A Program to Analyse the Origin of Noise in Ultra- Stable Quartz Crystal Resonators

Transcription

1 A Program to Analse the Origin o Noise in Ultra- Stable Quartz Crstal Resonators S. Galliou, F. Sthal, X. Vacheret, R. Brendel, P. Salzenstein, E. Rubiola Time and Frequenc Dept. FEMTO-ST Institute, UMR CNRS 6174 Besançon, France serge.galliou@emto-st.r Abstract In the mid 9s the quartz crstal oscillator attained a stabilit in the upper 1 14 (licker loor o the Allan deviation σ (τ), which occurs at τ =1..1 s). As a matter o act, the highest stabilit was obtained with bulk-acoustic-wave quartz crstal resonators at 5 MHz and at 1 MHz. Since, the research or higher stabilit seems to be at a standstill, while space applications are more and more demanding. FEMTO-ST Institute have started a research program on the origin o noise in 5 MHz and 1 MHz quartz crstal resonators, managed b The Centre National d Etudes Spatiales (CNES). Several European manuacturers o high-stabilit resonators and oscillators participate. This article reports on the present status and on the uture plans o this program. The irst part consists in the analsis o the sensitivit o selected resonators to various eternall-controlled parameters, like temperature, drive power, load impedance, series capacitance. The second part, planned, consists o listing the possible causes o noise, and o modeling their eects on requenc stabilit. Tests and measurements are mainl perormed on an advanced phase noise measurement sstem, recentl set up or this program. O course, this program is a unique opportunit to test various batches o 5 MHz and 1 MHz resonators provided b the industrial partners. I. INTRODUCTION To achieve the selected missions, space applications o precise localization, navigation and sciences require requenc stabilities and spectral purit that dramaticall increase. It is the case o clocks on board or PHARAO missions, and ultra stable oscillators (USO) or DORIS programs, or which the required requenc stabilit is about or better or τ rom 1 to 1 s. These stabilities are required either or ultra stable quartz crstal oscillators (DORIS program) or atomic clocks (PHARAO project) in which the ultra stable oscillator (USO) gives the limitation o stabilit. In these cases, ver low noise USO are required, and or this reason it is necessar to select and control the sources o noise o the quartz crstal resonator. DORIS program (Doppler Orbitograph and Radiopositioning Integrated in Space) is a Doppler satellite G. Cibiel Microwave and Time-Frequenc Dept. CNES Toulouse, France gilles.cibiel@cnes.r tracking sstem developed or precise determination and precise ground location. Its ultimate aim is to achieve an accurac o one centimetre. This instrument is on-board o TOPEX-POSEIDON, JASON1 and ENVISAT altimetric satellites, it also lew with SPOT series. Future DORIS will be embarked on JASON2, PLEIADES, ALTIKa, HY2, CRYOSAT2. The easibilit o quartz crstal oscillators ehibiting relative requenc stabilities that can reach over a ew seconds was clearl proven [3]. Unortunatel, their reproducibilit is still ar rom being sstematic whereas the demand is more and more severe in terms o speciications. Indeed, it is clear that the precision o localization b means o satellites or the precision o clocks used or snchronization in telecommunication sstems results in increasingl severe requirements on the perormances o the USO, at the limit o the know-how o toda. To reach the level o perormances required b current projects (PHARAO, JASON2, PLEIADES, ALTIKa, HY2, CRYOSAT2) and utures projects (mainl altimetric missions which need DORIS instrument), it is necessar to sort all the quartz crstal devices one b one, in terms o noise. The outputs are etremel weak (a ew %) to obtain perormances such as those required b PHARAO ( or τ = 1 s). To hope to improve the stabilit o USO, it is necessar to continue and go urther into works o investigations on the origin o noise in resonators. Currentl, the distribution o USO stabilit is centered on over a ew seconds, or best crstal units rom major European manuacturers. It is necessar to be able to shit it to 7, even , in production. This program is managed b the French space agenc CNES (Centre National d Etudes Spatiales) o Toulouse, is led b the FEMTO-Institute (UMR CNRS 6174) and involved major European manuacturers (AR Electronics Besançon France, Oscilloquartz Neuchatel Switzerland, Rakon Argenteuil France, Teme Troes France). This program is supported b the French space agenc CNES (Centre National d Etudes Spatiales) o Toulouse. Contract # R-S6/LN /7/$2. 27 IEEE 1176

2 II. GUIDING LINES OF THE PROGRAM The problem is comple and requires a long-term stud to end up on a noticeable improvement o the manuacturing processes o 5 and 1 MHz ultrastable resonators o 1-14 grades. One (ambitious) aim o the stud is to develop a model o the resonator noise rom investigations on the phsical origins o its noise. This will be perormed in two main steps. In a irst step o 18 months, and beore investigating phsical origins o noise in resonators, we schedule to investigate correlations between actual geometrical data, eternal parameters o inluence and the measured resonator parameters. For this stud according to a macroscopic point o view, our research aes are scheduled to improve the understanding o resonator noise: - Stud o resonators sensitivit to the drive level, - Stud o the load inluence, - Stud o the inluence o the temperature (dnamic eect, inluence o the operating point versus the turn over temperature), - Stud o the inluence o the requenc shit (pullup). These actions are based on an intensive use o the new bench or phase noise measurement recentl developed at the FEMTO-ST Institute [2]. Analsis will be perormed rom measurements made on samples o ultrastable resonators o various industrial batches. The second step will consist in building a noise model or bulk acoustic wave resonators rom a more microscopic basis. Previous actions are necessar to an urther development o such a model. Their results will condition the second step orientation. The latter will include a PhD work over duration o about 36 months. III. MEANS OF MEASUREMENT The irst step o this stud is essentiall based on the use o a phase noise measurement bench (Fig. 1) recentl developed at the FEMTO-ST institute, and still improved everda [1, 2, 4]. crstal resonator. Thus, the direct eeding o the driving source signal through onl one resonator does not permit to etract the resonator noise rom the output resulting noise. On the other hand, the source signal can be subtracted when passing though two identical arms equipped with identical resonators (the devices under tests (DUT)). Then the contribution o the source is cancelled while inner noise o both resonators is preserved because one resonator noise is dierent rom the other one. When the carrier suppression is achieved (less than -75 dbc is acceptable), the resulting signal onl made up noise rom both resonators, is strongl ampliied and mied with the source signal to be shited down to the low requenc domain and eventuall processed b the spectrum analzer. In such a wa, noise to be measured rom both resonators can be brought up at a higher level than the driving source noise. Moreover, the noise loor o the bench can be measured with resistors substituted or crstal resonators. Low Noise Source Calibration source X tal #A RF Ampli + 43 db DC Ampli + 54 db ν, P RF IF Vo g² FFT g²dc X tal #B Analzer 18 LO R π/2 Figure 2. Principle o the measurement bench. Figure 3 shows a tpical result. The measured -1 phase noise visible into the resonator bandwidth can be interpreted as a requenc to phase conversion. Basicall, the requenc licker noise generated b a resonator would be iltered b its own transer unction. L () (dbc/hz) ,1, Frequenc - Hz Figure 3. Tpical phase noise result rom two 5 MHz resonators under test. Figure 1. Measurement bench. Two data are etracted rom this graph: 1/ the resonator bandwidth equal to two times the intersection requenc o the -1 and -3 slopes. It gives the loaded Q-actor and, thus, the conversion coeicient o the requenc noise into phase noise. The general idea o this passive method (see Fig. 2) consists in reducing the noise o the source as much as possible. Indeed, when resonators ehibit a ver weak noise, the noise o the source is alwas higher than that o the quartz S ( ) = Sφ ( ) 2Q (1) L

3 2/ the measured value at 1 Hz rom the carrier gives the level o the resulting phase noise ( S φ ( = 1 Hz) ). As a consequence, according to the ollowing path (2), the Allan deviation o an oscillator equipped with such a nois resonator could be calculated, assuming that the dominant phase noise in the oscillating loop is that o the resonator: Sφ ( = 1 Hz) S ( = 1 Hz) (2) σ loor = 2 ln 2 S ( = 1 Hz) Beore the noise measurement, calibration must be perormed b means o a calibrated noise or sideband modulation (at.4 Hz in our case. See Fig. 2). Obviousl, preliminar tunings are also necessar: impedance matching, series capacitor adjustment o each resonator to be at at the driving source requenc, operating temperatures o each resonator. The latter have to be tuned careull at the turning points o each requenctemperature curve. Presentl, the resonator ovens ehibit a temperature stabilit o 2 µk over a measuring time o 1 s. The tuning capacitor o each resonator is also temperature-controlled. This guarantees a relative requenc stabilit loor better than or the usual operating conditions o the bench. Main eatures o our bench as completed toda are the ollowing: - Standard operating requencies: 5 MHz and 1 MHz (at other requencies, results depend on the driving source stabilit), - Noise loor: µw, µw, - Temperature tuning o crstal ovens: b steps o.5 C over the temperature range [7 C, 9 C], - Frequenc tuning 1/ o each arm with: a ew pf Ct a ew 1 pf, 2/ o the source requenc at.1 Hz. - Ultimate Allan deviation σ (τ) = or τ = 1 s. Details are given in [2] IV. TASKS DESCRIPTION The work o the irst stage has been divided in tasks according to their topics but, in act, the overlap each other. A. Task 1: provisioning and itting o high qualit resonators Ideall, it would be interesting to analze couples o resonators representative o various manuacturing processes and various tpes o resonators. This opportunit eists because several industrial partners are involved in the irst part o the program. Indeed, the stud will include measurements on the ollowing samples: - 5 MHz BVA tpe resonators provided b Oscilloquartz, Neuchâtel, Switzerland, - 5 and 1 MHz QAS tpe resonators rom Rakon, Argenteuil, France, - conventional 1 MHz resonators rom AR Electronic, Besançon, France - 1 MHz BVA resonators manuactured at the Institute FEMTO-ST, Besançon, France, - conventional 1 MHz resonators rom TEMEX Frequenc, Troes, France. In practice, the implementation o those resonators into the high stabilit bench ovens is not so eas because o their packaging variet, as shown in igure 4. Initiall, ovens have been designed or homemade 1 MHz BVA tpe resonators (cold weld HC4 enclosures o height 12 mm and diameter 2 mm) (ig 4). Whereas HC6 packages can easil be put in with minor modiications, on the other hand bigger cases such as HC12 or those o 5 MHz BVA resonators are more diicult to insert without reducing thermal perormances o the ovens. Speciic ovens with measurement adaptations have been perormed in this last case, to progress despite the limited length o time o 18 months or the irst step o this program. Figure 4. On let: various resonator cases (HC4, HC12, 5 MHz BVA). On right: the lower part o one resoantor oven whose HC4 housing is visibl smaller than the 5 MHz BVA enclosure lied aside. B. Task 2: Thermal eect It is well-known that temperature is a parameter o inluence on the requenc stabilit, unavoidable in the design o an oscillator as well as in a passive measurement bench. Beore beginning a stud on a noise model based on a phsical approach, temperature eects have to be evaluated at the 1-14 scale. Two main causes o requenc changes due to temperature are usuall identiied: - The irst one is the well-known static eect linked to the real position o the operating point T op versus the turn over point T top o the cubic requenc-temperature relationship. The relative requenc sensitivit versus temperature luctuations T around T op can be written as: a = = at T, (4) with [ ] 2 T = 2β + 6γ ( T T γ δt, where α, β, top ) δt + 3 γ are respectivel the irst, second and third coeicients o the requenc-temperature relationship, depending on the cut angles, T (usuall 25 C) is the reerence temperature which 1178

4 corresponding to the reerence requenc, and δ T = T op T is the temperature gap. top This is one o the most important adjustments to be done in an oven-controlled crstal oscillator (OCXO). As an eample, the usual SC cut whose controlledtemperature is set at.1 K (i.e. δt =.1 K) rom its turn-over point close to T top = 85 C, ehibits a coeicient value o a T = 1-9 K -1. This means that its temperature has to be controlled within T = 1 µk in order to get a requenc stabilit better than The second cause o requenc changes linked to temperature has a dnamic origin and is commonl modeled b a phenomenological coeicient as: capacitor having a pull-up eect, here so-called tuning capacitor C t (see ig. 5): using the component deinitions o ig. 5, the resulting requenc becomes with a good approimation, s C + C + C 1 (7) t = a ~ dt dt For the most simple SC cut resonator, the dnamic coeicient a ~ would be o a ew 1-7 K -1 s. This phenomenon includes various eects such as: - The thermal transer unction o the resonator, that is to sa the ratio o the inner temperature o the vibrating volume, assumed to be homogeneous, and that o the crstal case also assumed to be homogeneous. This transer unction obviousl depends on the mechanical mounting o the resonator according to whether the resonator is a BVA tpe or not or eample, what are its thickness (depending on the selected overtone) and diameter, etc? - Thermal gradients. Gradients into the resonator induce strains and then requenc shits. Anwa, all the possible origins o temperature changes are still to be identiied at the 1-14 scale. As previousl mentioned, means used in our bench to ilter and regulate the resonator temperature guarantee that ambient temperature changes are not a limiting actor o the resonator noise measurement. These means cannot be transposed directl in an oscillator structure because o their volume. So, the question o the resonator sensitivit to temperature at the 1-14 scale, in an oscillator, is still relevant. In addition, its series capacitor used or the requenc adjustment is also temperature-sensitive. This is wh; this stud is the opportunit to review the theoretical aspect o temperature eects. It will be supported b a set o noise measurements on various tpes o resonators (conventional, QAS, BVA, ) or dierent remote-controlled operating temperature (the temperature step is.5 C). This might permit to evaluate the limit o inluence o temperature in oscillators, i it eists. C. Task 3: Inluence o the tuning capacitor The resonator requenc has alwas to be tuned. Into each arm o the bench as in an oscillator, this is ulilled b a series (6) 1179 Figure 5. Electrical model o a crstal resonator whose motional parameters are L, C and R. C is its parallel capacitor whereas C t denotes the tuning series capacitor added to pull-up the overall resonant requenc. In terms o relative requenc shit: s C 2( C + Ct ) where s denotes the resonant requenc o the motional arm alone (i.e. L C (2π s ) 2 = 1), ver close to the series requenc o the resonator. As an eample, the addition o a tuning capacitor C t = 1 pf to a resonator ehibiting a 7 parallel capacitor C = 2 pf, gives 5 1. s Temperature sensitivit. This capacitor is obviousl also temperature sensitive. Thus, it induces relative requenc changes around the resonant requenc (the pulled up requenc) such as: k C t dct C As an illustration, numerical values o the coeicient t (8) (9) k C t are shown in Fig. 6, in the case o a commercial 5 MHz resonator. It takes values o a ew 1-6. That means that a tuning capacitor which ehibiting a temperature coeicient o a ew ppm / K will cause a relative requenc luctuations versus temperature o a ew 1-12 K -1. In that case, a relative requenc stabilit o a ew 1-14 could be reached provided that the tuning capacitor is temperature-controlled at better than 1/1 K around its operating temperature. This is not too much complicated to control but must be taken into account.

5 Figure 6. The coeicient k C relating the relative requenc luctuations t and the relative tuning capacitor luctuations, versus the capacitor value C t. Impedance sensitivit. The tuning capacitor modiies the overall impedance. In each arm o the bench, each resonator and its associated series capacitor are one element o a resistor bridge. Beore beginning the noise measurement, one o the preliminar adjustments consists in tuning each series capacitor in order to get the in both arms. When this operation is completed, the overall network o ig. 5 is equivalent to a resistance. In other words, its equivalent impedance Z() = R() + X() is reduced to Z( = ) = R( = ) = R R. Nevertheless, R is no more equal to the motional resistance R. Fig. 7 illustrates the inluence o C t on Z(). 12 Z modulus(db) kct (1-6 ) 4, 3, 2, 1,, Ct = 1 pf Ct = 1 pf Ct = 1 nf C t (pf) 4-1d -1Hz Hz 1Hz 2Hz 3Hz 4Hz 5Hz Frequenc-1MHz Figure 7. The modulus (in db) and the phase o the equivalent impedance Z() o the network in ig. 5. At the Z = R (the minimum value o the modulus) depends on C t. This seems obvious but leads to some consequences on values and possible noise sources i luctuations eist : - The impedance matching is no longer true i resistors o the bridge have values previousl set. - The dissipated power into the resonator has to be evaluated again b taking into account some correction with regard to the simple resistor R. - The real inner resonator temperature also depends on the real power dissipated into the resonator, as mentioned earlier. - The loaded qualit actor Q L is or R > R and not R (see ig. 8). Into the bench, 1d Z phase 5d d -5d Q R L = Q (1) R + RL where Q is Q-actor o the sstem {resonator + tuning capacitor} (ver close to the Q-actor o the resonator alone: see below), and R L is its global load resistor. Figure 8. An eample o the relative change o R versus C t. One easil understands that the more the luctuations o C t the more the implied luctuations o R. For the bench adjustments and calculations, one should be sure that these corrections are well applied. In addition, the could be noise sources i luctuations eist. All o this is also applicable to oscillators. Q-actor sensitivit. As previousl mentioned, the loaded Q- actor depends on the real equivalent resistor R o the sstem {resonator + C t }, which is a unction o C t, and on the qualit actor Q o this sstem. But, what about Q versus C t? Fig. 9 shows an approimation o the relative phaserequenc slope, where ϕ = ArgZ() close to. ϕ ϕ ϕ Here the slope is denoted Q L 2π dϕ ϕ = and d = 2 = 2 is the slope o the resonator without s R ϕ (R - R)/R (%) its tuning capacitor C t C t (pf) One can observe that the value o ϕ ϕ ϕ never eceeds 1 1-3, or a conventional high qualit resonator. This means that the Q-actor o the resonator plus its tuning capacitor C t remains close to the Q-actor o the resonator alone, whatever the C t value. Finall, in the requenc noise to phase noise conversion, R the loaded Q-actor, QL = Q, depends on R + R L 118

6 C t onl through R esonance, and not nearl through Q which remains close to the resonator Q-actor Q. (dϕ-dϕ)/dϕ (1-3 ),7,6,5,4,3, C t (pf) Figure 9. An eample o the relative phase-requenc slope versus C t, at the resonant requenc (which also depends on C t). D. Task 4: load impedance sensitivit One can wonder about the inluence o the mismatching o the bench with respect to the resonator impedance, in terms o resulting noise. This topic is obviousl closel related to that o the series capacitor sensitivit onto the resonator impedance as well as to that o the power sensitivit through the drive level dependenc or more simpl the non linear amplituderequenc eect. E. Task 5: sensitivit o the resonator noise to the drive level. The injected power into both arms o the bench is adjustable. Thus this makes possible to ecite the tested resonators in a broad power range covering the operating range o those resonators in oscillators (tpicall a ew tens o microwatts). The correlation between noise and drive level, i it eists, could be established in such a wa, or various tpes o resonators. Nevertheless, one can notice that changing the power dissipated into the resonator induces changes o its inner temperature and changes o the temperature gradients, that is to sa, as a consequence its resonant requenc (see B. Task 2: Thermal eect ). For high drive levels, a non linear eect, the so-called amplitude-requenc eect, also interacts on the requenc value. When changing the power level, man possible causes o requenc drit and requenc disturbances have then to be considered (i possible!). On ver low drive level (tpicall -1 dbm), measurements o motional parameters will also allow continuing the investigations concerning the correlation between the drive level dependenc (DLS) and noise o resonators [5] V. CONCLUSION Since a ew ears, quartz crstal oscillators seem to have reached their limit in terms o requenc stabilit. The still are attractive or their volume, relativel low consumption in stead state, especiall or space applications. The goal o this program is to determine and understand the mechanisms responsible o current limitation o resonator noise in order to reduce their susceptibilit and to evaluate their potentialit in a short and mean uture. To reach this goal, this program ederates several major French and European entities. REFERENCES [1] E. Rubiola, V. Giordano, "On the 1/ requenc noise in ultra-stable quartz oscillators," IEEE Transact. Ultrason. Ferroelec. Freq. Contr. vol. 54 no. 1 pp , Januar 27. Preprint available on and document arxiv:phsics/6211. [2] F. Sthal, X. Vacheret, S. Galliou, P. Salzenstein, E. Rubiola, G. Cibiel, "Advanced bridge instrument or the measurement o the phase noise and o the short-term requenc stabilit o ultra-stable quartz resonators", in these proceedings. [3] R. J. Besson, M. Moure, S. Galliou, F. Marionnet (ENSMM France), F. Gonzalez, P. Guillemot (CNES France), R. Tjoelker, W. Diener, A. Kirk (JPL USA), "1 MHz Hperstable Quartz Oscillators Perormances", joint meeting o the 13th European Fequenc and Time Forum and 1999 IEEE International Frequenc Control Smposium, Besançon France, pp , vol.1, Ma [4] F. Sthal, S. Galliou, P. Abbé, N. Franquet, X. Vacheret P. Salzenstein, E. Rubiola and G. Cibiel, " Thermal characterization o crstal ovens used in phase noise measurement sstem ", Proc. IEEE Int. Freq. Cont. Smp., Miamai, Florida, 5-7 June, pp , 26. [5] R. Brendel, M. Addouche, R. Brendel, E. Rubiola, G. Cibiel "Low drive level sensitivit (DLS) o quartz crstal resonators. " Proceedings o the 2th European Frequenc and Time Forum, Braunschweig, German, pp , March