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The scattering properties of multiple-layered interfaces each comprising metal strips periodically mounted on a lossy dielectric substrate are examined. The formulation employs the impedance sheet concept extended to multiple-layered periodic interfaces. The solution yields the currents as well as the transmitted and reflected fields. It is found that convergence is rapid, and the solution numerically stable. Results have been obtained for up to nine layers. By matching the complex transmitted and reflected fields to an actual dielectric slab, it is also possible to determine the refraction index and effective loss tangent of a strip-type artificial dielectric. Results thus obtained exhibited excellent agreement in refraction index with measurement and other theory when the medium is lossless. Moreover, it also now allows not only the quantitative examination of losses in artificial dielectrics but also the refraction index sensitivity to substrate thickness.