Analytical Formulation of a DNZ Rectangular MTM Unit Structure for mm Wave Applications

The analytical formulation using an equivalent circuit model derived in terms of RLC circuits of a rectangular Double Negative (DNZ) Metamaterial (MTM) unit cell for millimeter-wave (mm Wave) applications is presented in this article. The double-split dual-ring unit cell is designed on a 0.254 mm-thick substrate material Rogers RT/duroid 5880. It has an overall size of 3.05 mm × 2.85 mm. The model is developed considering all the losses, especially taking into consideration finite conductivity of conducting materials, finite resistivity of the dielectric material and the presence of dielectric substrate with metallic rings on top. It is possible to predict the exact resonance frequency of this particular structure by exploiting the proposed model. The numerical method shows 99% agreement to the analytical one which establishes the structure to be compatible for mmWave applications.