Rapid Design Optimization and Calibration of Microwave Sensors Based on Equivalent Complementary Resonators for High Sensitivity and Low Fabrication Tolerance

This paper presents the design, optimization, and calibration of multivariable resonators for microwave dielectric sensors. An optimization technique for the circular complementary split ring resonator (CC-SRR) and square complementary split ring resonator (SC-SRR) is presented to achieve the required transmission response in a precise manner. The optimized resonators are manufactured using a standard photolithographic technique and measured for fabrication tolerance. The fabricated sensor is presented for the high-resolution characterization of dielectric substrates and oil samples. A three-dimensional dielectric container is attached to the sensor and acts as a pool for the sample under test (SUT). In the presented technique, the dielectric substrates and oil samples can interact directly with the electromagnetic (EM) field emitted from the resonator. For the sake of sensor calibration, a relation between the relative permittivity of the dielectric samples and the resonant frequency of the sensor is established in the form of an inverse regression model. Comparisons with state-of-the-art sensors indicate the superiority of the presented design in terms of oil characterization reliability. The significant technical contributions of this work include the employment of the rigorous optimization of geometry parameters of the sensor, leading to its superior performance, and the development and application of the inverse-model-based calibration procedure.