Comparing Different Output Metrics of High-Resolution MEMS Weakly Coupled Resonant Tilt Sensors

Abstract

This article presents the theoretical analysis and experimental investigation of a weakly coupled resonant tilt sensor based on different output metrics, including mode frequency, amplitude ratio (AR), amplitude difference, and eigenstate. Especially, we investigate the sensitivity, linear working range, stability, and noise analysis by theoretical analysis and evaluation of experimental results. The tilt sensor sensing element is the weakly coupled resonators, the output metrics of which shift are proportional to the effective stiffness perturbation caused by changes in input inertial force along the sensitive axis when any tilt angular is applied to the tilt sensor. Furthermore, it is demonstrated that there is an optimal operating point for amplitude difference output through theoretical analysis. The experimental results show that the minimum input-referred angle noise densities of the tilt sensor based on the AR and amplitude difference are <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.03\times 10^{-{4}}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$9.10\times 10^{-{5}}\,\,^{\circ} /\surd $ </tex-math></inline-formula> Hz, respectively. In addition, the weakly coupled resonant tilt sensor based on the AR and amplitude difference outputs achieve resolutions of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$9.79\times 10^{-{5}\circ }$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$7.53\times 10^{-{5}\circ }$ </tex-math></inline-formula> with an integral time of 15 s, and the mode frequency output achieves a resolution of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.141\times 10^{-{5}\circ }$ </tex-math></inline-formula> with an integral time of 0.5 s. The experimental results demonstrate that based on amplitude difference output has the best long-term stability and based on the mode frequency output has better short-term stability. Additionally, it is demonstrated that the output based on the AR balances sensitivity, linear range, and long-term stability.