Synchronization mechanism within the blind zone of the differential resonant accelerometer

Within the range of the differential resonant accelerometer, a blind zone exists that leads to nonlinearity, noise, and zero output, thereby introducing uncertainty and degrading performance. Exploration of the underlying synchronization mechanism leads to an understanding of this uncertainty. In this study, the Huygens pendulum model was employed to explain how both anti-phase and in-phase synchronization coexist and transfer between each other, where jumps occur stemming from the different configurations of the potential wells of the resonator. Noise increase, attributed to phase slip, was observed before and after synchronization, potential to be utilized to detect shocks in the surroundings. Consequently, the entire process of synchronization within the blind zone was verified, and the frequency stability, bias instability and resolution of the accelerometer were greatly improved.

Methods
The experimental platform was equipped with a precise optical dividing head (SJJF-1, TIANHE, Shanghai, China)(SJJF-1, TIANHE, Shanghai, China), a precise gating ruler, a extra high-precise adjustable thermostat-container, two universal frequency counters (KEYSIGHT 53230A), a multimeter (KEYSIGHT 34461A), a network analyzer ((Digilent Analog Discovery 2), and an oscilloscope (Agilent Technologies DSO5012A). The movies were recorded by camera and processed by Adobe Premiere.

With the adjustment of the optical dividing head to the horizontal position through the agency of the calibrator and installation of the accelerometer upon the precise optical dividing head, the accelerometer was rotated counterclockwise for a round inside the high precision adjustable thermostat container at 50 ◦C. The dividing head was rotated to 0◦, 90◦, 180◦, and 270◦ position, where the 0◦ position corresponds to 0 g input for the accelerometer, 90◦ to 1 g input, 180◦ to 0 g input, and 270◦ to −1 g input. In the rotary experiment, because the sensitive direction of accelerometer is z-axis of the sensitive structure, the input acceleration a is calculated a=g*sin(θ) where g is the gravity and θ is the angle between the input axis of accelerometer and direction of gravity. Frequency output of resonators were recorded by two universal frequency counters. Phase of resonators were recorded by an oscilloscope. Amplitude-frequency and phase-frequency curves were recorded by a network analyzer. Impedance curves of resonators were recorded by a Impedance analyzer (KEYSIGHT E4990A). The Allan deviation is widely used for modeling random errors in inertial devices, in which the bias instability is represented by the slope value of 0 in the dual logarithmic coordinate diagram, referring to low-frequency zero bias jitter caused by random fluctuations in internal circuits and temperature changes and characterizing the variation of zero bias over time. The output acceleration density of the resonant accelerometer is measured in same period and sampling rate.

Movies are about phase locking, phase slips, rotary experiment, and variation of phase of resonators in shock.

Movie S1 is about phase locking with resonator 2 leading in anti-phase synchronization at first; Movie S2 is about phase locking with resonator 1 leading in anti-phase synchronization at first; Movie S3 is about phase slips in which phase of resonator 1 slides right relative to that of resonator 2; Movie S4 is about phase slips in which phase of resonator 1 slides left relative to that of resonator 2; Movie S5 is about rotary experiment; Movie S6 is about the variation of phase of resonators in shock (in in-phase synchronization); Movie S7 is about the variation of phase of resonators in shock (resonator 1 leading in anti-phase synchronization); Movie S8 is about the variation of phase of resonators in shock (resonator 1 leading in in-phase synchronization); Movie S9 is about the variation of phase of resonators in shock (resonator 2 leading in anti-phase synchronization); Movie S10 is about the variation of phase of resonators in shock (resonator 2 leading in in-phase synchronization). All movies were merel processed by montage and subtitles.