Novel Complementary Resonator for Dielectric Characterization of Substrates Based on Permittivity and Thickness

This article presents a novel complementary resonator featuring high sensitivity, low fabrication cost, and improved performance. The proposed structure consists of a complementary concentric square and circular ring resonator (CCSCRR) with multiple splits to enhance the inductance of the resonator. The proposed CCSCRR is coupled to a microstrip transmission line (MTL) with an impedance of $50 \Omega $ to create a high-sensitivity sensor. The lumped element equivalent circuit is employed to explain the sensor's operating principle. The geometric parameters of the CCSCRR are optimized to resonate at 15 GHz, and the optimized sensor is fabricated on 0.762-mm-thick dielectric substrate AD250 ( $\varepsilon{r}$ = 2.5 ± 0.04). Dielectric materials with relative permittivity ranging from 2.5 to 10.2 and thickness from 0.508 to 1.905 mm are employed to investigate the properties of the proposed sensor and to carry out its calibration. Based on the measured resonant frequencies of the CCSCRR sensor when loaded with different materials under test (MUTs), an inverse regression model is constructed to predict the permittivity of the MUT. Comparisons with the state-of-the-art microwave devices show that the proposed design is superior in terms of sensitivity, dielectric characterization reliability, and the applicability scope in terms of the MUT's thickness and permittivity.