Equivalent circuit model for left-handed metamaterials

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Abstract
A general equivalent circuit model to calculate the effective permeability of various configurations of split-ring resonators (SRRs) is presented. In the proposed model, each column of the SRR units along the axis of the rings is modeled as a quasisolenoid under magnetic induction. The inductance per ring of the infinite column of these rings is calculated, assuming all the rings in this column support the same current. The electromagnetic coupling between these individual columns of the rings is integrated into this circuit model, which is then applied to a two dimensional cross embedded split-ring resonator. The agreement between the predicted results and numerical simulations shows the efficiency of the model in predicting the frequency band of negative permeability.