Quasi-static analysis of materials with small tunable stacked split ring resonators

This paper presents a quasi-static analysis of a metamaterial consisting of a three-dimensional array of small tunable stacked split ring resonators (SSRRs). The resonance frequency of the proposed resonator structure can be controlled by adjusting the auxiliary lumped elements which are inserted between the split of each ring. In addition, the size of the ring resonator can be reduced to an order of 0.01 lambda. that is one tenth that of the split ring resonator (SRR) by choosing the proper lumped elements. The analysis is based on the quasi-static Lorentz theory, and the generalized matrix representation of the macroscopic constitutive relations of the composite medium is calculated.