Investigation of drive level dependencies of higher overtones in SC quartz resonators

In this paper we illustrate our experimental investigations of drive level dependencies of two higher overtones (the 5^th and the 7^th ones), as well as of the main mode (the 3^rd overtone) of several different stress compensated (SC) quartz resonators. The drive level dependencies of basic parameters in the simple Butterworth-Van Dyke one-port equivalent circuit of the particular mode were derived from the impedance vs. frequency responses measured in the vicinity of the particular modes, while temperature of the investigated resonator was maintained approximately at the lower turnover point temperature of the main mode. In the 3^rd overtone 10-MHz SC quartz resonators, for example, the 5^th overtone or the 7^th overtone (the c-modes, i.e. the slow thickness-shear modes of vibration) can be exited simultaneously along with the main c-mode, with assistance of an appropriate dual-mode or multi-mode crystal oscillator (DMXO or MMXO); and the resonator self-temperature-sensing can be reliably implemented [1], [2], [3]. Level of amplitudes of particular modes, which are simultaneously excited in DMXO or MMXO, has impact on short-term, as well as on long-term frequency instabilities of generated signals; hence drive levels of individual c-modes have to be set-up properly in the oscillator circuit.