On the Capacitance of Slotted Metamaterial Resonators for Frequency-Variation Permittivity Sensing

This paper reports a theoretical study on the capacitance of slotted metamaterial resonators, valid for complementary split ring resonator (CSRR), complementary spiral resonators (CSR), dumbbell defect ground structure resonators (DB-DGS), etc. The analysis is useful for the design of dielectric constant microwave sensors implemented by means of these resonant particles, and based on frequency variation, namely, on the effects that the variation in the dielectric constant of the material under test (MUT) generate on the resonance frequency of the sensing particle, the output variable. Contrary to previous works, where it is assumed that both the MUT and the substrate are semi-infinite in the vertical direction, it is considered in this paper that the substrate has an arbitrary finite (and even small) thickness. The analysis is supported by electromagnetic simulations and experiments, which point out the potential of the method to determine the dielectric constant of the MUT from the measured resonance frequency of the resonator covered with the MUT and simple mathematical expressions.