Identification of the Zero-Stiffness Condition in Closed-Loop MEMS Accelerometers

Near-zero stiffness is a condition that is proven to be beneficial for noise and stability of MEMS accelerometers. However, when applied to open loop accelerometers, it greatly reduces the bandwidth and the Full Scale Range (FSR) because the devices are operated close to pull-in. On the other hand, closed-loop accelerometers can be operated in near-zero, or even at negative, stiffness, thanks to the control loop that avoids the pull-in instability. However, identifying precisely the point at which the zero-stiffness condition is met is challenging in closed-loop devices since the input/output transfer vs frequency does not depend on the tuned resonance frequency. Therefore, this work proposes a method to identify the zero-stiffness condition in closed-loop MEMS accelerometers. The accelerometer can be tuned with an external tuning voltage applied to dedicated parallel-plate tuning electrodes. The zero-stiffness condition is identified exploiting a trimmable digital reference and its peculiar transfer function to the system output. The experimental measurements show that the sensor performances improve when operated in the zero (or near-zero) stiffness regime. Indeed, the bias instability (BI) and the zero-g offset (ZGO) temperature stability improve from 7 μg to 5 μg and from 22000 ppm/K to 560 ppm/K, respectively. At the same time, the scale factor, the velocity random walk (VRW) and the FSR are not affected by the stiffness condition and remain equal to about 10 mV/g, 7 μg/√Hz and ±100 g, respectively.