An Accurate Approach of Mathematical Modeling of SRR and SR for Metamaterials

Abstract

In the proposed work, we used two miniaturized resonant inclusions, spiral resonators (SRs) and split ring resonators (SRRs) used in practical implementation of metamaterials. A spiral resonator is modeled on a Rogers's duroid substrate of permittivity 2.2. This structure is numerically analysed inside a rectangular waveguide with electromagnetic solver. A full wave simulation of a double split ring resonator with same design parameters is performed inside a waveguide. The transmission minimum frequency of SR is evaluated for varying number of turns in SR where as it is accessed for varying number of rings in SRRs. The full wave simulated transmission minimum frequency is compared with frequency derived from equivalent circuit model of each respective model. In this paper, the expressions derived for resonant frequency are simplified for evaluating effective dielectric constant of substrate after incorporation of metallic inclusion. It is found that the analytically calculated resonant frequency is in close agreement with full wave numerically analyzed frequency. It is also confirmed that SR decrease the electrical dimensions of the resonant inclusions to a great extent as compared to SRR, while synthesizing artificial metamaterials.