A CSRR-Based Microwave Sensor for Characterizing Multiple Magneto-Dielectric Materials

Microwave resonator-based sensors primarily exploit the changes in resonant frequency and quality factor to characterize magneto-dielectric (MD) materials loaded on the sensor’s hotspot zones, where strong electromagnetic (EM) fields are present. However, a difficulty arises in characterizing the electric permittivity and magnetic permeability simultaneously due to their similar impact on the sensor’s resonant frequency and quality factor. This challenge is further complicated by the cross-sensitivity effects when characterizing multiple MD samples, which is important for applications requiring high sensitivity. This work presents a microwave sensor consisting of a <inline-formula> <tex-math notation="LaTeX">$2\times 2$ </tex-math></inline-formula> array of complementary split ring resonators (CSRRs) for simultaneously characterizing the permittivity and permeability of MD materials. Four sensing zones with highly concentrated electric fields were created to characterize the complex permittivity, while four zones with highly concentrated magnetic fields were implemented to measure the complex permeability of multiple MD samples with high sensitivity and low cross-sensitivity. The sensor’s measured resonant frequency and quality factor, when loaded with the samples, were used to extract the real and imaginary parts of permeability and permittivity. To validate the proposed method, a prototype of the sensor, operating at 2.9 GHz with a quality factor of 250, was fabricated and tested with multiple MD testing samples. The results demonstrate a strong correlation (0.021 for <inline-formula> <tex-math notation="LaTeX">$\varepsilon _{r}$ </tex-math></inline-formula> and 0.02 for <inline-formula> <tex-math notation="LaTeX">$\mu _{r}$ </tex-math></inline-formula>) between the reference data and the experimental values with high sensitivity (58 MHz/<inline-formula> <tex-math notation="LaTeX">$\varepsilon _{r}$ </tex-math></inline-formula> and 26 MHz/<inline-formula> <tex-math notation="LaTeX">$\mu _{r}$ </tex-math></inline-formula>).