Microwave sensor design with directional coupler-based CSRR structure for the characterization of the dielectric properties of solid materials

This study proposes a novel planar microwave sensor operating in the L- and S-bands to determine the relative permittivity of solid dielectric materials. The sensor incorporates multiple Complementary Split Ring Resonator (CSRR) structures integrated with a directional coupler to enhance the electric field intensity and improve sensitivity. Resonance frequency shifts observed in the transmission (S21), coupling (S31), and isolation (S41) coefficients enable the separate determination of relative permittivity for three parameters. The sensor performance was determined with simulation and measurement data on commonly used dielectric materials, including Rogers 5880, Rogers 5870, AD255C, AD300D, Rogers 3003, Rogers 4835, FR-4, Rogers 3006, and TMM10i. The proposed sensor demonstrated a high sensitivity of 7.2 % in transmission and coupling configurations, as well as 7.5 % in isolation configuration. Frequency detection resolution reached up to 210.8 MHz for transmission and isolation, and up to 177.5 MHz for coupling in this study. Mathematical models were developed using nonlinear surface fitting methods to estimate relative permittivity, accounting for resonance frequency shifts and material thickness. The models produced maximum errors of 0.48 %, 0.45 %, and 0.0804 % for measurements based on S21, S31, and S41, respectively. Fabricated on a cost-effective FR-4 substrate, the sensor provides a practical and efficient solution for characterizing solid dielectric materials.