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We propose to model periodic structures by equivalent multiconductor transmission lines (MTLs). The developed technique is based on a multimodal representation of the periodic structure unit cell, such as required for periodically loaded MTLs and periodically loaded waveguides with higher order evanescent mode interaction between cells. Compared to commonly employed periodic structure analyses which only provide the dispersion diagram, the proposed method provides all the parameters needed to accurately model the excitation and matching of finite-size periodic structures. The usefulness of the method is illustrated by means of two examples of negative-refractive-index metamaterials. First, a loaded MTL known as the shielded mushroom is analyzed. The proposed technique allows addressing the fundamental issue of the excitation of the different propagating Bloch modes supported by such a structure. Second, a split-ring resonator and wire metamaterial is analyzed. The method is shown to accurately represent the coupling between cells, thereby providing an enhanced design tool compared to the dominant-mode analysis usually employed for this type of metamaterials.