Equivalent-Circuit Model for Quartz Resonators Effects of Finite Element Analysis, Acceleration, and Mass Loading

Abstract

In radar equipments and communication systems, quartz resonators are key components. So as to enhance the resonator performances, the development of accurate modelings taking into account the environment interaction (temperature, acceleration, magnetism, …) is one of the major economic and strategic stakes. The main idea is to produce a realistic modeling. In literature, a lot of modelings are based on finite element analysis. But, for industrial applications, it is essential to link these accurate modelings to electric simulation softwares, such as Spice. Moreover, it is necessary to develop a simple computation method in order to answer the industrial time constraints. The idea is to use a Butterworth-Van Dyke (BVD) model based on an electrical equivalent circuit with, as input data, the studied natural frequency and the antiresonance frequency of an accurate finite element modeling. For the numerical example, a SC-cut (Stress-Compensated cut) quartz resonator is studied in this article for its fundamental thickness-shear resonance, the third and the fifth overtone. The influence of the model mesh quality, the electrode mass-loading, and the acceleration sensitivity on the motional parameters are analyzed. First, the choice of the finite element number along the thickness axis is crucial for the computation accuracy of the motional parameters. Then, the more the electrode material has a high density, the more the mass loading has a strong influence of the motional parameter values. Finally, the motional parameters are not really influenced by the acceleration field.