Effective sampling-rate characterization of digital MEMS vibration sensing systems and implications for calibration

The calibration of digital MEMS sensing systems for vibration measurements (here intended as a single measuring chain, including the digital accelerometer sensor and the supporting microcontroller) presents unique challenges, particularly due to the variability in effective sampling rate introduced by the internal clocks of MEMS. This variability, in terms of mean sampling rate different from the nominal one and its standard deviation or short-term variability (hereinafter denoted in terms of jitter), introduces systematic effects in frequency and amplitude determination, respectively, that are usually neglected during standard calibration procedures. The aim of this work is to provide simple, practical methods for estimating the effective sampling rate and its intrinsic short-term variability in MEMS sensing systems using time- or frequency-domain analysis, offering a balance between accuracy and usability. An analytical expression is also derived to evaluate the impact of jitter on sensitivity determination. These methods are experimentally applied to 25 nominally identical digital MEMS accelerometer systems, characterizing both their mean sampling rates and the jitter. Results show that the actual sampling rates differ notably from the nominal value up to 5.2 % while exhibiting negligible short-term variability, under the investigated conditions. These findings provide a foundation for improving calibration protocols of digital MEMS sensors in dynamic applications.