Research On Methods Of Mode Simulation And Equivalent Electrical Parameters Calculation Of AT-cut High Fundamental Frequency Quartz Crystal Resonator

Quartz crystal resonator（QCR）is a passive crystal oscillator with stable temperature frequency characteristics,low loss and high Q value.It is the mainstream frequency selection device in the current market.Because the finite element method（FEM）has the advantages of simple calculation and can be applied to complex models,it is very suitable for the study of resonators.At present,the finite element simulation research of resonator is mainly aimed at the small vibration of each vibration mode of QCRs below 50MHz,which can not meet the needs of high-frequency development of resonator and is difficult to be directly applied to the design and manufacture of resonator in industry.Therefore,it is necessary to find a finite element method that can accurately simulate the vibration of QCRs with high fundamental frequency,and obtain the electrical performance parameters of resonator on this basis,so as to better guide the design and manufacturing process of resonator.The main results of this paper are as follows:The 96 MHz fundamental frequency AT-cut QCR with great application potential was selected as the research object,and 96 MHz QCR samples were prepared as the comparison of finite element simulation.According to the actual dimensions of the resonator,the two-dimensional finite element simulation method based on Tiersten scalar differential equation,mass equivalent method,surface element method and shell element method were used to simplify the model and simulate the QCR.The vibration frequencies and modes of the thickness shear mode of the resonator under several simulation methods were compared.It was found that the surface element method could better reflect the actual thickness shear vibration of 96 mhz quartz crystal resonator.The electrical performance parameters of quartz crystal resonator were simulated and analyzed by surface element method,and the loss introduced by electrode plate and packaging was compensated by setting additional damping ratio.When the damping ratio was 2.85×10^-5,the relative error of static capacitance C₀ was 0.78%,the relative error of dynamic capacitance C₁ was 0.78%,the relative error of dynamic inductance L₁ was 1.41%,and the relative error of resonator resistance R₁ was 0.43%.The simulation of the electrical performance parameters of the resonator had achieved good results,which showed that the calculation method of the electrical parameters of the resonator based on the surface element method proposed in this paper could be used to guide the actual design and process optimization of quartz crystal resonator.The finite element simulation of the resonator with the same total electrode thickness and different electrode thickness distribution on the upper and lower surfaces was carried out,and the electrical parameters and the factory value Q were calculated.It was found that with the increase of the thickness ratio of the upper and lower electrodes,the thickness shear frequency of the resonator increased,and the quality factor of the electrical performance of the quartz crystal resonator decreased.Therefore,in the actual production,the thickness of the upper and lower surface electrodes should be consistent as much as possible.