F. Sthal

Phase noise measurements of 10-MHz BVA quartz crystal resonators

In this paper, we review a new piece of equipment that allows one to characterize the phase noise of crystal resonators using a phase bridge system with carrier suppression. This equipment allows one to measure the inherent phase stability of quartz crystal resonators in a passive circuit without the noise usually associated with an active oscillator. We achieved a system noise floor of approximately -150 dBc/Hz at 1 Hz and -160 dBc/Hz, at 10 Hz. A SPICE characterization of the carrier suppression system is given. An investigation of the phase modulation (PM) noise in 10 MHz BVA, SC-cut quartz crystal resonator pairs is presented.

Temperature-compensated cuts for length-extensional and flexural vibrating modes in GaPO/sub 4/ beam resonators

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 GaPO/sub 4/. In this paper, the possibility of temperature-compensated cuts in GaPO/sub 4/ is investigated for length-extensional and flexural vibrating modes. A theoretical investigation of rectangular cross-section GaPO/sub 4/ 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 GaPO/sub 4/ for length-extensional and flexural modes. Some temperature-compensated cuts of GaPO/sub 4/ exhibit inversion points at high temperatures.

Thermal compensation in GaPO 4 beam resonators: experimental evidence for length extensional mode

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

Temperature compensated cuts in LGT crystal microresonators using length extensional mode

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.

Frequency-temperature behavior of langasite rectangular beam resonators vibrating in length extension

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.

Study of LGS crystal micro-resonators using flexure mode: Temperature-compensated cuts

In this paper, new experiments have been carried out on LGS crystal to highlight the existence of temperature compensated cuts for flexure vibration. The micro-resonators are square cross section tuning forks whose arms are vibrating in flexure-mode with clamped-free boundary conditions. Frequency versus temperature behaviors have been measured for several cut angles. The results of our experiments show that there is a first order temperature-compensated cut for Langasite crystal resonators vibrating in flexion at room temperature.

Temperature-compensated cuts for vibrating beam resonators of gallium orthophosphate GaPO/sub 4/

A theoretical investigation of rectangular cross-section GaPO/sub 4/ vibrating beam resonators is proposed. Flexural modes are the basic vibrating mode of tuning forks used in quartz wrist watches, and can also be used as sensors. Very little work, if any, has been done for vibrating beam resonators in GaPO/sub 4/. The goal is then to investigate the possibility of temperature-compensated cuts for all three kinds of vibrations in GaPO/sub 4/: extensional, flexural, and torsional modes by analytical methods. Modeling temperature effects is achieved by the approximate but classical method of varying effective elastic constants, beam dimensions and crystal mass density versus temperature. Temperature-compensated cuts are found in GaPO/sub 4/ for length extensional modes and flexural modes. For vibrating beams, some of temperature-compensated cuts of GaPO/sub 4/ exhibit inversion points at high temperatures.

Frequency-temperature behavior of flexural quartz resonators by means of Timoshenko's model

The frequency of a flexural resonator and its frequency-temperature behavior usually are computed by Bernoullis 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)thetas cut resonator when the shear stress and the rotary inertia have been taken into account. Comparisons between the classical approximation arid 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

Modeling of a short-term stability measuring system of quartz crystal resonators

A new numerical model of a short-term stability measuring system of quartz crystal resonators is presented. It is based on the phase bridge method using a pair of resonators driven by a low-noise source. The output signal, obtained with a phase detector, is proportional to the phase difference introduced by the resonators. The numerical transfer function of each bridge path is given by the model. The output spectral density of the phase fluctuations is computed from these transfer functions and the numerical approximation of the low-noise source. The model was applied to third overtone, SC-cut, 10 MHz BVA quartz crystal resonators. It enables the rejection of the source noise versus the resonant frequency of quartz crystal resonators to be quantified.

Characterization of quartz crystal resonators on phase modulation noise without an oscillator

In the time domain, two methods are investigated to classify the phase noise of the resonators. A numerical model of frequency stability of ultra stable quartz oscillator is used to obtain the power spectral density of the phase fluctuations of an oscillator which contains the test resonator. The measurements of the phase noise of the quartz crystal resonators are obtained with a crystal resonator tester. New LD-cut 10 MHz BVA quartz crystal resonators are investigated.