Circuit for continuous motional series resonant frequency and motional resistance monitoring of Quartz Crystal Resonator Sensors in Fluid Media by parallel capacitance compensation

Authors: A. Arnau, T. Sogorb, P. Ventura, Y. Jiménez

Event: 3th Acoustic Wave Sensor Workshop, Taos, New Mexico,USA (2001)


For a complete characterization of quartz crystal resonator sensors, it is necessary the measurement of their electrical conductance (G) and susceptance (B) in a certain bandwidth around resonance. This is usually done with impedance analyzers and is particularly useful in liquid environment, where the resonator loss is high and the capacitances in parallel with the motional impedance of the sensor have a great effect on its electrical admittance. This complete characterization permits a reasonably coherent fit of a BVD model to the measured admittance, since specific points of the measured G and B can be associated with BVD parameters without incurring significant error in most cases. However, impedance analyzers are very expensive and not always suitable for in situ measurements, principally for a simultaneous multi-sensor characterization. Alternative characterization of the resonator around resonance is also used by measuring the voltage transfer function of a simple circuit in which the resonator is included. In these cases, a mathematical fit of a BVD model, in which the motional capacitance is normally considered constant and equal to that of the unperturbed sensor, is made for determining the remaining parameters. This mathematical fit normally produces, in these cases, a high correlation between parallel capacitance and motional inductance. Actually, the effect of parallel capacitances is negligible near the series resonant frequency. Thus, special oscillators have been designed to operate near the true motional series resonant frequency and, additionally, to provide the measurement of the motional resistance. However, the higher the resonator loss is, the higher the frequency error between the oscillation frequency and the true motional series resonant frequency is, and complicated adjustments have to be made to minimize this error.

A phase locked loop based circuit has been specifically designed for compensating parallel capacitance effects in quartz resonator sensors. This circuit provides a continuous measurement of the true motional series resonant frequency and motional resistance. The system permits the calibration of the effective capacitive compensation and gives an indirect measurement of this capacitance. Additionally, the circuit maintains one side of the resonator grounded, so that the parasitic capacitances due to the fluid can be more easily controlled.