The non-linear equivalent circuit of the vibrating Y-cut GaPO4 resonator

In this work, a new form of solution resulting from non-linear equivalent electrical circuit of the piezoelectric (YX1)0deg GaPO₄ resonators is given. The influence of the excitation current on the resonant frequency and its mathematical description makes necessary the introduction of a non-linear impedance characteristic of the piezoelectric resonator. This influence was modeled by the non-linear electrical equivalent circuit; the equivalent series resistance, equivalent motional inductance, 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 Y-cut GaPO₄ resonator and the first current harmonics or phases-frequency dependence of the excited resonator, respectively, are derived. Amplitude jumps are discussed