Characterization of miniaturized metamaterial resonators coupled to planar transmission lines through parameter extraction

In this paper, a method for obtaining the electrical characteristics of metamaterial resonators coupled to planar transmission lines is proposed. This parameter extraction technique is based on the comparison between the measured (or full wave electromagnetic simulated) transmission and reflection characteristics of a host line loaded with such resonators and those obtained from its lumped element equivalent circuit model (previously reported by some of the authors). The resonant particles considered in this study are split ring resonators, spiral resonators, and other electrically small resonant particles based on two metal levels. The interest in this technique lies in the lack of analytical models providing the electrical parameters of several of the considered ultrasmall resonator topologies (due to their complexity). From the extracted parameters, it is concluded that the circuit models predict very accurately the frequency responses of the considered structures for the different resonators under study. There is an increasing interest in the synthesis of metamaterial transmission lines with extremely small unit cell size. In order to achieve dimensions close to (or even below) λg /100, it is imperative to use complex resonator topologies that combine broadside coupling and extremely elongated metallic strips (etched in different metal levels connected through vias). This justifies the proposed technique. Thus, this work is useful in aiding the synthesis of microwave components based on resonant type metamaterial transmission lines. © 2008 American Institute of Physics.