A Novel Fractal Hilbert Curve-Based Low-Cost and Highly Sensitive Microwave Sensor for Dielectric Characterization of Liquid Materials

This work proposes a fractal Hilbert curve-based low-cost, easy-to-fabricate, highly sensitive, and noninvasive microwave sensor for the dielectric characterization of liquids. The sensor’s design comprises the second iteration of Hilbert curve fractal geometry and is fabricated on low-cost FR-4 material with an overall dimension of
$0.28\,\,\lambda _{{0}} \times 0.224\,\,\lambda _{{0}} \times 0.012\,\,\lambda _{{0}}$
. The liquid-under test (LUT) is placed in a closed vicinity of the high electric field region to achieve better sensitivity. The central operating frequency of the sensor is 3.035 GHz for air, and the variation in resonant frequencies of a range of liquids is observed to determine their respective dielectric characteristics. A maximum shift of 1.68 GHz in the resonant frequency was observed for deionized water, and a maximum
${Q}$
-factor of 283.14 was observed for ethanol. The curve fitting technique determines the values of the dielectric constant and loss tangent. For various considered cases in the dielectric permittivity range of 1–79, the root-mean-square errors of retrieved parameters are found to be less than 0.1%. Our proposed design with affordability, compact footprint, and ease of operation exhibits superior performance over the state-of-the-art in terms of sensitivity for the characterization of a wide range of liquid materials.