Predicting phase noise in crystal oscillators

An enhanced phase noise model [1] allows to predict the phase noise in crystal oscillators. It is based on an improvement of the mathematical analysis proposed by G. Sauvage [2]. In this model, power spectral densities of phase fluctuations are computed in different points of the oscillator loop. They are calculated from their correlation functions. The resonator caused noise as well as the amplifier caused noise are taken into account and distinguished. In order to validate this model, the behavior of about ten of 10 MHz quartz crystal oscillators is observed and analyzed. These oscillators have been chosen in a facility production. Resonators have been selected according to the value of their resonant frequency and their motional resistance. We attempt to measure separately the amplifier and resonator caused noises by means of a passive method. The phase noise of the overall oscillator working in closed loop is provided by the usual active method. Theoretical and experimental results are compared and discussed.