A Comsol analysis of packaging structures and parameters of quartz crystal resonators

By nature, acoustic wave resonators are structurally dynamic components undergoing constant vibrations in the vicinity of resonant frequency at their functioning mode, which is definitely adversary with other components used in the same board and product. One particular concern in the design and packaging of acoustic wave resonators is that all packaging parameters and structures will cause changes of device performance in terms of frequency, circuit parameters, and thermal sensitivity, among others. We start with a complete finite element analysis model of a quartz crystal resonator with the consideration of structural complications including packaging, while the quartz crystal blank is analyzed with the Mindlin plate equations of five vibration modes for coupled thickness-shear vibrations. Other parts of structure are formulated with the three-dimensional theory of elasticity from Comsol. With this finite element model, many of the key features and parameters of the quartz crystal resonator are consider...