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Development of a 10 MHz Oscillator Working with an LGT Crystal Resonator: Preliminary Results Joël Imbaud, Member, IEEE, Serge Galliou, Jean Pierre Romand, Philippe Abbé, and Roger Bourquin, Member, IEEE Abstract—Presently, to our knowledge, measurement of the noise of langatate (LGT) crystal oscillators has not previously been reported. First results of such a measurement are given in this paper. They have been obtained from 10 MHz resonator prototypes tested with a dedicated electronics. The main steps of the resonator manufacturing are described in this paper. Good quality factors, close to 1.4 106, have already been achieved on the 5th overtone of the thickness shear mode of LGT Y cuts, even if the energy trapping should still be optimized. The motional parameters of these resonator prototypes are quite different from those of usual quartz crystal resonators. As a consequence, dedicated sustaining electronics have been designed. The explored options are reported to justify the implemented one. Moreover, the high thermal sensitivity of LGT crystal resonators (parabolic f-T curve) requires that particular attention be paid to the oven thermal stability. This important feature is also pointed out in the paper. The preliminary version of the resulting system exhibits a relative frequency stability of 6 10−12.

I. Introduction

U

ntil now, LGS (La3Ga5SiO14) and LGT (La3Ga5.5Ta0.5O14) crystal resonators have been qualified in terms of quality factor, temperature effect, isochronism defect, and material quality. Because of their promising Q-f product (quality factor × frequency) [1]– [13], LGT crystal resonators appear to be good candidates for use in ultra stable oscillators (more than LGS crystal resonators). Indeed, their quality factors could be greater than those of high-quality quartz crystal resonators: typically, more than Q = 2 106 at f = 10 MHz for LGT crystal resonators [2], [3] against Q = 1.3 106 for usual SC cut quartz crystal resonators at the same frequency. The best quartz crystal oscillators can exhibit a short-term stability close to σy(τ) = 1.10−13, when referring to the standard deviation measured from the Allan variance, at measuring times of τ = 1 s. Presently, there is no data on the noise of LGT resonators and, of course, on the stability of associated oscillators. Our objective is to evaluate the shortManuscript received October 31, 2007; accepted April 13, 2008. This work was supported by the French “Délégation Générale pour l’Armement (DGA)” under contract # 01.34.033. The authors are with the Laboratoire de Chronométrie d’Electronique et de Piézoélectricité (LCEP) Department, Franche Comté Electronique Mécanique Thermique et Optique—Sciences et Technologies (FEMTOST) Institute, Besançon, France (e-mail: [email protected]). Digital Object Identifier 10.1109/TUFFC.883 0885–3010/$25.00

term stability of oscillators equipped with plano-convex LGT crystal resonators. This requires optimization of the design of the resonators and the development of oscillators adapted to such resonators having lower impedance than quartz resonators. The main features of the first prototypes of LGT crystal resonators, designed in our laboratory, are first detailed: their Q-factors on the selected overtone and associated motional parameters. Their thermal sensitivity is also compared with that of the usual quartz crystal SC-cut resonator. The next section includes different ideas of sustaining electronics circuits that have been simulated and tested to lead to the selected one, used for the first measurements of frequency stability. A short overview of the thermal conditioning and optimizing of the oscillator is given in Section IV. Finally, the resulting frequency stabilities obtained at this step of the work, still in progress, are described in the last section. II. Characteristics of LGT Crystal Resonator Prototypes Temperature-compensated cuts in LGT crystal have been sought, but no doubly rotated cut better than the simple rotated cut (the Y-cut) has been found. Unfortunately, this Y-cut exhibits a frequency-temperature curve that is parabolic and not the cubic curve obtainable with quartz resonators’ SC-cut. The energy trapping of the vibration is performed by means of a plano-convex shape. The definition of these plano-convex resonators has been determined from theoretical calculus and simulation based on the Tiersten theory [14]. Moreover, the material coefficients that are needed in the theoretical models have been measured in our laboratory. Indeed, coefficient values available in the literature are very scattered. We have used the same criteria used for AT- or SC-cut quartz resonators, i.e., the radius of curvature is such that the amplitude of vibration at the border of the disk is less than 1.10−6 times the amplitude at the center. The selected configuration is a 10 MHz Ycut, with a thickness of 0.68 mm, electrode diameter of 3 to 4 mm and working on its 5th overtone. According to the Tiersten theory [14], its expected parameters are as follows: motional resistance R = 36 Ω, parallel capacitor C0 = 4 pF for a Q-factor = 1.106.

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TABLE I. Plano-Convex Resonators Parameters (Without Bridge). OT

1 (2 MHz)

R (Ω) Q-factor R (Ω) Q-factor

3 (6 MHz)

5 (10 MHz)

R#1 Curvature radius = 115 mm, C0 = 17 pF 1.7 11.7 7.8 259 814 484 352 1 407 569 R#2 Curvature radius = 230 mm, C0 = 18 pF 2.7 3.7 5.7 136 356 115 978 1 381 794

Frequency values have been rounded off. Fig. 1. Resonator on its base plate (a) without bridges; (b) with bridges.

Nevertheless, our results are different in practice. We observe that models applied for trapping quartz crystal resonators require some adjustments. In fact, Tiersten’s model is an asymptotic model where the edge boundary conditions are rejected to infinity. Thus, if the radius of curvature is small, the model is less accurate. In our work, the optimization of the radius curvature has been performed experimentally (see Fig. 1 and Fig. 2). Let us add that Tiersten’s model has another limit: the mechanical aspect is treated according to a 3-D approach but only 1-D dependence of the electric field is taken into account. In other words, practical adjustments are always necessary for a given configuration. All our resonators were made with the same process, and manufacturing details are given in [4]. Today, 4 prototypes are usable. They consist of • Two samples, so-called “standard” resonators, whose electrode diameter is 8 mm; see Fig. 1(a). Fig. 2 shows measurements of their Q-f product versus the overtone number for 3 different curvature radii. Table I

details some measured motional resistors and the corresponding Q-factors. • Two samples with electrodes diameter of 3.5 mm. The latter have been submitted to an ultrasonic machining to make bridges (positioned in such a way to have a zero-force sensitivity to diametral compression) separating the active part (with a diameter of 10.2 mm) to the dormant support; see Fig. 1(b). The goal of this specific machining is to reduce the transmissions of mechanical stresses from supports to the resonant disc. The main drawback of this type of resonator is obviously its manufacturing complexity. Such a structure is similar to the BVA type [15] resonator. At least it can be seen as a first step toward this special type of electrodeless resonator. Fig. 3 and Table II are related to this type of resonator. As mentioned earlier, the use of our LGT resonators has also taken into account their temperature sensitivity. In fact, there is no more favorable frequency to temperature behavior than the parabolic one of the Y-cut. The frequency-temperature curve of an LGT crystal Y-cut is less favorable than a quartz crystal SC-cut as shown in Fig. 4. The frequency at the turnover temperature is

Fig. 2. Q-f product (quality factor × frequency) versus overtone rank of LGT crystal resonators without bridges and with various curvature radii.

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Fig. 3. Q-f product (quality factor × frequency) versus overtone rank of LGT crystal resonators with bridges, and with various curvature radii..

shifted by more than 1 kHz from the frequency at ambient temperature, compared with approximately 200 to 300 Hz for the SC-cut. It is interesting to compare the frequency-temperature sensitivity of LGT Y-cut resonator to well-known quartz crystal resonators in real working conditions. In a temperature control system, the practical operating temperature Top is shifted from the ideal turning temperature Ti, where df/dT(Ti) is zero. Then, due to this temperature offset Top − Ti, the relative frequency y = (f − f0) / f0 is sensitive to temperature according to the following relationship:

curve (see Fig. 4), and T0 is the reference temperature, usually 25°C. Eq. (1) is illustrated in Table III and Fig. 5 for various types of resonators. The langatate crystal Y-cut is 10 times more sensitive to temperature than the quartz crystal SC-cut. Therefore, the temperature control in the OCXO version should be developed and realized with great care. III. The Sustaining Electronics Topology

dy 2 Our first designs were developed for maximizing the (Top) = [ 2b + 6c (Ti - T0 ) ](Top - Ti ) + 3c (Top - Ti ) . loaded Q-factor of resonators. One difficulty is the low dT (1) motional resistance of the LGT crystal resonators: 10 times lower than quartz crystal resonators as shown in where b and c are, respectively, the second- and third-or- Table IV. The conventional Colpitts-oscillator topology der coefficients of the conventional frequency-temperature has been adapted to accept resonators with very low motional resistance, while working with a relatively high biasing current. Fig. 6 shows a sketch of an oscillating loop where 2 junction field effect transistors in parallel (JFETs) provide a high current-source solution and so reduce the output impedance of this transistor stage. Moreover, the

TABLE II. Plano-Convex Resonators Parameters (With Bridges). OT R (Ω) Q-factor Fig. 4. Frequency-temperature effect of LGT crystal resonator (in this example, it is the resonator without bridges) compared with that of a quartz crystal SC-cut.

R (Ω) Q-factor

1 (2 MHz)

3 (6 MHz)

5 (10 MHz)

R#3 Curvature radius = 100 mm, C0 = 9 pF 52 13.1 23 000 427 588 1 113 R#4 Curvature radius = 100 mm, C0 = 9 pF 53.7 15.3 21 476 373 750 759

Frequency values have been rounded off.

10.6 460 16.2 072

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TABLE III. The a, b, c Coefficients and the Local Derivative of Top (with Top − Ti = 0.1 K) for Different Materials and Cuts. Ti Quartz Crystal SC cut 72°C Quartz Crystal LD cut [16…18] 77°C Langatate crystal Y cut 64°C

a 10−6

b K−1

0.85 1.23 10−6 K−1 5.6 10−6 K−1

10−9

c K−2

13.3 14.6 10−9 K−2 7.8 10−8 K−2

10−12

dy/dT (Top) K−3

60.5 36.1 10−12 K−3 8.8 10−11 K−3

9.5 10−10 K−1 1.8 10−9 K−1 1.5 10−8 K−1

 

TABLE IV. SC-cut Quartz Crystal Resonator vs. Y-cut LGT Crystal Resonator. Optimized SC-cut Quartz Crystal C mode Overtone (OT) R (Ω) ROT - R@ 10 MHz R@ 10 MHz C0 (pF) f (MHz) Q (106)

Y-cut LGT Crystal (R#3)

B mode

1 476

3 92

5 368

+420%

0

+300%

3 60 35%

C mode 1 52

3 13

5 11

+372%

+18%

0

3 3.3 0.1

10 1.3

10 16.6 0.5

10.9 1.45

2.04 0.02

6.12 0.4

10.2 1.1

 

high input impedance of the circuit improves the loaded Q-factor. Simulations show that a loaded Q-factor of QL ≈ 870 000 can be reached for the resonators R#1 and R#2 with the topology of Fig. 6, i.e., this is equivalent to a very modest (33%) degradation in the resonator unloaded Q-factor. Nevertheless, this is obtained when the resonator is modeled by just the interesting motional branch. Actually, because of the low motional resistances of the 1st and 3rd overtones, the oscillator inevitably starts on a lower overtone than the expected one. Experiments have confirmed this fact. As highlighted in Table IV, the resistance ratio between resonant modes is much more disadvantageous in the case

Fig. 5. Slope of the relative frequency y at Top versus (Top – Ti).

of our LGT crystal resonator than for a standard SC-cut quartz crystal resonator. To avoid starting on unwanted overtones, the oscillator must contain an additive selective filter. On the other hand, the Q-factor of the desired (5th) overtone has to be preserved as much as possible. As a consequence, the topology of Fig. 6 has evolved toward a topology including a passband filter. In the same time, JFETs have been abandoned for bipolar junction transistors (BJTs). Indeed, JFETs device characteristics uncertainties are larger than BJTs ones, which make adjustments more complicated. Fig. 7 shows a resulting schematic; the loss resistances of the inductances are not shown in the schematic. Their values are between 60 and 80 ohms in our case. In com-

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frequency adjustment at 10.0 MHz has been skipped on these prototypes). Moreover, its electrodes are the smaller ones (Ø 3.5 mm), which gives a C0 value close to 10 pF (instead of 18 pF for electrode diameter of 8 mm). As shown in Fig. 8, the loaded Q-factor can be evaluated from the derivative of phase with respect to the frequency at the oscillating frequency for which the total phase of the open loop transfer function is zero whereas its gain modulus is larger than one. Using this method, the loaded Q is evaluated as QL ≈ 570 000, i.e., 52% of the unloaded Q-factor, as following:

df df

=2 fosc

QL QL 180 rdHz . -1 = 2 × deg .Hz-1. fosc fosc p

(2)

IV. Thermal Conditioning

Fig. 6. A JFET Colpitts oscillating loop authorizing high biasing current.

parison with the crystal impedance (~10 ohms), these inductor resistances values are high, leading to a Q-factor degradation. That is why a 2-transistor topology is used instead of the typical Colpitts oscillator with a LC filter used to eliminate the B-mode (see Table IV) in the case of the quartz crystal SC cut. The circuit of Fig. 7 that has been implemented could probably still be improved: basically, a 2-stage amplifier is not an ideal solution for a low-noise application. Simulations have been performed with the values of the resonator R#3. Its motional resistance is the lowest on the overtone of interest (5th) at 10.2 MHz (the step of

The parabolic frequency-temperature of the Y-cut LGT resonator leads to a relative frequency to temperature sensitivity of about 1.5 10−8 K−1 for an operating point set at 0.1°C from the turnover temperature (this is a realistic adjustment of the setting point value of the temperature control system). As a comparison, a conventional SC-cut quartz crystal resonator exhibits a sensitivity of about 1 10−9 K−1 in the same conditions. Obviously, a double oven is absolutely necessary for adequate thermal control of the LGT crystal oscillator. The temperature control set up is described in Fig. 9 and Fig. 10. The overall system is enclosed into a shell of thermal insulating foam. The first stage of the thermal control consists of copper housing, the top of which cap is temperature-controlled. The printed circuit boards of the sensitive electronics (oscillating loop and isolation ampli-

Fig. 7. Oscillating loop schematic of the test oscillator. In practice, the ouput at the collector of Q2 is then connected to an isolation amplifier followed by an output amplifier.

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Fig. 9. Ovenized system overview.

Power spectral densities of relative frequency fluctuations Sy( f ) or phase fluctuations Sφ( f ) cannot be entirely deduced from the Allan variance σy2(τ). Remember that the Allan deviation slope in τ −1 corresponds to Sϕ( f ) in f −1 and/or f 0, and a τ −1/2 slope corresponds to Sϕ( f ) in f −2 and/or f −1 (white noise of frequency and/or flicker of phase). A τ 0 slope corresponds to Sϕ( f ) in f −3 (flicker of frequency), according to the following relationship: sy(t) =

Fig. 8. Simulation results of the open-loop transfer function of circuit of Fig.7, driven and loaded by itself, versus frequency. The upper plot is the derivative of the phase versus frequency and the lower the open loop gain.

fier) are mounted to the external temperature-controlled housing by means of insulating links. They are themselves finely temperature-controlled with the inner crystal oven. This second stage of the ovenized system is the core of the system, in which the crystal oven is sandwiched between printed circuit boards. Both temperature regulators are conventional ones: the current temperature is sensed by a thermistor and the regulator electronics actuates a couple of heating transistors and resistors. For measuring the efficiency of the overall ovenized system, an SC-cut quartz crystal resonator has been substituted for the LGT-crystal resonator and excited on its B-mode. This mode acts like a temperature sensor because of its high temperature sensitivity of about −300 HzK−1. The thermal gain of the system has been evaluated to about 300, which is quite good but not still excellent. V. Noise Measurements The available resonator has a resonant frequency at 10.2 MHz. The oscillator constructed using this resonator has been compared with a 10.0 MHz quartz crystal reference of medium but sufficient quality (no 10.2 MHz reference was available in the lab at the time of the measurements). As a consequence, only Allan deviation measurements have been performed (see Fig. 11).

=

2 ln 2 ´ S y(f = 1 Hz) 2 ln 2 ´

1 2 fosc

× S j(f = 1 Hz).



(3)

As a consequence, an Allan deviation floor of σy(τ) = 6 10−12 would lead to Sφ( f ) ≈ −85 dBrd2/Hz at f = 1 Hz, in the f −3 area. It must be specified that a large frequency drift of about 1 10−10 per hour is observed on the prototype oscillator. Thus, measurements of frequency instabilities over averaging times longer than 100 s would be irrelevant, or a Picinbono variance would be more appropriate but not so interesting in our case. In fact, measurements have been performed on an oscillator working with a very “young” resonator and turned on from less than a few days. In addition, the most important point about the aging is that the tested resonator, as well as others described above, has not been submitted to annealing. Indeed, this operation is still to be set up and needs many trials. At this level of the study, the only information that can be extracted from the results of Fig. 11 is that an LGT crystal oscillator is able to reach, at least, a few 10−12. Presently, we are not convinced of measuring the resonator noise over averaging times of a few seconds. Indeed, observing a noise floor that already starts from 0.1 s is not usual: one can suspect the sustaining amplifier to make noise in such an area. Our sustaining amplifier is, unfortunately, a 2-stage amplifier. Thus, its phase noise is obviously greater than a single-stage circuit for an equivalent driving power. Special efforts will have to be made to find such a low-phase noise amplifier with a set of components values compatible with our LGT resonator. Otherwise, keeping in mind the high temperature sensitivity of LGT crystal cuts, a possible tuning imperfection of the temperature regulator could also be partly responsible for the frequency instability rising for long sample times.

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Fig. 10. The copper housing and the inner sandwich printed circuit board (PCB)/crystal oven/printed circuit board. The copper housing is then wrapped in an insulating foam.

Fig. 11. Allan deviation measurement.

VI. Conclusion This paper reports, for the first time, on the short-term frequency stability of oscillators employing LGT crystal resonators as the frequency control element. The good Q-f product obtainable in resonators has been previously established, but in-oscillator, short-term frequency stability performance has not. These preliminary results are quite disappointing at this level of our work. It is still difficult to analyze them and probably too early to reach any conclusions. Indeed, a few improvements can be expected from the following remarks. • Investigations on LGS and LGT from various suppliers have shown that a large disparity of material quality exists. We have to find high-quality crystals. • Experiments prove that the criterion of energy trapping adapted for quartz crystal resonators is not directly transposable to LGT crystal resonators. Par-

ticularly, the method of energy trapping calculation must be corrected. • The tested oscillator is very simplified and far from being optimized. A lot of work has still to be done. • The thermal control aspect of the oscillator design is predominant and obviously not favorable for ultrastable applications. A high-quality temperature control is then absolutely necessary. Our thermal conditioning for prototyping can also evolve. Quartz crystal resonators and their associated oscillators have undergone continuing improvement for more than half a century. Langasite-family crystals have been studied less than 20 years. As a consequence, the preliminary results described above must be considered as results of an immature research path. The capability of LGT crystal oscillators for ultra-stable applications cannot be judged yet from present results. We are still working on their future potential.

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Acknowledgment The results reported here are due to the efforts of a number of staff members in the chronometry, electronics, and piezoelectricity department of the FEMTO-ST Institute, whom the authors are pleased to acknowledge. References [1] Y. Kim, “Amplitude-frequency effect of Y-cut langanite and langatate,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 50, no. 12, pp. 1683–1688, 2003. [2] R. C. Smythe, R. C. Helmbold, G. E. Hague, and K. A. Snow, “Langasite, langanite, and langatate bulk-wave Y-cut resonators,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 47, no. 2, pp. 355–360, 2000. [3] R. C. Smythe, “Material and resonator properties of langasite and langatate: A progress report,” in Proc. IEEE Int. Frequency Control Symp., 1998, pp. 761–765. [4] J. Imbaud, A. Assoud, R. Bourquin, J. J. Boy, S. Galliou, and J. P. Romand, “Investigations on 10 MHz LGS and LGT crystal resonators,” in Proc. Joint Mtg. Eur. Frequency Time Forum-IEEE Int. Frequency Control Symp., 2007, pp. 711–714. [5] J. Imbaud, S. Galliou, J. P. Romand, P. Abbé, and R. Bourquin, “Noise measurements of 10 MHz LGT crystal oscillators,” in Proc. Joint Mtg. Eur. Frequency Time Forum-IEEE Int. Frequency Control Symp., 2007, pp. 1251–1254. [6] A. Assoud, J. J. Boy, K. Yamni, and A. Albizane, “IR and N-IR spectrometry characterizations of LGS crystal and family,” J. Phys. IV France, vol. 126, pp. 47–50, 2005. [7] F. C. Klemenz, “High-quality 2 inch La3Ga5.5Ta0.5O14 and Ca3TaGa3Si2O14,” in Proc. 29th Int. Conf. Advanced Ceramics and Composites, 2005, pp. 68–73. [8] S. Jen, B. C. C. Teng, M. M. C. Chou, B. H. T. Chai, T. T. Lee, and J. Gwo, “Experimental investigation of the BAW device potentials of singly rotated Y-cut ordered langasite-structure crystals,” in Proc. IEEE Int. Frequency Control Symp., 2002, pp. 307–310. [9] Y. Kim, “Amplitude-frequency effects of Y-cut langanite and langatate,” in Proc. Joint Mtg. Eur. Frequency Time Forum-IEEE Int. Frequency Control Symp., 2003, pp. 631–636. [10] J. J. Boy, E. Bigler, R. Bourquin, and B. Dulmet, “A theoritical and experimental study of the force-frequency effect in BAW LGS resonators,” in Proc. IEEE Int. Frequency Control Symp., 2001, pp. 223–226. [11] C. Klemenz, M. Berkowski, B. Deveaud-Pledran, and D. C. Malocha, “Defect structure of langasite-type crystals: S challenge for applications,” in Proc. IEEE Int. Frequency Control Symp., 2002, pp. 301–306. [12] A. N. Gotalskaja, D. I. Dresin, S. N. Schegolkova, N. I. Saveleva, V. V. Bezdelkin, and G. N. Cherpoukhina, “Langasite crystal quality improvement aimed at high-Q resonators fabrication,” in Proc. IEEE Int. Frequency Control Symp., 1995, pp. 657–666. [13] Y. Kim, “Thermal transient effect of Y-cut langanite and langatate,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 51, pp. 613–616, 2004. [14] D. S. Stevens and H. F. Tiersten, “An analysis of doubly rotated quartz resonators utilizing essentially thickness modes with transverse variation,” J. Acoust. Soc. Am., vol. 29, no. 6, pp. 1811–1826, June 1986. [15] R. J. Besson, “A new ‘electrodeless’ resonator design,” in Proc. 31st Annu. Frequency Control Symp., 1977, pp. 147–152. [16] N. Gufflet, R. Bourquin, and J. J. Boy, “Isochronism defect for various doubly rotated cut quartz resonators,” in Proc. Joint Mtg. Eur. Frequency Time Forum-IEEE Int. Frequency Control Symp., 1999, pp. 784–787. [17] N. Gufflet, R. Bourquin, and J. J. Boy, “Measurements on doubly rotated quartz resonators with very low isochronism defect,” in Proc. 14th Eur. Frequency Time Forum, 2000, pp. 108–111. [18] S. Galliou, F. Sthal, J. J. Boy, R. Bourquin, and M. Mourey, “Recent results on quartz crystal LD-cuts operating in oscillators,” in IEEE Int. Ultrasonics Ferroelectrics Frequency Control Joint 50th Anniv. Conf., 2004, pp. 475–477.

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Joël Imbaud (M’07) was born in Riom, France. He received the engineer degree in mechanical and microtechnical sciences and the master degree in electronic and optical sciences from the Ecole Nationale Supérieure de Mécanique et des Microtechniques (ENSMM) of Besançon, France, in 2005. Since 2005, he has been working as a Ph. D. degree student on LGX material family and cryogenic oscillators in the time-frequency department (Laboratoire de Chronométrie d’Electronique et de Piézoélectricité [LCEP]) of the FEMTO-ST Institute. Serge Galliou received the mechanical engineering degree from the Ecole Nationale Supérieure de Mécanique et des Microtechniques (ENSMM) of Besançon, France, in 1980. In 1982, he received the doctor engineer degree in vibrations and oscillators. He joined the Laboratoire de Chronométrie d’Electronique et de Piézoélectricité (LCEP) of Besançon in 1980 and, since 1985, he also has been teaching electronics and signal processing at ENSMM, where he is now professor. His research interests include topics such as precise temperature control, noise reduction, and design of various types of crystal oscillators (miniature oscillators, dual mode oscillators, ultra stable oscillators). Industrial partners who partly support these research topics are European manufacturers of ultra stable resonators and oscillators and institutions like the Délégation Générale pour l’Armement (DGA) and Centre National d’Etudes Spatiales (CNES) whose needs include radar applications or measuring and positioning systems, dedicated to onboard or ground uses. He currently manages the Piezoelectric Resonators and Ultrastable Oscillators Team in the LCEP Department of the FEMTOST Institute of Besançon. Jean Pierre Romand received the Superior Technician degree from the Lycée Victor Berard of Morez, France, in 1987. Since 1992, he has specialized in precision grinding and polishing and also in the manufacturing of very high quality crystal resonators. He joined the Laboratoire de Chronométrie d’Electronique et de Piézoélectricité (LCEP) of Besançon, France, in 2000.

Philippe Abbé received the Superior Technician degree from the Lycée Victor Hugo of Besançon, France, in 1995. In 2000, he received the Assistant Engineer degree. He joined the Laboratoire de Chronométrie d’Electronique et de Piézoélectricité (LCEP) which became Frequency and Time department of the FEMTO-ST Institute of Besançon in 2004. He is working on the associated measurements and metrology of ultra-stable oscillators and, more recently, cryogenic oscillators. Roger Bourquin (M’97) was born in Valentigney, France, in 1947. He received the M.S. degree in 1969, the Doctorat of University degree in 1971, and the Doctorat d’Etat degree in 1979 from the University of Franche-Comte, France. In 1970, he joined the Ecole Nationale Superieure de Mecanique et des Microtechniques (ENSMM) as an assistant professor and was appointed as a professor in 1989. From 1969 to 1971, he was with the Laboratory of Atomic Clock (CNRS) of Besançon where he worked in the field of electron spin resonance instrumentation, and in 1971, he joined the Laboratory of Chronometry, Electronics, and Piezoelectricity (LCEP) of ENSMM. Since 2004, he has been with the FEMTO-ST Institute (University of FrancheComte/CNRS/ENSMM) as head of the LCEP Department. He is currently working on nonlinear effects in piezoelectric crystals and devices, and on piezoelectric resonators and their use as frequency output sensors.