Modified Modeling Method of Quartz Crystal Resonator Frequency-Temperature Characteristic With Considering Thermal Hysteresis

• Published in: IEEE transactions on ultrasonics, ferroelectrics, and frequency control ferroelectrics, and frequency control, 2021-03, Vol.68 (3), p.890-898
• Main Authors: Deng, Xiaogang, Wang, Shubin, Huang, Xianri, Liu, Hao, Cui, Baochun
• Format: Article
• Language: English
• Subjects: Artificial neural networks; Compensation; Crystals; Deviation; Extreme learning machine (ELM); Frequency control; frequency-temperature characteristic; Hysteresis; Machine learning; Modelling; Optical resonators; Oscillators; Polynomials; Quartz; quartz crystal resonator; Quartz crystals; Resonant frequency; Resonators; Temperature; thermal hysteresis
• ISSN: 0885-3010; 1525-8955
• DOI: 10.1109/TUFFC.2020.3014887

The frequency-temperature ( {f} - {T} ) characteristic of quartz crystal resonators is an important topic closely related to the frequency-deviation compensation in the design of cost-effective oscillators. Traditional studies depict the {f} - {T} characteristic as a polynomial function (usually a cubic function). However, this omits the thermal hysteresis phenomenon and cannot provide a very accurate frequency compensation. To handle this issue, this article is to propose two modified {f} - {T} characteristic modeling methods with considering the thermal hysteresis. First, to reflect the thermal hysteresis property of quartz crystal resonators, a two-directional {f} - {T} model is designed by introducing two individual submodels for describing the increasing and decreasing temperature stages, respectively. Furthermore, to integrate the submodels and provide the more accurate frequency-deviation estimation, a holistic {f} - {T} characteristic model based on double-hidden layer extreme learning machine (DHL-ELM) is presented. Different from the basic ELM model, two hidden layers, including one deterministic nonlinear mapping and one random nonlinear activation layer, are constructed for a better description of {f} - {T} characteristic. To validate our studies, an experiment system is applied to obtain the testing data of the real crystal resonators, and the applications demonstrate the effectiveness of the proposed methods.