Nonlinear Frequency Response of Second Harmonic Generation in SAW IDT Resonators

A general purpose finite element model that yielded directly the nonlinear frequency response of the second harmonic generation in SAW IDT resonators was developed. The model enabled us to study the effects of the nonlinear material constants, voltage drive, duty factor, and IDT geometry on f-2f nonlinear interactions. Specifically we have applied our model to the study of nonlinear frequency response of second harmonic generation in lithium niobate YX-127 degrees SAW IDT resonators. Lithium niobate was chosen because a complete set of its nonlinear material constants was known and published in the literature. A complete set of nonlinear piezoelectric equations along with their material constants for a lithium niobate YX-127 degrees SAW IDT 836 MHz resonator was implemented in a finite element program. Two sets of finite element matrix equations were derived for the fundamental SAW mode and its 2nd harmonic mode, respectively. We demonstrated how two frequency domain interfaces could be coupled together to simulate the f-2f nonlinear interactions. The fundamental Rayleigh SAW mode was excited by a drive voltage at the IDT that in turn generated the 2nd harmonic mode at twice the frequency. A higher voltage drive lead to higher 2f interactions. Effects of the 2nd harmonic generation on the fundamental SAW mode and its Q were observed when the voltage drive was greater than 0.5V. For example, when the drive voltage was 0.1V the fundamental mode was clean. But when the drive voltage was increased to 0.5V the fundamental mode exhibited Q reduction and stronger f-2f interactions were observed, namely, there were stronger interactions of the 2f BAW mode with the f SAW mode. There was an optimal duty factor of 0.4 to 0.5 for the least f-2f interactions. Thinner electrode thickness resulted in stronger f-2f interactions.