Abstract
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.
Highlights
Resonance frequency and dissipation measurements of mechanical oscillators, such as quartz crystal resonators (QCR) and cantilevers, are widely used in electrochemistry [1,2,3,4], surface science [5,6,7] and biosensors [8,9,10,11] to quantify processes on the surface
An oscillator is driven by sweeping the frequency spanning around its nominal resonance frequency and the admittance spectrum is fitted with an equivalent electrical circuit to estimate the resonance frequency and dissipation
Being an analytical formula-based method operating at a fixed frequency and requiring no numerical fitting, the fixed frequency drive (FFD) method offers some unique potential for a greater degree of multiplexability and single-chip integration as discussed below
Summary
Resonance frequency and dissipation measurements of mechanical oscillators, such as quartz crystal resonators (QCR) and cantilevers, are widely used in electrochemistry [1,2,3,4], surface science [5,6,7] and biosensors [8,9,10,11] to quantify processes on the surface. The time resolution, i.e. the time for measurement of one resonance frequency or dissipation datapoint, is limited in most practical cases, with a trade-off between the speed of data acquisition and noise. The frequency sweep needs to have a minimal number of steps in order to achieve an acceptable quality of the nonlinear fitting, with the time per step inversely proportional to the resonance bandwidth to avoid artefacts from transient processes. To achieve acceptable noise in practice after accounting for these requirements, it is difficult to lower the time per measurement, which comprises the data acquisition time and the fitting time, below 500 ms with most current impedance analysers [30]. There is no reported data on noise at this speed with real experiments
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