Deciphering split ring resonators: understanding theoretical validation and simulation implications

Abstract

Abstract This study presents a comparative analysis of analytical calculations and simulation results of a single-ring split ring resonator (SRR). A simulated SRR made of aluminum, designed in high frequency structure simulator (HFSS), with the resonant frequency of 3.97 GHz with transmission loss of −47.7 dB. The initial gap, width, and thickness of the ring are set at 1 mm, 1 mm, and 3 mm, respectively. These geometrical parameters are subsequently varied in simulations, and theoretical calculations are conducted for each variation using Python 3.10 code to facilitate comparative analysis. The analytical calculations reveal certain limitations in accurately modeling the impact of fringing and radiation, particularly when dealing with smaller dimensions. Although there exist slight disparities between the simulated and calculated outcomes, it is evident that the theoretically derived results exhibit a close correspondence with simulated responses, particularly for dimensions that are not excessively small. This observation underscores the confirmation that an augmentation in the gap of the Split Ring Resonator (SRR) leads to an elevation in the resonant frequency. Furthermore, by maintaining a constant inner radius and adjusting the outer radius to modulate the width of the SRR, a decrease in the resonant frequency is noted with an increase in the width of the metallic ring. Similarly, an increase in the thickness of the ring contributes to a reduction in the resonant frequency This comprehensive investigation provides a valuable methodology for corroborating theoretically derived results with simulation data. Additionally, the research underscores the diverse resonances that can be achieved by fine-tuning the gap, width, and thickness of the split ring resonator, highlighting the significance of selecting these dimensions carefully to attain specific resonant frequencies.