Methods for the robust measurement of the resonant frequency and quality factor of significantly damped resonating devices

For many applications, resonating sensors can be designed which exhibit excellent sensitivity of the resonant parameters (resonant frequency and quality factor) to the wanted physical parameters. When the resonant parameters are to be derived from measured data, the utilized signal processing algorithm significantly affects the precision of the obtained results, in particular, when the resonance is impaired with spurious contributions. In particular, for systems with low Q-factors (e.g., electromechanical resonators in viscous liquids with Q < 100), the measurement precision suffers from various unwanted spectral components induced by parasitic effects of the resonator and measurement errors. In order to separate the adverse effects from the ideal second-order characteristics, three related methods for estimating the parameters of second-order resonant systems are introduced in this paper extending established methods. To this end, the spectrum is separated into a component induced by a second-order resonant system and an unknown background spectrum.