Quartz Resonator & Oscillator Tutorial

3-6

X-ray topographs (21•0 plane) of various modes excited during a frequency

scan of a fundamental mode, circular, AT-cut resonator. The first peak, at

3.2 MHz, is the main mode; all others are unwanted modes. Dark areas

correspond to high amplitudes of displacement.

3200

3400

3600

3800

0 db.

-10 db.

-20

-30 db.

-40 db.

Frequency, in kHz

Response

3200

MHZ

3256

3383

3507

3555

3642

3652

3707

3742

3802

3852

Resonant Vibrations of a Quartz Plate


	Resonators of finite dimensions have complicated mode specra. “Unwanted” modes occur above the main resonance, as is shown above. These unwanted (also called “spurious”) modes are especially troublesome in filter applications. In oscillator applications, controlling the unwanted modes is not as critical because, as long as the unwanted modes are at least 10 dB below the main mode, the oscillation will be at the main mode. Contouring, and “energy trapping” rules are used to minimize the unwanted modes. The energy trapping rules consist of certain relationships between the electrode and plate dimensions.
	As Shockley, et. al pointed out, “energy trapping” and the concepts of “cutoff frequency” and exponentially decaying waves in piezoelectric resonators are similar to the well-know such phenomena in microwave and optical cavities (related to total internal reflection).
	Mindlin has been quoted as having said about spurious modes “they aren’t spurious; they are supposed to be there…the theory predicts them!”
	-------------------------
	K. Haruta and W. J. Spencer, "X-ray Diffraction Study of Vibrational Modes," Proc. 20th Annual Symposium on Frequency Control, pp. 1-13, April 1966, AD-800523. Copies available from National Technical Information Service.
	W. J. Spencer, "Observation of Resonant Vibrations and Defect Structure in Single Crystals by X-ray Diffraction Topography," in Physical Acoustics, Vol. V, W. P. Mason and R. N. Thurston, Eds., Academic Press, New York, 1968.
	B. Capelle, J. Detaint, A. Zarka, Y. Zheng and J. Schwartzel, “Mode Shape Analysis Techniques Using Synchrotron X-ray Topography,” Proc. 44th Ann. Symp. On Frequency Control, pp. 416-423, 1990.
	W. Shockley, D. R. Curran & D. J. Koneval, “Energy Trapping and Related Studies of Multiple Electrode Filter Crystals,” Proc. 17th Ann. Symp. On Frequency Control, pp. 88-124, 1963.
	W. Shockley, D. R. Curran & D. J. Koneval, “Trapped Energy Modes in Quartz Crystal Filters,” J. Acoustical Soc. Amer., vol. 41, pp. 981-993, 1967.