ABSTRACT
In this paper, the phase noise of aluminum nitride (AlN) contour-mode resonators is investigated using a passive measurement system with carrier suppression. The purpose is to make careful measurements of the performance of AlN resonators in order to better understand and clarify previously reported frequency instability in these devices. The resonant frequencies of the resonators are around 220 MHz. The motional parameters, the thermal behavior, and the nonlinear power effect of these resonators have been evaluated. Then, the principle of the noise measurement system is reviewed, and the resonator conditioning is shown. Finally, the noise measurements of the resonators are presented and discussed.
ABSTRACT
The amplitude-frequency effect is a well-known phenomenon in quartz crystal resonators. It can distort the results of short-term stability measurements. In our case, results are computed from phase noise measurements in passive bridge systems. This article presents a method to correct computation of short-term stability from passive measurements.
ABSTRACT
Although criticized by many, Handel's quantum model for 1/f noise remains the only model giving a quantitative estimation of the level of intrinsic 1/f noise in quartz crystal resonators that is compatible with the best experimental results. In this paper, we reconsider the volume dependence in this model. We first argue that an acoustic volume, representing the volume in which the vibration energy is trapped, should be used instead of the geometrical volume between the electrodes. Then, we show that because there is an implicit dependence of the quality factor of the resonator with its thickness, the net effect of Handel's formula is not an increase of noise proportionally to the thickness of the resonator, as could be naïvely expected, but a net decrease when thickness increases. Finally, we show that a plot of Q(4)Sy versus the acoustic volume, instead of the usual Sy plot, could be useful to compare the quality of acoustic resonators having very different resonance frequencies.
Subject(s)
Micro-Electrical-Mechanical Systems/instrumentation , Micro-Electrical-Mechanical Systems/methods , Models, Chemical , Oscillometry/methods , Quartz/chemistry , Computer Simulation , Electric Impedance , Scattering, RadiationABSTRACT
Quartz length-extension resonators have already been used to obtain atomically-resolved images by frequency-modulation atomic force microscopy. Other piezoelectric materials such as gallium orthophosphate (GaPO(4)), langatate (LGT), and langasite (LGS) could be appropriate for this application. In this paper, the advantages of langasite crystal are presented and the fabrication of similar microsensors in langasite temperature-compensated cuts by chemical etching is proved. A monolithic length extension resonator, with a tip at its end, is obtained which constitutes a real advantage in regard to the existing quartz devices.
ABSTRACT
In this letter, experimental investigation of frequency-temperature effects in langatate rectangular cross-section beams are presented. It is shown that a first-order temperature compensated cut exists for the first vibrating mode of length extension.
ABSTRACT
Temperature effects in gallium orthophosphate (GaPO4) vibrating beams are reported. In addition to the well-known, thickness-shear AT-cut, temperature-compensated cuts exist in GaPO4 for length extensional modes. Experimental evidence of a temperature-compensated cut in GaPO4 rectangular beam resonator vibrating in length extension is given.
Subject(s)
Acoustics/instrumentation , Computer-Aided Design , Electronics/instrumentation , Gallium , Models, Theoretical , Transducers , Computer Simulation , Equipment Design , Equipment Failure Analysis , Phosphates , Temperature , VibrationABSTRACT
This paper shows that first order temperature compensated cut exists in Langasite rectangular cross-section beam vibrating in length extensional mode. Theoretical and experimental investigations of frequency-temperature effects are given.
ABSTRACT
The frequency of a flexural resonator and its frequency-temperature behavior usually are computed by Bernoulli's classical approximation. This approach is valid for beams with a large length-over-thickness-ratio. For shorter beams, the effects of shear stress and rotary inertia may play a significant role for temperature-compensated resonators. These effects have been taken into account for isotropic beams. The aim of this paper is to discuss the extension of the shear coefficient in the case of an anisotropic material and to compute the frequency-temperature characteristic of an (XYt)theta cut resonator when the shear stress and the rotary inertia have been taken into account. Comparisons between the classical approximation and this treatment are given for quartz. Furthermore, the numerical predictions obtained by means of different sets of data available for thermal sensitivities of elastic coefficients are compared.
ABSTRACT
Flexural modes are the basic vibrating mode of tuning forks used in quartz wrist watches; they also can be used as the basis for sensors. Very little work, if any, has been done for vibrating beam resonators in GaPO4. In this paper, the possibility of temperature-compensated cuts in GaPO4 is investigated for length-extensional and flexural vibrating modes. A theoretical investigation of rectangular cross-section GaPO4 vibrating beam resonators is accomplished by analytical methods. Modeling temperature effect is achieved by the approximate but classical method in which the effective elastic constants, beam dimensions, and crystal mass density are varied as a function of temperature. Temperature-compensated cuts are given in GaPO4 for length-extensional and flexural modes. Some temperature-compensated cuts of GaPO4 exhibit inversion points at high temperatures.
ABSTRACT
In order to predict the phase noise in crystal oscillators an enhanced phase-noise model has been built. With this model, the power spectral densities of phase fluctuations can be 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. To validate this enhanced model, the behavior of a batch of 10 MHz quartz crystal oscillators is observed and analyzed. The tested batch has been chosen in a facility production. Their associated resonators have been selected according to the value of their resonant frequency and their motional resistance. Open-loop and closed-loop measurements are given. 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.
ABSTRACT
Leeson's is the basic model for predicting oscillator noise. A mathematical analysis of this "heuristic" model has been proposed. Both models do not detail the relative importance of the amplifier transfer function associated to its own noise with regard to that of the resonator. In this paper, an improved version of those previous models is presented. The phase noise generated by the amplifier and the one generated by the resonator are differentiated without considering their origins, such as the conversion of amplitude modulation noise into phase modulation noise. The power spectral densities of phase noise at various points of the oscillator loop are calculated from their respective correlation functions. As a consequence, the influence of the inner amplifier and resonator noises on the resulting oscillator noise is predictable. The model is especially attractive to the makers of widely used quartz oscillators. The resulting oscillator noise is easily obtained from the oscillator open-loop noise. An example of the phase-noise modeling of the Clapp quartz crystal oscillator is simulated and discussed.
