Since a few decades, frequency control technology has been at the heart of modern day electronics due to its huge areaof applications in communication systems, computers, navigation systems or military defense. Frequency controldevices provide high frequency stabilities and spectral purities in the short term domain. However, improvement of theperformance of these devices, in terms of frequency stability, remains a big challenge for researchers. Reducing noise inorder to increase the short term stability and avoid unwanted switching between channels is thus very desirable. It iscommonly admitted that the fundamental limitation to this short-term stability is due to flicker frequency noise in theresonators. In this manuscript, a first chapter recalls some basic facts about acoustic, crystallography and definitions oftime and frequency domain needed to explore ultra-stable resonators and oscillators. The second chapter is devoted to asummary of the literature on flicker frequency noise. Then, the third chapter concerns our studies on Handel’s quantum1/f noise model, which although criticized by many, is still the only one that provides an estimation of the flooramplitude of 1/f noise that is not invalidated by experimental data. In the fourth chapter, another approach, based on thefluctuation-dissipation theorem, is used in order to put numerical constraints on a model of 1/f noise caused by aninternal (or structural) dissipation proportional to the amplitude and not to the speed. The last chapter is devoted toexperimental results. An ultra-stable resonator used during this study is described. Phase noise measurements on severalbatches of resonators are given. Measurements of resonator parameters have been done at low temperature in order tocorrelate them with noise results. Another approach with a procedure that use transient pseudo periodic oscillations andput to their limits the capacities of presently available digital oscilloscopes, is presented, in order to assess rapidly thequality of various resonators. Finally, conclusions and perspectives are given.

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Study on the origin of 1/f in bulk acoustic wave resonators

Phase noise represents signal instabilities in the frequency domain and is assessed through power measurements at various offsets from the carrier frequency. Herein, the phase noise of a clock generator is analyzed and modeled. Sources for the phase noise of the clock output at the resonance frequency are identified, including the power supply, the heat sink, and the external crystal. Low-frequency resonance is detected and validated to be caused by the external crystal grounding design. Solutions to decrease crystal-related noise are proposed and validated. In addition, the sensitivity based on the signal-to-noise ratio is proposed and verified with measurements, to numerically analyze the effects of power supply noise on clock phase noise. The proposed phase noise sensitivity is extracted from the measured phase noise results and can be used to estimate the phase noise and jitter of different power supply noises. The extraction and prediction method are validated with different buffer types including LVDS, HCSL, LVPECL, and LVCMOS in a device under test with the given design. 

Phase Noise Analysis of Clock Generator by Using Phase Noise Sensitivity

Phase noise represents signal instabilities in the frequency domain and is assessed through power measurements at various offsets from the carrier frequency. Herein, the phase noise of a clock generator is analyzed and modeled. Sources for the phase noise of the clock output at the resonance frequency are identified, including the power supply, the heatsink, and the external crystal. Low-frequency resonance is detected and validated to be caused by the external crystal grounding design. Solutions to decrease crystal-related noise are proposed and validated. In addition, the sensitivity based on the signal-to-noise ratio is proposed and verified with measurements to numerically analyze the effects of power supply noise on clock phase noise. The proposed phase noise sensitivity is extracted from the measured phase noise results and can be used to estimate the phase noise and jitter of different power supply noises. The extraction and prediction methods are validated with different buffer types, including low-voltage differential signal, high-speed current steering logic, low-voltage positive emitter-coupled logic, and low-voltage complementary metal–oxide–semiconductor, in a device under test with the given design.

In this paper, quartz crystal resonators have been cut from a quartz crystal block usually used to grow new generations of quartz crystal blocks. The blank realization and the topology of the resonator prototype are exposed. The resulting resonators are SC-cut with a 5 MHz resonant frequency. Then, we report the first noise measurements made on these quartz crystal resonators. A comparison of these resonators is given in terms of motional parameters and Q factors, and the results are presented according to the position of the resonators inside the mother crystal block.

P. Abbe

Papers

Noise of quartz resonators according to their origin in the mother crystal