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

Abstract

In this paper, we investigate how additive noise, e.g. thermomechanical noise, impacts the resolution of modelocalized resonant sensing architectures based on two passivelycoupled 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 openloop, and compared to those obtained with other approaches based on actively-coupled resonators.

Resolution limit of mode-localised sensors

“…We can improve the resolution limit by decreasing the value of it. Second, for 2-DoF mode-localised sensors, the frequency-output metric has a better resolution limit than the AR-based output metric since κQ ≫ 1 is necessary for resolving two peaks in the frequency response of two outer resonators [25]. However, we cannot conclude that the frequencyoutput metric is better than the AR output metric since the resolution limit of the AR output metric can be improved by increasing DoFs in the system.…”

“…Compared with the resolution model [25] in which the resolution limit is independent of κ, as illustrated in Table 1, our model reveals that the ultimate resolution of mode-localised sensors can be improved by decreasing the coupling factor κ. We can see from (18) that δx 1 + δx 2 and δx 1 − δx 2 are not the same as the minus sign in δx 1 − δx 2 and has influences on other items except N 1 and N 2 .…”

“…We assume the frequencies of the first mode (in-phase mode) is ω 1 , and the second mode (out-of-phase mode) is ω 2 . So, in particular, when ǫ = 0, F 1 = F , the rest of the driving force is equal to zero, and ω in (9) equals the resonant frequency ω 1 , which is the resonant frequency of the first mode for mode-localised sensors [25]. Thus, we can attain AR, sensitivity and the resolution limit of 2, 3 and 4-DoF resonant systems.…”

“…We can see from (18) that δx 1 + δx 2 and δx 1 − δx 2 are not the same as the minus sign in δx 1 − δx 2 and has influences on other items except N 1 and N 2 . This accounts for our different resolution model in comparison with [25] in which δx 1 − δx 2 is regarded as a whole.…”

“…https://engine.scichina.com/doi/10.1007/s11432-020-2974-9 In particular, when ǫ = 0 and ω in (9) equals to the resonant frequency ω 1 , which is the resonant frequency of the first mode for mode-localised sensors. ǫ = 0 means there is no disturbance from outside, and we use this condition which is the same as conditions in [14,25] to establish the resolution model, and then we can get…”