Drive level dependence of the resonant frequency in BAW quartz resonators and his modeling.

The influence of the excitation current on the resonant frequency and its mathematical description makes necessary the introduction of a nonlinear impedance characteristic of the piezoelectric resonator. This influence was modeled by the nonlinear electrical equivalent circuit; the equivalent series resistance and equivalent motional capacitance are taken to be functions of the amplitude of the excitation current by means of the relations derived in the work. The equivalent circuit was analyzed by the method of equivalent linearization. The relationships between the amplitudes of voltage applied on the AT-cut resonator and the first current harmonics or phase-frequency dependence of the excited resonator, respectively, are derived. Amplitude jumps and dynamic temperature change phenomena are discussed.