Stability of crystal osciallators

Analogous to a spectral line, the output of an oscillator can be characterized by two parameters, the width of the line and its position on the frequency scale. The line width is determined by the signal to noise ratio and the position of the line by the phase relation in the oscillator loop. Using simple models, equations are derived for the limitations due to thermal noise wl1ich express the frequency stability of an oscillator in terms of the integration time, the pover level and the qualit~r factor of the circuit. Experimental data indicates that the limits on frequency stability set by thermal noise are being approached for integration times shorter than one tenth of one second. For longer time intervals, the present day oscillators are limited by the stability of the circuit elements which control the phase relation in the oscillator loop and not by thermal noise. The possibility that the quartz crystal unit has an equivalent noise resistance larger than its effective resonance resistance is ruled out.