Transmission line model with X-circuit for a metamaterial layer made of pairs of dogbone-shaped planar conductors

In this paper we analyze the propagation through a metamaterial in planar technology recently proposed. The metamaterial basic constituent cell consists of a pair of tightly coupled conductors that supports two main resonance modes corresponding to either a symmetric or an antisymmetric current distribution in the pair. We present an equivalent X-shaped lumped circuit network to be interposed in the transmission line (TL) model of propagation across a metamaterial layer to reproduce its electric and magnetic resonances. We show that reflection and transmission features of a periodic array of dogbone pairs as well as its dispersion diagram are accurately predicted by this simple but effective model.