The complete analytical formulation of periodic structures using metamaterials formed with split ring resonators (SRRs) is developed. The periodic structure modeling is based on coplanar waveguide transmission line method and network parameters. The full effect of mutual inductances in the array design is integrated for the first time using curve fitting techniques with electromagnetic simulator. The simplified equivalent circuit including the effect of mutual inductance is presented. The proposed formulation is then used to design a unit cell composed of two SRRs of the sensor array. The analytical method is then verified with simulation results. The prototype of the unit cell has then been manufactured and measured at different frequencies. The analytical, simulation, and measurement results are compared, and agreement has been confirmed.
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