SYNCHRONIZATION IN MICROMECHANICAL GYROSCOPES

In this paper, we study the occurrence of synchronization between the two degenerate resonance modes of a micro disk resonator gyroscope. Recently, schemes involving the simultaneous actuation of the two vibration modes of the gyroscope have been implemented as a promising new method to increase their performance. However, this strategy might result in synchronization between the two modes, which would maintain frequency mode-matching but also may produce problems, such as degrading stability and sensitivity. Here, we demonstrate for the first time synchronization between the degenerate modes of a micro-gyroscope and show that synchronization dramatically reduces frequency instability at the cost of increased amplitude instability. INTRODUCTION Synchronization describes the tendency of weakly-coupled oscillators to track each other's frequency. This phenomenon has been observed for centuries in various fields in science, describing human's internal clock modulated by daylight periodicity [1], the behavior of grasshoppers singing in harmony [2] or fireflies’ flashes emitted at once and with the same period [3]. Nowadays, synchronization is implemented in technologies, providing beat stability in dysfunctional hearts thanks to pacemakers [4] and enhancing telecommunication systems [5]. With the development of micro-technologies, synchronization has also been studied in Micro-ElectroMechanical Systems (MEMS), locking the micro-oscillator's frequency to an external generator [6] or to another MEMS [7] in order to reduce their frequency fluctuations, one of the main sources of noise in microsensors. More specifically in MEMS Gyroscopes, frequency fluctuations are intensively investigated since they directly affect the stability of the gyroscope [8]. Different methods have been suggested in order to reduce these fluctuations [9], but most of them rely on active feedback while synchronization passively fixes the resonance frequency. This paper focuses on the implementation of synchronization in a Disk Resonator Gyroscope (DRG) and the resulting outcomes of this technique. In the first part, we will describe the device and the gyroscope’s working regime. We will then explain the synchronization implementation between one mode of the gyroscope and an external oscillator. In the following part, we will present the implementation of mutual synchronization between the two modes of the gyroscope. In the last part, we will discuss the performance of the gyroscope operated with these techniques. THE DISK RESONATOR GYROSCOPE The micro-gyroscope is a silicon disk with a diameter of 600μm and a thickness of 40μm (Fig. 1), first time presented in [10], made through the epi-seal process [11]. The device is anchored at the center and is surrounded by electrodes. As we apply a voltage difference between the electrodes and the device, we can drive the resonant modes of the disk, tune the resonance frequency [10], control the nonlinearity [12] and detect the vibration amplitude. In our disk, the gyroscope operation is based on the actuation of the two in-plane 2θ wineglass modes (described in the following as X and Y modes), the dynamics of which are described by the following equations: ̈ + ∆ ̇ + + + 8