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Analysis of the impact of statistical variations on transmission-line based metamaterial structures

Localization theory is employed to investigate the impact of statistical variations in material parameters and lumped-element values on the transmission properties of transmission-line based metamaterial structures. The theory yields closed-form expressions for the calculation of the propagation constant of the disordered structure that are shown to provide an accurate alternative to the more expensive Monte Carlo approach. Application of the theory to the investigation of the transmission properties of a negative refractive index structure demonstrates its use for expedient assessment of the impact of statistical variations in unit cell length and in the values of the lumped reactive elements used in the definition of the structure.