Experimental study and theoretical prediction of aging induced frequency shift of crystal resonators and oscillators

Frequency shift, due to quartz crystal resonator aging, has been identified as one of the most important quality control problems of quartz crystal products. The problem becomes more significant due to the device miniaturization and high precision standards for telecommunication applications. Since aging induced frequency shift occurs during a long time frame, it is necessary to predict the long-term behavior of the devices based on the short-term data obtained under an accelerated environment. One the other hand, frequency shift is associated with quite large random variation, and thus, a proper probabilistic theory should be used for analyzing test data and for developing a reliable prediction model. Accelerated testing was performed for various types of crystal resonators under elevated temperatures. The frequency shifts of the devices were measured at different testing periods. Markov chain model was used to characterize the frequency shift of the devices. The obtained short-term test results were used for calibrating the probabilistic transition matrix of Markov chain model. The model can then be used for predicting the long-term frequency shift. The time-temperature superposition principle in viscoelasticity was adopted to address the shift in time under different temperatures. (C) 2003 Elsevier Ltd. All rights reserved.