The main objective of this article is to demonstrate by performing experimental measurements how the equivalent capacitance C0 changes when a fluid sample such as water is in contact with the crystal and to relate this change with the relative permittivity of the fluid. These measurements were compared with simulations of traditional models like Butterworth-Van Dyke (BVD). To obtain the change of C0 when the crystal is in contact with water, the relation between the series resonance frequency (fs) and frequency at minimum impedance with zero phase (fr) is used. To know these values, a new way of finding principal parameters in quartz crystal resonator (QCR) sensors, such as series resonant frequency (fs), half band half width (Γ) and maximum peak of conductance (Gm), is proposed; both for an unperturbed crystal and a crystal loaded with a liquid. The method consists in measuring the current (I) that flows through the crystal and the voltage (V) between electrodes at frequency values near to resonance (sweep frequency). Additionally, the susceptance |B| of the crystal is also measured, multiplying the 90 degrees shifted current of the crystal and its voltage, using a mixer. The DC component of this operation is proportional to the susceptance of the crystal. With the magnitudes of the admittance and susceptance, the real value of the conductance |G| is obtained for each frequency value in the sweep. The conductance and susceptance curves were fitted with a summation of Gaussian and sine functions respectively with the minor RMSE possible. The proposed method has been compared with simulations done in COMSOL Multiphysics in order to verify the experimental results with simulation data. MATLAB curve fitting toolbox was used to fit the experimental curves.
Carvajal Ahumada, L. A., Peña Pérez, N., Herrera Sandoval, O. L., Del Pozo Guerrero, F., & Serrano Olmedo, J. J. (2016). A new way to find dielectric properties of liquid sample using the quartz crystal resonator (QCR). Sensors and Actuators, A: Physical, 239, 153–160. https://doi.org/10.1016/j.sna.2016.01.021