Non-contact Measurement Of Complex Permittivity Based On Sub-wavelength Resonance

Complex permittivity is an important parameter to reflect the interaction between matter and electromagnetic measuring. The measurement of complex permittivity of materials is of significant importance in scientific research and industrial applications. So far there have been many complex permittivity measurement methods, such as capacitance methods, transmission line methods, resonance cavity methods and free space methods. All the methods have their own advantages and shortcomings, In this paper, we introduced the electrically coupled, high-Q-factor sub-wavelength split-ring resonators (SRRs) to the non-contact measurement of complex permittivity.The SRRs are originally used for the metamaterials, and later have also been used in the microwave filter. With deep sub-wavelength dimensions, SRRs have higher Q factors than regular half-wavelength microstrip resonators. This characteristic has been noticed and used in the contact measurement of dielectric contacts in the past years. For contact measurements based on SRRs, the disadvantage is the significant impact to the measurement results due to the existence of thin air gaps between the SUT and SRRs. The latter issue seriously impacts the precision of such contact measurements.In this paper, we introduce the deep sub-wavelength, high-Q factor, electrically coupled SRRs to the non-contact measurement of complex permittivity at high frequencies. With non-contact measurements, SUT are no longer directly placed on the SRR, and therefore the air gap issue can be effectively avoided. Another major difference between the contact and non-contact measurements is that in non-contact measurements, the change of the impedance and the reflection coefficient, rather than the change of resonance frequency in contact measurements, will be measured. Rayleigh approximation based algorithm is also derived for the new setup, providing a linear retrieval equation for the measured scattering parameters. Simulation and experimental results verify the effectiveness of the proposed approach. The method is able to non-contact measure small-sized samples in open spaces and suitable for massive, repeated measurements of complex permittivity of liquids and bio-materials, which has a good application prospect.