Scale Factor Instability Noise in Mode-Split Open-Loop MEMS Gyroscopes

This paper presents analyses of scale factor instability noise (SIS) in mode-split, open-loop MEMS gyroscopes. As the name indicates, scale factor instability noise is a stochastic variation of a gyroscope's scale factor. If analyzed via Allan deviation measurement, it appears as bias instability proportional to the applied angular rate. We propose a theoretical model for the root causes of scale factor instability and validate it against measurements using 14 triaxial, consumer-grade devices and a high-precision rate table. The mechanisms are separated into contributions of 1/f noise of the analog-digital converter (ADC) gain and 1/f noise on the central mass voltage $V_{cm}$ acting electro-mechanically on the entire system through frequency tuning. The latter mechanism is separated further into effects of sense resonator gain and phase instability with susceptibilities of about -5%/V each. Our findings are substantiated by voltage variation experiments. The model can explain the observed scale factor instability noise of about 0.013 dph/dps or 3.6 ppm in full.