Ultimate Limits of Differential Resonant MEMS Sensors Based on Two Coupled Linear Resonators

In this paper, we investigate how additive noise, e.g., thermomechanical noise, impacts the resolution of mode-localized resonant sensing architectures based on two passively coupled linear resonators. Existing work suggests that the ultimate resolution of these sensors can be improved by decreasing the coupling coefficient of the resonators. The present work gives an analytical proof that this result does not hold, and that the resolution of such sensors is actually independent of the coupling strength. These results are established for different output metrics and operating points, in closed loop and in open loop, and compared to those obtained with other approaches based on actively coupled resonators.