Sensitivity, noise, and resolution in QCM sensors in liquid media

The use of quartz-crystal oscillators as high-sensitivity microbalance sensors is limited by the frequency noise present in the circuit. To characterize the behavior of the sensors, it is not enough to determine their experimental sensitivity, but, rather, it is essential to study the frequency fluctuations in order to establish the sensor resolution. This is fundamental in the case of oscillators for damping media, because the level of noise rises due to the strong decline of the quality factor of the resonator. In this paper, a comparative study of noise and resolution is presented with respect to the frequency and the quality factor. The study has been made using four oscillators designed to be used in quartz-crystal microbalance sensors in damping media. The four circuits have been designed at increasing frequencies in order to improve the sensitivity or frequency change per unit of measurand. Also, the present theoretical resolution limit or best resolution achievable with a microbalance oscillator using an AT resonator is determined, since this does not depend on frequency. However, when operating in liquid, the damping of the resonator makes the resolution diminish due to a worsening of the quality factor. The relationship between the resolution limit and the frequency and characteristics of the liquid medium is determined. The resolution worsens when the density and viscosity of the liquid is increased. However, in this case, an increase in frequency implies a small increase in resolution. Therefore, we find that when working below the maximum quality factor, for similar values, the resolution can be improved by elevating the work frequency.