Determination of the effective constitutive parameters of active transmission line metamaterials

This paper presents an alternative approach, based on the transmission line theory, for determination of the attenuation constant (α), phase constant (β), characteristic impedance (Z_o), refractive index (n), effective permittivity (ε) and effective permeability (μ) for active transmission line (TL) metamaterial. When active elements are introduced into the lossy TL meta-material, the gain acquired from the active elements should be evaluated quantitatively against the attenuation due to the loss in order to avoid ambiguities in determining the signs of the effective constitutive parameters. In stead of directly determining the characteristic impedance from S-parameters, we introduce the reflection coefficient as an intermediate quantity to assist solving the characteristic impedance. This paper shows demonstration of this method with an example of active TL metamaterial.