Resonator/Oscillator response to liquid loading

The resonant frequency of a thickness-shear mode resonator operated in contact with a fluid was measured with a network analyzer and with an oscillator circuit. The network analyzer measures changes in the device's intrinsic resonant frequency, which varies linearly with (ρη)(1/2), where ρ and η are liquid density and viscosity, respectively. The resonator/oscillator combination, however, responds differently to liquid loading than the resonator alone. By applying the operating constraints of the oscillator to an equivalent-circuit model for the liquid-loaded resonator, the response of the resonator/oscillator pair can be determined. By properly tuning the resonator/oscillator pair, the dynamic range of the response can be extended and made more linear, closely tracking the response of the resonator alone. This allows the system to measure higher viscosity and higher density liquids with greater accuracy.