Modified Split Ring Resonators Sensor for Accurate Complex Permittivity Measurements of Solid Dielectrics

Abstract

In this paper, a sensor using modified Split Ring Resonators (SRRs) is designed, simulated, fabricated, and used for advanced investigation and precise measurements of the real part and imaginary part solid dielectrics’ permittivity. Adding vertical strips tightly coupled to the outer ring of the SRR leads to the appearance of two resonant frequencies at 1.24 GHz and 2.08 GHz. This modified geometry also assures an improved sensitivity. Using the full wave electromagnetic solver, both the unloaded and loaded sensors are investigated. The numerical simulations are used to develop a mathematical model based on a curve fitting tool for both resonant frequencies, allowing to obtain analytical relations for real and imaginary parts of permittivity as a function of the sample’s thickness and quality factor. The sensor is designed and fabricated on 1.6 mm thick FR-4 substrate. The measurements of different samples, such as transparent glass, acrylic glass, plexiglass, and Teflon, confirm that the modified SRR sensor is easy to implement and gives accurate results for all cases, with measurement errors smaller than 4.5%. In addition, the measurements highlight the importance of the second resonant frequency in the cases in which numerical limitations do not allow the usage of the first resonant frequency (1 mm thick sample).