Self-identification of differences between aging rates of two frequencies excited in the dual-mode crystal oscillator

In this paper we introduce an extension of the self-temperature-sensing of stress compensated (SC) quartz resonator based on simultaneous excitation of two overtones (3^rd and 5^th overtone) - the slow thickness-shear modes (i.e. the c modes) in dual-mode crystal oscillator (DMXO). The extension is based on implementation of a self-identification of the differences between aging rates (long-term frequency instabilities) of the two mode´s frequencies simultaneously excited in the quartz resonator. Processing of two excited c mode´s frequencies enables to predict their shifts due to resonator´s temperature variations in a wide range, where the characteristics of the c modes are free from significant anomalies.