Optimization of Split-Ring and Split-Ball Resonators for Effective Permittivity and Volume Fraction Extraction

Abstract

Material specifications are required in variety of fields like pharmaceutical, chemical, biological, metallurgical, petro-chemical, food processing/grading, forestry, mining, aerospace, equipment manufacture and quality control applications. When a composite/liquid mixture is prepared by mixing two or more ingredients/liquids, effective permittivity is a function of volume fraction and individual permittivity of constituents. Numerous techniques and methods are in practice for finding effective permittivity and other properties of composite/solution. For obtaining accurate results for low loss materials, resonant perturbation technique is given preference to others. Improved accuracy can be expected by increasing sensitivity of resonant structures. Split-ring resonator for compositional analysis (detection of small changes in volume fraction) of mixture comprising of ethanol and methanol was initially studied. A novel concept of split-ball resonator for such analysis with enhanced sensitivity has been proposed. Proposed empirical formulas for output parameters of split-ball resonator structure have been worked out. Optimization algorithm has been developed to further enhance sensitivity of the two structures by utilizing statistical tools. Large deviations in output parameters and hence sensitivity obtained for optimized resonators. Regression equations obtained for relating output parameters with resonators’ geometry. Sensitivity and comparative analysis with other similar works pertaining to volume fraction and effective permittivity has been performed. Due to optimization, these analyses for moderate/medium as well as high loss material were demonstrated. Bivariate cubic expressions for volume fraction and permittivity of mixture as a function of output parameters have been obtained.