Particle Swarm Optimized High-Sensitivity Rotating Multiple Concentric Complementary Split-Ring Resonator (RMCCSRR) Sensor for Dielectric Material Characterization

Achieving both high accuracy and sensitivity in dielectric material characterization remains a persistent challenge for planar microwave sensors. This paper proposes a novel rotating multiple concentric complementary split-ring resonator (RMCCSRR). The design employs multiple concentrically nested complementary split-ring resonators (CSRR) integrated with a 50 Ω microstrip transmission line, achieving distinct resonant frequency at 2.85 GHz, 5.55 GHz and 7.53 GHz on a 0.508 mm thick Rogers 5880 substrate. The key innovation is the introduction of independent rotation angles for each concentric CSRR. This rotational degree of freedom enables fine-tuning of the EM field distribution and inter-resonator coupling, significantly enhancing interaction with the material under test (MUT). Particle swarm optimization (PSO) is employed to precisely determine the optimal rotation angles. An inverse regression model, utilizing Scikit-learn machine learning algorithms, is developed to predict the complex permittivity of the MUT based on the measured three resonant frequencies and the known sample thickness. Experimental validation demonstrates a maximum relative sensitivity of 9.04% and a maximum permittivity prediction error of 6.30% (average error:3.63%).