A technique is presented that allows one to measure directly the fluctuations of the natural resonant frequency of quartz crystal resonators in a passive circuit. This technique greatly aids in modeling the noise in both crystal resonators and crystal controlled oscillator circuits. Definite changes of slope in the spectral density of the frequency fluctuations,as a function of frequency offset from the natural resonant frequen of the crystals indicate that several mezanisms are contributing to the frequency instabilities in crystals. Our measurements also indicate that the electronics in the oscillators seriously degrade the frequency stability for sample times less than 100 S. The effects are especially dramatic for times less than 1 S.
Download Full PDF Version (Non-Commercial Use)