Metasheets are ultra-thin sheets built from sub-wavelength resonators designed in order to achieve certain frequency-dependent transmission behaviour. A semi-analytical approach based on an equivalent circuit representation is proposed to calculate the microwave transmission through metasheets which consist of 2D periodic arrays of planar circular metal rings with and without substrate. The electromagnetic response of the metasheet can be controlled by changing the radius and periodicity of the circular rings. In the semi-analytical approach, the equations for impedances of the equivalent circuit are parameterized and fitted to match the values of transmission coefficients obtained by full-wave simulations at selected frequency points. Such an approach permits an optimization of the metasheet design with a very small number of full-wave numerical simulations. It is shown that the results of the semi-analytical approach match well with full-wave simulations and measurements within a reasonable range of radius and periodicity values.
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