4-68
L(f)
10g amplitude @ 100 Hz
G  = 1.4 x 10-9 per g
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f
NOTE: the “sidebands” are spectral
lines at ±fV from the carrier frequency
(where fV = vibration frequency).  The
lines are broadened because of the finite
bandwidth of the spectrum analyzer.
Vibration-Induced Sidebands
As shown in the references, for small modulation index , i.e.,   f/fv = (A)fo/fv<0.1, sinusoidal vibration produces spectral lines at  fv from the carrier, where fv is the vibration frequency.  For an ideal sine wave, the “sidebands” are spectral lines (i.e., delta functions) not spectral densities.  Most of the power is in the carrier, a small amount is in the first spectral line pair, and the higher order spectral lines are negligible.  On a spectrum analyzer, the spectral lines appear to be sidebands - due to the finite bandwidth of the spectrum analyzer.


R. L. Filler, "The Acceleration Sensitivity of Quartz Crystal Oscillators:  A Review," IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 35, No. 3, pp. 297-305, May 1988.

J. R. Vig, C. Audoin, L. S. Cutler, M. M. Driscoll, E. P. EerNisse, R. L. Filler, R. M. Garvey, W. L. Riley, R. C. Smythe, and R. D. Weglein, "Acceleration, Vibration and Shock Effects - IEEE Standards Project P1193," Proc. 1992 IEEE Frequency Control Symposium, 763-781, 1992; also, The Effects of Acceleration on Precision Frequency Sources, U. S. Army Laboratory Command Research and Development Technical Report SLCET-TR-91-3, March 1991, AD-A235470.