∑-Δ based force-feedback capacitive micro-machined sensors: Extending the input signal range

Operating MEMS capacitive sensors in negative feedback mode results in improved bandwidth, and lower sensitivity to process and temperature variation. Feedback operation is achieved by applying a feedback voltage to the actuation electrodes of the sensor, generating a corresponding feedback-force on the sensor proof mass. To overcome, the non-linearity of the quadratic voltage-to-force relation in capacitive feedback, a two-level voltage feedback signal is often used. Therefore, a singlebit Σ-Δ modulator represents a practical way to implement force-feedback sensors interface systems. However, single-bit Σ-Δ modulators have a limited input-range that is less than the available full-scale dictated by the actuation voltage value. This is caused by quantizer overload, and the consequent reduction in quantizer effective gain as the input signal approaches full-scale. In this work, a solution is proposed that allows extending the input signal range of Σ-Δ based capacitive sensors beyond the limit imposed by single-bit operation. The proposed technique is applied to the design of a MEMS based accelerometer, and results in an increase in the input signal range from 35g to 40g, and an improvement in signal-to-noise ratio from 130.2dB to 137.3dB, at the same actuation voltage level.