A decouple-decomposition noise analysis model for closed-loop mode-localized tilt sensors

Kunfeng Wang; XingYin Xiong; Zheng Wang; Liangbo Ma; BoWen Wang; WuHao Yang; Xiaorui Bie; ZhiTian Li; XuDong Zou

doi:10.1038/s41378-023-00614-z

A decouple-decomposition noise analysis model for closed-loop mode-localized tilt sensors

Microsyst Nanoeng. 2023 Dec 21:9:157. doi: 10.1038/s41378-023-00614-z. eCollection 2023.

Authors

Kunfeng Wang^{1

2

3}, XingYin Xiong¹, Zheng Wang⁴, Liangbo Ma^{1

2}, BoWen Wang^{1

2}, WuHao Yang¹, Xiaorui Bie¹, ZhiTian Li¹, XuDong Zou^{1

2

4}

Affiliations

¹ The State Key Laboratory of Transducer Technology, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing, China.
² School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing, China.
³ Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA USA.
⁴ Shangdong Key Laboratory of Low-altitude Airspace Surveillance Network Technology, QiLu Aerospace Information Research Institute, Jinan, China.

Abstract

The development of mode-localized sensors based on amplitude output metrics has attracted increasing attention in recent years due to the potential of such sensors for high sensitivity and resolution. Mode-localization phenomena leverage the interaction between multiple coupled resonant modes to achieve enhanced performance, providing a promising solution to overcome the limitations of traditional sensing technologies. Amplitude noise plays a key role in determining the resolution of mode-localized sensors, as the output metric is derived from the measured AR (amplitude ratio) within the weakly coupled resonator system. However, the amplitude noise originating from the weakly coupled resonator's closed-loop circuit has not yet been fully investigated. This paper presents a decouple-decomposition (DD) noise analysis model, which is applied to achieve high resolution in a mode-localized tilt sensor based on a weakly coupled resonator closed-loop circuit. The DD noise model separates the weakly coupled resonators using the decoupling method considering the nonlinearity of the resonators. By integrating the decoupled weakly coupled resonators, the model decomposes the weakly coupled resonator's closed-loop circuit into distinct paths for amplitude and phase noise analyses. The DD noise model reveals noise effects at various circuit nodes and models the system noise in the closed-loop circuit of the weakly coupled resonators. MATLAB/Simulink simulations verify the model's accuracy when compared to theoretical analysis. At the optimal operating point, the mode-localized tilt sensor achieves an input-referred instability of 3.91 × 10^-4° and an input-referred AR of PSD of 2.01 × 10^-4°⁄√Hz using the closed-loop noise model. This model is also applicable to other varieties of mode-localized sensors.

Keywords: Electrical and electronic engineering; Sensors.