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Nonlinearly coupled sets of piezoelectric field equations in the frequency domain were derived for the nonlinear propagation of finite amplitude waves in piezoelectric bulk acoustic wave (BAW) and surface acoustic wave (SAW) devices. To verify their accuracy, we have embedded these sets of equations in the finite element method (FEM) of COMSOL Multiphysics software, and compared the FEM results with both analytical and experimental results found in the published literature. The nonlinear frequency responses for both plano-and contouredplate resonators of AT-cut quartz were investigated under various voltage drives, circuit resistances and quality factors. The proposed equations with FEM have also been employed to study 33.3 MHz very high frequency (VHF) quartz resonators showing that under different conditions of how well the third overtone mode (f3) matches third harmonic (3f), and how the fractional frequency shift of the third overtone mode (f3) occurs as a function of the fundamental mode current. Furthermore, we have studied the nonlinear harmonic generation of an 840 MHz 128° Y-cut Xpropagating (128° YX) LiNbO3 SAW resonator. Second harmonic (H2) and third harmonic (H3) modes were observed to occur respectively at two-times (2f) and three-times (3f) frequencies of fundamental frequency (f) when such resonators were driven with high power. The effects of substrate thickness, bottom surface conditions of the substrate, and different circuit connections on the H2 and H3 generation were simulated and compared with available measurements. Current proposed sets of equations are general and could be used for the study of nonlinear resonance, amplitude-frequency effect and harmonic generation in any piezoelectric devices provided that the necessary nonlinear material constants are known.
This article was published in the following journal.
Name: IEEE transactions on ultrasonics, ferroelectrics, and frequency control
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