Quartz Resonator & Oscillator Tutorial

Attenuation

Normalized Frequency (referenced to the fundamental c-mode)

-20

-10

-30

-40

1.0

1.10

1.88

3.0

3.30

5.0

5.50

5.65

c(1)

b(1)

a(1)

c(3)

b(3)

c(5)

b(5)

a(3)

3-15

a-mode: quasi-longitudinal mode

b-mode: fast quasi-shear mode

c-mode: slow quasi-shear mode

Mode Spectrograph of an SC-cut


	In the above mode spectrograph of an SC-cut resonator, the Nth overtone of mode m is labeled m^(N) (after Ballato). The frequency of each resonance is normalized to that of the fundamental c-mode. The modal attenuations vary with resonator design. In the above example, the b-modes’ strengths are greater than the c-modes’ (which is often the case). Therefore, the oscillator must include mode selection circuitry in order to insure that the oscillator operates on the desired c-mode.


	A. Ballato, "Piezoelectric Resonators," in B. Parzen, Design of Crystal and Other Harmonic Oscillators, pp. 66-122, John Wiley and Sons, Inc., 1983.

	J. A. Kusters, M. C. Fischer, J. G. Leach, "Dual mode operation of temperature and stress compensated crystals," Proc. of the 32nd Annual Frequency Control Symposium, 1978. pp. 389-397.

	R. Bourquin, J.J. Boy, B. Dulmet, “SC-cut Resonator With Reduction of b-mode Electrical Response,” Proc. 1997 IEEE Int’l Frequency Control Symposium, pp. 704-709.