Mathematical Model of a Rectangular Double Negative Meta-Structure for 5G Applications

This article introduces the mathematical formulation of a proven rectangular double negative (DNZ) metamaterial (MTM) structure using a lumped element circuit model in terms of RLC components for millimeter-wave (mmWave) 28 GHz applications. The structure is developed on a 0.254 mm-thick substrate material: Rogers RT/duroid 5880 with an area of 8.7 mm2. The model accounts for different losses inherent in the system; a series resistance to take into account the losses in the conductor and a shunt resistance to describe the losses in the dielectric substrate, addressing the finite conductivity of conducting materials, the finite resistivity of the dielectric material, and the presence of a dielectric substrate with metallic rings on top. By incorporating these factors, it is possible to precisely predict the resonance frequency associated with this specific structure, however limits the formulation from being applied to other shapes. Numerical validation demonstrates a good agreement with analytical predictions, affirming the model's reliability. The study provides a robust analytical foundation and numerical validation for the double negative metamaterial unit cell, advancing the mmWave 5G wireless technology field.