Improved circuit model for left-handed lines loaded with split ring resonators

In this letter, an improved lumped element equivalent circuit model for left-handed lines based on split ring resonators (SRRs) is presented and discussed. It is rigorously demonstrated that although the previously accepted circuit model of these metamaterial transmission lines (a π circuit) provides a good description of device behavior, its electrical parameters do not actually describe the physics of the structure. Conversely, the parameters of the improved equivalent circuit model are representative of the different elements of the structure, including the SRRs, the shunt inductive elements and the host line. It is also shown that the proposed model can be transformed to a π model which is formally identical to the previous reported model of SRR-based left-handed lines. With this transformation, the main relevant characteristics of these left-handed lines are perfectly interpreted.