Effective Electromagnetic Parameters of Metamaterial Transmission Line Loaded With Asymmetric Unit Cells

In this paper, we propose the generalized extraction procedure for retrieval of the effective constitutive parameters for a metamaterial transmission line loaded with asymmetric unit cells. The asymmetric unit cell is replaced with a transmission line immersed in equivalent bianisotropic medium described by effective parameters ε, μ, and Z_c, and bianisotropic parameters u and η. The proposed retrieval procedure is applied to novel dual-band unit cells and compared with the standard Nicolson-Ross-Weir (NRW) method that is originally developed for the symmetric unit cell and then extended to the asymmetric one using the averaged value of reflection coefficients. It has been shown that, in case of pronounced asymmetry, the NRW method gives only the exact value of refraction, but effective permittivity and permeability are considerably different from the exact values since they are calculated by means of the approximate value of characteristic impedance.