Miniaturized Metamaterial Microwave Sensor with ML Assisted Optimization for Label-Free Liquid Sensing

This work presents the design and analysis of a compact single-negative (SNG) metamaterial sensor based on a meandered-line configuration for high-resolution microwave sensing of liquids. The sensor, fabricated on a low-cost FR-4 substrate with a unit cell size of 10 × 10 × 1.575 mm³, operates at frequency of 5-11 GHz. The structure demonstrates strong resonance characteristics, including a reflection coefficient (S11) dip of –32 dB and a transmission coefficient (S21) level of -28 dB, indicating excellent impedance matching and field confinement. The sensing capability was validated using five essential bio oils (peppermint, citrus, eucalyptus, lavendar, and rosmary) with known relative permittivity values ranging from 2.5 to 3.25. The presence of each material under test (MUT) induced a consistent 200 MHz shift in resonance frequency, with a calculated normalized sensitivity of 6.94%. The sensor’s design was further optimized using random forest and extra trees predictive model and quantitatively assessed using mean squared error and R² score. The meandered structure and single-negative behavior contributed to a high quality factor (70.36, 64.33, 59.23, 54.86, 54.64) and enhanced dielectric interaction with an average relative error of less than 1.1%, confirming strong reproducibility. These results confirm the sensor’s utility for compact, non-invasive, and permittivity characterization in skin care and liquid sensing applications.