Direct Measuring the Amplitude Ratios of Weakly Coupled Resonators Employing Automatic Amplitude Control

Abstract

Since the eigenstate-modulated weakly coupled resonators (WCRs) characterize the detected signals by measuring the amplitude ratios of weakly coupled resonant units, the convenient and accurate extraction of amplitude ratios becomes critical for high-performance applications of all mode-localized sensors. This article proposes a modular hybrid measurement and control scheme based on automatic amplitude control to measure the amplitude ratios of weakly coupled resonant systems directly. The amplitude of one resonant unit is stabilized at a constant value by the automatic gain control (AGC), and the amplitude of the other resonant unit is adopted as an alternative for the amplitude ratios. A micromachined mode-localized sensor for acceleration measurement at atmospheric pressure is adopted to verify the feasibility of the proposed measurement and control scheme. Experiment results demonstrate that the tested mode-localized accelerometer prototype has a mechanical sensitivity of 0.2693 V/g with bias stability of 30.82 mg and a noise floor of 657.59 μg/Hz <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sup> . Furthermore, the proposed output metric's profile is consistent with the amplitude ratios and maintains approximate background noises compared with the conventional amplitude ratio measurement method. Our proposal omits the algebraic division operations of vibration amplitudes, thereby simplifying the subsequent signal processing of mode-localized sensors.