FREQUENCY TRIMMING OF THE STW RESONATORS WITH WORKING FREQUENCY UP TO 1 GHZ

This paper presents the data for frequency trimming of the single port STW resona-tors in a frequency range of 500–1000 MHz by plasma chemical etching method. The main parameters of resonators after frequency trimming are given: frequency tolerance <±100·10–6, quality factor of 8600–9500, equivalent elements needed for use of the STW resonators.

Oven-Controlled MEMS Oscillator with Integrated Micro-Evaporation Trimming

This study reports an oven-controlled microelectromechanical systems oscillator with integrated micro-evaporation trimming that achieves frequency stability over the industrial temperature range and permanent frequency trimming after vacuum packaging. The length-extensional-mode resonator is micro-oven controlled and doped degenerately with phosphorous to achieve a frequency instability of ±2.6 parts per million (ppm) in a temperature range of −40 to 85 °C. The micro-evaporators are bonded to the resonator, integrated face-to-face, and encapsulated in vacuum. During trimming, the micro-evaporators are heated electrically, and the aluminum layers on their surfaces are evaporated and deposited on the surface of the resonator that trims the resonant frequency of the resonator permanently. The impact of the frequency trimming on the temperature stability is very small. The temperature drift increases from ±2.6 ppm within the industrial temperature range before trimming to ±3.3 ppm after a permanent trimming of −426 ppm based on the local evaporation of Al. The trimming rate can be controlled by electric power. A resonator is coarse-trimmed by approximately −807 ppm with an evaporation power of 960 mW for 0.5 h, and fine-trimmed by approximately −815 ppm with an evaporation power of 456 mW for 1 h. Though the Q-factor decreases after trimming, a Q-factor of 304,240 is achieved after the trimming of −1442 ppm.

A Study on the Trimming Effects on the Quality Factor of Micro-Shell Resonators Vibrating in Wineglass Modes

Frequency trimming based on mass and stiffness modification is an important post-fabrication process for micro-shell resonators (MSRs). However, the trimming effects on the quality factor are seldom studied, although they may have great influence on the performance of the resonator. This paper presents a study on the quality factor (Q-factor) variation of trimmed micro-shell resonators (MSR). Thermoelastic damping (QTED) and anchor loss (Qanchor) are found to be the dominant energy loss mechanisms resulting in the reduction of the overall Q-factor, according to finite element method (FEM). The effects of different trimming methods on QTED and Qanchor are studied here, respectively. It is found that trimming grooves ablated in the rim of the resonator can cause a ~1–10% reduction of QTED, and the length of trimming groove is positively related to the reduction of QTED. The reduction of QTED caused by the mass adding process is mainly related to the thermal expansion coefficient and density of the additive and contact area between the resonator and additive masses. Besides, the first and second harmonic errors caused by asymmetrical trimming can cause a 10–90% reduction of Qanchor. Finally, trimming experiments were conducted on different resonators and the results were compared with FEM simulation. The work presented in this paper could help to optimize the trimming process of MSRs.

Trimming of Imperfect Cylindrical Fused Silica Resonators by Chemical Etching

The cylindrical resonator gyroscope (CRG) is a kind of solid-state gyroscope with a wide application market. The cylindrical resonator is the key component of CRG, whose quality factor and symmetry will directly affect the performance of the gyroscope. Due to the material properties and fabrication limitations, the actual resonator always has some defects. Therefore, frequency trimming, i.e., altering the local mass or stiffness distribution by certain methods, is needed to improve the overall symmetry of the resonator. In this paper, we made further derivation based on the chemical trimming theory proposed by Basarab et al. We built up the relation between the frequency split and the balanced mass to determine the mass to be removed. Chemical trimming experiments were conducted on three cylindrical fused silica resonators. The frequency splits of the three resonators were around 0.05 Hz after chemical trimming. The relation between frequency split and balanced mass established from experimental data was consistent with the theoretical calculation. Therefore, frequency split can be reduced to lower than 0.05 Hz under rigorous theoretical calculation and optimized chemical trimming parameters.