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Analysis of Frequency Locations of the In-Harmonics in Quartz Surface Acoustic Wave Resonators Using Helmholtz Equations

Preventing spuriousness in a quartz surface acoustic wave (SAW) resonator is important for maintaining reliability in digital communication systems because it reduces phase noise quality of signals. For such a resonator, the in-harmonic modes, which are also undesirable responses in the direction of the lengthwise x-coordinate and the transversal y-coordinate, have been studied. We show that the governing equation of the resonator is given by a Helmholtz equation, and we obtain equations corresponding to the resonance frequencies. We solve them theoretically for transverse modes, and numerically using a T matrix for longitudinal modes. We obtain a frequency-mode chart of a one-port quartz SAW resonator and obtain adequate agreement of accuracy with in-harmonics that involve two-dimensional modes. Furthermore, we study mesa-structure-type SAW resonators to determine a method of controlling the frequency arrangement.