Extension of the frequency aging model of crystal resonators and oscillators by the Arrhenius factor

The aging of quartz crystal resonators has been a key requirement of the product development and broad applications in signal generation and processing of many mission and life critical functions. Among many aging models for the analysis of long-term behavior of quartz crystal resonators, the Arrhenius model is widely accepted for most materials in engineering applications and physical process including quartz crystal resonators. A series of testing were conducted in different industrial laboratories in Japan and Germany to collect essential aging data of quartz crystal resonators and oscillators with the consideration of time, temperature, and frequency changes. The measurement data is merged and analyzed to extract different parameters of aging models for evaluation and validation. Finally, after careful examinations of parameters from different aging models, it is suggested that the Arrhenius model with modification is to be considered for the aging standard and further analysis are made with selected parameters.