Cubic frequency temperature dependence in periodic structures of recessed electrodes on quartz

It is shown that the cubic frequency temperature characteristic of a surface acoustic wave (SAW) quartz resonator with electrodes positioned at the groove bottoms can be obtained. The admittance characteristics of periodic structures of aluminum electrodes positioned at the groove bottoms of a quartz substrate were calculated using FEM analysis and periodic Green´s function method. The temperature coefficients of quartz material constants as well as temperature variations of geometrical dimensions of a unit cell were included in calculations. The temperature dependency of resonant frequency at the upper end of the reflection stop band shows cubic behavior with maximum frequency deviation +/-10 ppm in the temperature range from -30° to +80°C. The compensation of a non-zero second order temperature frequency coefficient can be possible due to temperature variation of the reflection coefficient in the periodic structure of electrodes and grooves.