Characterization of a CRLH TL Unit Cell by Nicholson-Ross-Weir (NRW) Method Nabil Dakhli and Fethi Choubani Innov’COM Laboratory Higher School of Communications of Tunis, Sup’COM Carthage University Jacques David ENSEEIHT, France Abstract—In this paper, the characteristics of a composite right- and left- handed (CRLH) transmission line unit cell is discussed. Characterization is based on the effective medium concept by using Nicholson-Ross-Weir method. This technique manipulates the scattering parameters obtained from full-wave simulation of the CRLH unit cell. The retrieval process is needed to determine the equivalent circuit model which consists of the series interdigital capacitor (IDC) and shunt grounded stub inductor (SGSI) in asymmetric configuration. According to this method, the complex effec- tive permeability and permittivity can fully define an artificial structured metamaterials, considered in general inhomogeneous mediums. Index Terms—Asymmetric and unbalanced CRLH, parameters extraction, effective medium, Nicholson-Ross-Weir Method. I. I NTRODUCTION Metamaterials (MMTs) or Left-handed materials (LHMs), a concept proposed by Veselago in 1968 [1], are characterized by negative permeability and permittivity, thus can support a backward-wave due to the antiparallel phase and group velocities. The MMTs have drained numerous microwave applications such as antennas, couplers, resonators and phase shifters. In literature there are two general approaches for analyzing and designing metamaterials. The first, is the transmission line approach. As implemented in, for instance [2][3], negative permeability and permittivity in a one- or two-dimensional case can be considered as a left-handed (LH) transmission line (TL), however this type of TL do not exist practically because of the parasitic effects. Thus, a composite right/left- handed (CRLH) transmission line is realized and represented by periodic cascaded units, each unit is modeled by an equivalent electric circuit which comprises a series inductance and a shunt capacitance as well as a series capacitance and a shunt inductance. Most of these units are a combination of distributed-element capacitors and inductors. For the analysis of this approach, equivalent electric circuit (EEC) in conjunc- tion with network theory are used to obtain the LC parameters for each distributed-element separately. This process provides an acceptable equivalent circuit response compared with the one obtained by full-wave simulation, but the mutual coupling of unit cells and their losses are difficult to compute. The second general approach is the effective-medium ap- proach. In this approach MMTs are treated as effectively homogeneous because of the dimensions of its scattering elements which are much smaller than the wavelength. The fundamental of this method is based on Nicolson-Ross-Weir (NRW) approach, by adopting some techniques knowing for robustness [4][5], effective constitutive parameters ε eff and μ eff are extracted from S parameters of the unit and an equivalent electric circuit can be modeled for balanced and symmetric CRLH TL unit cell [6] or for unbalanced and asymmetric one [7]. In this paper, first an unbalanced and asymmetric CRLH TL unit cell composed of IDC and SGSI is shown in Fig. 1. Second, a theoretical study of NRW procedure is developed to retrieve the effective parameters of the structure. Third, characterisation of the CRLH unit cell is built up by studying its propagation constant phase. Finally, a comparison between the obtained results from the response of the equivalent electric circuit and full-wave simulation is given. II. NICOLSON-ROSS-WEIR RETRIEVAL PROCEDURE Fig. 1 shows the physical configuration of the CRLH TL unit cell used in this paper to characterise by NRW retrieval method. Wt Unit Cell Gfinger Dvia Reference Plane 1 Reference Plane 2 Lstub Wfinger Wstub Microstrip 1 Microstrip 2 Lfinger Fig. 1. Layout of the unit cell and its dimensions. IDC: L finger = 10mm and W finger = G finger =0.5mm. SGSI: W stub =1mm, D via = 0.8mm and L stub =9.5mm