The second harmonic generation in piezoelectric resonators

The effect of frequency-amplitude, nonlinear dependence of vibration amplitude on applied voltage and second-order harmonic (SH) generation are the main manifestations of nonlinear behaviors in piezoelectric resonators. These nonlinear effects will degrade the resonator as a frequency-control device. On the other hand, they do suggest some directions to determine high-order elastic and piezoelectric constants of piezoelectric materials. In the present paper the theoretical and experimental studies are reported, addressing the SH generation of resonators due to medium nonlinearity. Experiment was carried out for Z-cut LiNbO₃ to observe the SH vibration at the free surface of an electrically excited thin plate. Its amplitude is measured by a capacitive detector which is able to be calibrated absolutely, showing that the strongest efficiency of SH generation appears near the frequency of anti-resonance, as predicted by the corresponding theory using successive approximation. Mathematical solution to the problem relates the SH amplitude to high-order constants of piezoelectric crystals. Further development is expected to apply this technique to measurement of material parameters by means of the aforementioned nonlinear coefficients