a useful equivalent circuit. The mechanism of SRRs is explained with more familiar terms than in [1]. In addition, we provide a method of realizing the negative permeability over a large bandwidth. It is believed that the presented modeling will provide significant convenience and flexibility for the realization of the left-handed materials. Ⅱ. Novel Modeling of a Ring Resonator (SRRs)We have modeled the ring resonator using an equivalent circuit. The dimensions of the ring resonator and its orientation with respect to the given transverse electromagnetic (TEM) wave are depicted in Fig. 1. The wave travels in the z-direction with the electric and magnetic fields oriented in the x-and y-directions, respectively. The radius of the loop is r and the radius of the ring is rring. The side length of the unit cell is a. C is the value of the chip capacitor. It is inserted for resonance of the ring resonator which has some inductance L originally. The total resistance R of the ring resonator is given bywhere Rr is the radiation resistance, Rl is the ohmic resistance, and RL is an additionally loaded resistance which is 0 originally, but can be added ...

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“…The field can be reinforced or weakened at the center position controlling a resonance frequency of the IFGR. The operation principle of the IFGR is similar to that of a split-ring resonator (SRR) to realize artifical metamaterials [12]- [15].…”

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