Phase noise limitation due to amplitude frequency effects in state-of-the-art quartz oscillators

During the past two decades very important advances have been accomplished in reducing the phase modulation (PM) noise in state-of-the-art bulk wave quartz crystal oscillator. Various limitations have been significantly reduced, especially those related to dynamic temperature fluctuations, temperature gradients, 1/f noise in the electronic and amplitude frequency effects. Amplitude frequency effects have been studied in the past because they are so large in AT-cut resonators. The introduction of the SC-cut significantly reduced the sensitivity to amplitude fluctuations as well as the sensitivity to temperature fluctuations. The amplitude frequency effect in modern SC-cut resonators at 5 or 10 MHz is, however, far from negligible and its importance relative to temperature effects and 1/f amplifier noise must now be reexamined to chart the path to further advances in short-term stability. In this paper we show comparisons of the amplitude frequency effect in traditional 5 MHz AT-cut resonators to our results obtained with 5 MHz BVA AT-cut, 5 MHz BVA SC-cut, 10 MHz BVA AT-cut and several designs of 10 MHz BVA SC-cut resonators. We also compare these measurements with those obtained from 100 MHz resonators. A simple model in which an additional noise source arising from the amplitude frequency effect is introduced in the input of the resonator excited at a given power. This permits us to estimate the contribution of the amplitude frequency effect to σ_y(τ)