Supplementary information files for article: 'Simple and ultrafast resonance frequency and dissipation shift measurements using a fixed frequency drive'

Supplementary information files for article: '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.

本文补充信息文件：'使用固定频率驱动进行简单且超快速共振频率和损耗位移测量的新方法'。本文提出了一种测定机械振荡器共振频率和损耗的新方法。通过应用Butterworth-Van Dyke等效电路推导出的解析表达式，可以直接从在固定幅度和频率的驱动下获取的每个阻抗数据点中确定共振频率和损耗，无需进行数值拟合或测量死时间，这与传统的阻抗或阻尼振荡分析相比有所不同。该方法实现了超高时间分辨率和优异的噪声性能，同时所需的仪器相对简单。通过在14.3 MHz石英晶体谐振器（QCR）上进行惯性负载和粘性负载实验的阻抗分析方法进行了成功的定量验证。在液体中，通过快速针尖触碰到硫醇自组装单分子层功能化的QCR时产生的瞬态过程所关联的共振频率位移，以112 μs的时间分辨率进行了测量，这比已报道的最快石英晶体微天平快近两个数量级。基于简单且快速的固定频率驱动（FFD）方法测定共振频率和损耗，具有更高的可复用性和更容易在单个硅芯片上实现，从而带来规模经济的优势。