Dynamic Responses of Electrically Driven Quartz Tuning Fork and qPlus Sensor: A Comprehensive Electromechanical Model for Quartz Tuning Fork

A quartz tuning fork and its qPlus configuration show different characteristics in their dynamic features, including peak amplitude, resonance frequency, and quality factor. Here, we present an electromechanical model that comprehensively describes the dynamic responses of an electrically driven tuning fork and its qPlus configuration. Based on the model, we theoretically derive and experimentally validate how the peak amplitude, resonance frequency, quality factor, and normalized capacitance are changed when transforming a tuning fork to its qPlus configuration. Furthermore, we introduce two experimentally measurable parameters that are intrinsic for a given tuning fork and not changed by the qPlus configuration. The present model and analysis allow quantitative prediction of the dynamic characteristics in tuning fork and qPlus, and thus could be useful to optimize the sensors' performance.