Design Considerations of Miller Oscillators for High-Sensitivity QCM Sensors in Damping Media

In this paper, a new contribution to the design of quartz crystal oscillators for high-sensitivity microbalance sensors used in liquid media is presented. The oscillation condition for a Miller configuration was studied to work in a wide dynamic range of the resonator losses. The equations relating the values of the active and passive components with the maximum supported damping and mass were obtained. Also, the conditions to obtain a stable frequency according to the resonator damping (R_Q), the static capacity (C_p) and the filter frequency (f_F) were found. Under these conditions, the circuit oscillation frequency will be proportional to the resonant series frequency and does not depend on the previous parameters (R_Q, f_F, and C_p). If these conditions cannot be satisfied, the expression of the oscillation frequency is given and the discrimination of these effects is obtained through resonator frequency measurements.