This paper presents a reduced order model of metamaterial transmission lines. The metamaterial transmission line can be regarded as a ladder network characterized by propagating and evanescent modes generated by negative permeability and permittivity. Quasi-closed form of poles and residues are computed, taking advantage of the periodic structure of such type of structure, thus leading to an efficient time domain macromodel. Furthermore, the same methodology can be also efficiently used when the metamaterial is characterized in terms of equivalent dispersive and lossy permeability and permittivity over a frequency range. A model order reduction (MOR) technique is proposed allowing to reduce the computational effort in carrying out time domain simulations and allowing fast parametric models generation. In addition, the capability of the proposed method to properly reproduce the physics of metamaterials and to reduce the computational complexity due to the dispersive behavior of such artificial materials is demonstrated by the numerical results.
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