## Transient analysis of finite multi-conductor transmission line metamaterials (MTL-MMs) based on discrete green's function (DGF) and macro-modelling techniques

A new systematic macro-modelling technique for transient analysis of finite multi-conductor transmission line metamaterials (MTL-MMs) based on a Dyadic discrete Green's function (DGF) approach is proposed. Governing discrete voltage-based equations for one- and two-dimensional (1-D and 2-D) MTL-MMs are derived using a rigorous MTL analysis. Applying the idea of the Dyadic DGF solution to these equations, the impedance matrix representation of a finite open-ended MTL-MM is represented in a rational form, where the corresponding poles and residues can be identified exactly. The resulting pole/residue macro-model is converted into a state space model which is compatible to SPICE circuit simulator. The proposed macro-modelling technique significantly reduces the CPU time for transient analysis of 2-D electromagnetic band gap (EBG) structures embedded in large multi-layer printed circuit boards or volumetric NRI slabs with interaction with free space waves which can be modelled as an MTL-MM system. The usefulness of the proposed macro-model is illustrated by three sample MTL-MMs including 1-D shunt node negative refractive index ( NRI ) slab and 2-D two- and three-layered shielded EBG structures. The obtained results from the proposed macro-modelling technique are presented and compared with those obtained using a full-wave simulator, confirming the validity of the proposed model.