Raymond Besson

Theoretical and experimental studies of the force-frequency effect in BAW LGS and LGT resonators

It is well known that, for quartz crystal, mechanical and/or thermal stress sensitivities prevent the achievement of ultimate performances of bulk acoustic wave piezoelectric resonators. It is important to check these effects in newly developed Langasite (LGS) and Langatate (LGT) resonators. A theoretical and experimental study of the force-frequency effect (denoted by the K/sub f/ coefficient) in Y-cut LGS thickness-shear resonators, working at various overtone modes, is presented. Theoretical predictions are based on Tiersten theory of wave propagation in a pre-stressed medium. For LGS crystals, 3/sup rd/ order nonlinear elastic constants have been published and used here for modeling the behavior of thickness-shear resonators submitted to diametrical compression. A comparison between theoretical predictions and experimental measurements is presented. In the case of LGT crystal, numerical data of the third order elastic coefficients are not available at this time. Only experimental measurements of Kf coefficient are presented in order to compare the behaviors of LGS and LGT Y-cut resonators.

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 /spl sigma//sub y/(/spl tau/).

A space oscillator with cylindrical oven and symmetry

A cylindrical oven whose axis is the axis of the 10 MHz quartz resonator (in HC 40 can) is studied. Thermal flux is canalized on its axis at a place where the thermistor is located. Thermal exchanges include conduction and radiation effects, reduced, however, by the use of a dual envelope. The oven is studied through a scheme which uses electric analogs, and results are obtained for external temperatures between -25 degrees C and +60 degrees C. The thermistor is located on the resonator can where temperature is very close to the turnover point. The analytical modeling uses oven symmetry. Thermal regulation design includes a frequency analysis between 0.001 Hz and 10 Hz, with a 60-dB gain. A response analysis to temperature steps and to linear temperature variation (0.5 degrees C/mn) is also performed. The thermal gain and dynamical behavior of oven electronics is deduced. Insertion of a correction network with phase advance in oven electronics yields a fast oven response. The oscillator improvements in space conditions are described.<<ETX>>

A phase noise model to improve the frequency stability of ultra stable oscillator

The goal of this study is to set up an improved model of the frequency stability behavior of the oscillating loop. A computer aided analysis is performed in which the transfer functions of the loop can be entirely described. This allows to predict phase noise performance of a given design. As a result the model provides ultimate limits of an oscillator concerning f/sup 0/, f/sup -1/, f/sup -3/ and f/sup -4/ phase noise versus the quartz resonator parameters for a given electronics noise. The model can also be used the opposite way to determine electronics noise for desired performances of an oscillator. Basic definitions are first recalled. The paper includes a description of the improved model that we developed starting from the Leesons model. This improved model is in good agreement with experimental results obtained from 10 MHz crystal oscillators with SC cut quartz resonator.

Acceleration sensitivity of BVA resonators

Acceleration sensitivity of a quartz resonator is usually attributed to the design of the unit. BVA technologies have largely participated to g-sensitivity reduction since 1977. At that time it was claimed that symmetry of the unit structure was fundamental. More recently it has been demonstrated by Tiersten that g-sensitivity could vanish to zero for perfect symmetry (including blank geometry, mounting, etc...). Under those conditions BVA technologies have to be considered in a general discussion on g-sensitivity reduction, because they may help to draw interesting conclusions. In this paper we show that BVA technology is adequate for very low g-sensitivity and why. By very low g-sensitivity we understand largely under 1/spl times/10/sup -10//g in industrial production. Furthermore the influence of some construction parameters and/or lack of symmetry due to manufacturing have been studied through finite element analysis. Results are shown and commented on (orientation of mounting, off centering of contour, off centering of grooves). We then compare these theoretical values to experimental ones. Experimental data are obtained by two methods: measurements under random vibrations and/or sinusoidal vibrations; measurements of frequency deviation in 2g tip over tests. Finally practical design in view of state of the art units is commented on together with production statistics.

An oscillator for space

These last years a new 10 MHz quartz crystal oscillator family has been designed in LCEP with the support of the French space agency (CNES). It is intended for space applications especially. In this paper, the description of its general features is followed by two parts. The first one described the methodology which has been developed for designing such an oscillator. This part deals with the modeling of noise as well as the mechanical and thermal structure of the oscillator. The second part summarizes main experimental results. This obviously includes the frequency stability of the oscillator and its behavior when various disturbances occur in its environment. We particularly took care of its sensitivity to external temperature changes at the atmospheric pressure and mainly under vacuum. Exhibited frequency sensitivities to a magnetic field and vibrations are also provided.

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.

A quartz standard automatic frequency adjustment system

A system is presented that automatically adjusts the frequency of a quartz standard unit to the frequency of a reference unit. The quartz standard automatic frequency adjustment system (AFAS) has automatic adjustment which starts as soon as the signal to be frequency adjusted appears. The adjustment value is held between two successive adjustment procedures with minimum signal degradation. The adjustment is made through a change of the varicap voltage. A phase-locked loop with controlled self-oscillation is used. AFAS includes a phasemeter comparing phases between the reference signal and the signal to be frequency adjusted. The output of the phasemeter is shaped so as to trigger a specific numerical block which works as a without-zero integrator. The without-zero integrator also ensures the storage of adjustment as soon as frequencies are close enough. The end of the frequency adjustment procedure is determined by use of self-oscillation counting. Among other results, it is found that at 5 MHz the frequency difference range is Delta f/f=2*10/sup -6/, and the residual frequency difference after adjustment is 4*10/sup -12/.<<ETX>>