Metamaterial-Inspired Complementary Split Ring Resonator Sensor and Second-Order Approximation for Dielectric Characterization of Fluid

A metamaterial-based complementary split ring resonator (CSRR) structure is used to develop a sensor for dielectric characterization of fluids. The fluid present in the vertical column interacts with the fields around the CSRR causing a shift in the transmission coefficient curve (S21\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{21}$$\end{document}). An empirical relationship can be established between the dielectric properties and the resonance frequency and Q-factor. This relationship is used for the dielectric characterization of the fluid. A second-order polynomial function is employed for a better curve fitting of the data to achieve higher accuracy in the prediction of complex permittivity (ε′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \varepsilon ' $$\end{document} and ε′′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \varepsilon '' $$\end{document}). Multi-variate polynomial regression is used to determine the coefficients of the polynomial function. The proposed sensor predicts the permittivity of the sample with high accuracy. The design is very simple and the sample can be easily changed by replacing the glass tube. The sensor has very high sensitivity and requires a very little volume of the sample.