Simple and ultrafast resonance frequency and dissipation shift measurements using a fixed frequency drive

A new method for determination of resonance frequency and dissipation of a mechanical oscillator is presented. Analytical expressions derived using the Butterworth-Van Dyke equivalent electrical circuit allow the determination of resonance frequency and dissipation directly from each impedance datapoint acquired at a fixed amplitude and frequency of drive, with no need for numerical fitting or measurement dead time unlike the conventional impedance or ring-down analysis methods. This enables an ultrahigh time resolution and superior noise performance with relatively simple instrumentation. Quantitative validations were carried out successfully against the impedance analysis method for inertial and viscous loading experiments on a 14.3 MHz quartz crystal resonator (QCR). Resonance frequency shifts associated with the transient processes of quick needle touches on a thiol self-assembled-monolayer functionalised QCR in liquid were measured with a time resolution of 112 μs, which is nearly two orders of magnitude better than the fastest reported quartz crystal microbalance. This simple and fast fixed frequency drive (FFD) based method for determination of resonance frequency and dissipation is potentially more easily multiplexable and implementable on a single silicon chip delivering economies of scale.