Making use of mode matching method, a theoretical analysis of a metamaterial layer is presented. The unit cell of the structure is modeled by a TEM waveguide, and the metamaterial element is supposed as a discontinuity in the waveguide. Analyzing the structure using this model, mathematical relations between s-parameters of a metasurface are extracted. It is evident that the variation of each s-parameter is limited to an arc of circle on Smith chart. The key factors determining the location of each circle on plane are specified. Moreover, a discussion on the role of metasurface element in the determination of s-parameters of the structure is given. The variations of scattering transfer parameters on the plane are determined, too. The steps needed to derive these relations are described. Using these relations, simple and straightforward formulas are devised which can be used to predict the response of the metasurface. Finally, some metasurfaces will be analyzed by full-wave method. The new relations are well-agreed with simulation results.
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