Novel Quartz Crystal Cuts for SAW Substrates with Cubic Frequency-Temperature Relations

This study focused on the searching of new cuts for SAW substrates of triply-rotated quartz with cubic frequency-temperature (f-T) relationship by solving the equations of the first and second derivatives of the f-T function. First we established the f-T function of SAW, which was presented in matrix form and was based on the thermal incremental field theory. Next the wave velocity was obtained by the golden search method. Then the first two derivatives of the f-T function were calculated by multi-point finite difference formula. Finally, solving the nonlinear equations of the first two derivatives in the whole range of triply-rotated quartz, we obtained some new cuts with high inflection temperature Ti about 85°C.