Parametric Investigation and Analysis of an Electric-LC Resonator by Using LC Circuit Model

Electric-LC resonators (ELCs) metamaterials, as a kind of common structures, have been extensively investigated from microwave to terahertz frequencies. In this paper, we present a LC circuit model to analyze electric-LC resonator. With the reliable and closed formulas of the effective inductance and capacitance, the expressions of electric and magnetic resonance frequencies were obtained, which is suitable to discuss the resonance characteristic under the normal incidence case. Meanwhile, the mutual relationships among the permittivity, permeability, refractive index, and structure parameters can be explored by using the obtained expressions. Numerical simulations and theoretical calculations reveal that the width and length of the gaps are some of the critical parameters determining the resonator frequency of the example metamaterial. This study provides valuable information for designing the desired left-hand metamaterial at some specific frequency points.