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AD-A256 373I hlll Ii II1! I liii 11111l1111 Iii
Research and Development Technical ReportSLCET-TR-92-1 (Rev. 1)
Introduction to Quartz FrequencyStandards
John R. Vig DTICArmy Research Laboratory ILECTE
S• GT. 14 9an .
October 1992 D .
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Approved for public release.Distribution is unlimited.
92-27049'
ARMY RESEARCH LABORATORYElectronics and Power Sources DirectorateFort Monmouth, NJ 07703-5601, U.S.A.
093
NOTICES
Disclaimers
The findings in this report are not to be construed as an
official Department of the Army position, unless so desig-nated by other authorized documents.
The citation of trade names and names of manufacturers inthis report is not to be construed as official Governmentindorsement or approval of commercial products or servicesreferenced herein.
Form AAWm~wdREPORT DOCUMENTATION PAGE O11 ffn A "8
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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVEREDOctober 1992 Technical Report
4. TITLE AND SUBTITLE S. FUNDING NUMBERS
Introduction to Quartz Frequency Standards PE: 1L1PR: 62705
-6. AUTHOR(S) TA: AH94
John R. Vig
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 6. PERFORMING ORGANIZATIONREPORT NUMBER
Army Research LaboratoryElectronics and Power Sources Directorate SLCET-TR-92-1 (Rev. 1)ATTN: SLCET-EFFort Monmouth, NJ 07703-5601
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADORESS(ES) 10. SPONSORING/ MONITORINGAGENCY REPORT NUMBER
11. SUPPLEMENTARY NOTESThis report is a revision of Technical Report SLCET-TR-92-1, same title, dated March 1992, AD-A248503. An earlier version ofthis report was prepared for publication in the Tutorial volume of the Proc. of the 23rd Annual Precise Time and Time Interval(PTTI) Applications and Planning Meeting. The Meeting was held 3-5 December 1991 in Pasadena, CA.
IZa. OISTRIBUTION/AVAILAIIUTY STATEMENT 12b. DISTRIBUTION CODE
Approved for public release; distribution is unlimited.
13. ABSTRACT (Maimum 200 words)
The fundamentals of quartz frequency standards are reviewed. The subjects discussed include: crystal resonatorsand oscillators, oscillator types, and the characteristics and limitations of temperature-compensated crystal oscillators(TCXO) and oven-controlled crystal oscillators (OCXO). The oscillator instabilities discussed include: aging, noise,frequency vs. temperature, warmup, acceleration effects, magnetic field effects, atmospheric pressure effects,radiation effects, and interactions among the various effects. Guidelines are provided for oscillator comparison andselection. Discussions of specifications are also included, as are references and suggestions for further reading.
14. SUBUECT TERMS Oscillator, clock, frequency standard, frequency control, frequency 15. NUMBER OF PAGES
stability, time, timing devices, quartz, quartz crystal, quartz oscillator, atomic clock, 56atomic frequency standard, stability, aging, noise, phase noise. 16. PRICE COWE
17, SECURITY CLASSifICATION 18. SECURITY CLASSIFICATION 1I. SECURITY CLASSIFICATION 10. iTATION Of ABSTRACTOF REPORT OF THIS PAGE OF ABSTRACT
Unclassified Unclassified Unclassified UL
NSN IS40-01-280-5500 Standard Form 298 (Rev 2-89)Prfecrad • byANSI Std -1WIS
Table of Contents
Pane
Introduction 1
II. Crystal Oscillators 1
A. Generalized Crystal Oscillator 11. Oscillator Basics 12. Crystal Unit Equivalent Circuit 23. Stability versus Tunability 54. Quartz and the Quartz Crystal Unit 6
B. Oscillator Categories 13C. Oscillator Circuit Types 15
Ill. Oscillator Instabilities 17
A. Accuracy, Stability and Precision 17B. Aging 18C. Noise in Frequency Standards 19
1. The Effects of Noise 192. Noise in Crystal Oscillators 20
D. Frequency versus Temperature Stability 211. Static Frequency versus Temperature Stability 212. Dynamic Frequency versus Temperature Effects 253. Thermal Hysteresis and Retrace 27
E. Warmup 28F. Acceleration Effects 29G. Magnetic-Field Effects 33H. Radiation Effects 34I. Other Effects on Stability 36J. Interactions Among the Influences on Stability 37
IV. Oscillator Comparison and Selection 39
V. Specifications, Standards, Terms, and Definitions 43
VI. For Further Reading £Aoesston For 44
eNTIS GRA&IVII. References DTIC TAB 14Unannounced 3Just ificatitor
By
iii Distribution/
Availability Codd'
Avail and/orDisat Speoial
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Flaures
Figure Paae
1. Crystal oscillator - simplified circuit diagram. 2
2. Equivalent circuit of a mechanically vibrating system. 3
3. Equivalent circuit of crystal unit with load capacitor. 3
4. Reactance versus frequency of a crystal unit. 4
5. Zero-temperature-coefficient cuts of quartz. 8
6. Typical constructions of AT-cut and SC-cut crystal units: (a) two-pointmount package; (b) three- and four-point mount package. 9
7. Resonator vibration amplitude distribution for a circular plate with circular
electrodes. 10
8. Drive level dependence of frequency. 11
9. Drive level dependence of crystal unit resistance. 11
10. Modes of motion of a quartz resonator. 12
11. Frequency versus temperature characteristics of AT-cut crystals,showing AT- and BT-cut plates in Y-bar quartz. 13
12. Crystal oscillator categories based on the crystal unit's frequencyversus temperature characteristic. 14
13. Oscillator circuit types. 15
14. Oscillator outputs. 16
15. Accuracy, stability and precision examples for a marksman, top, andfor a frequency source, bottom. 17
16. Computer-simulated typical aging behaviors; where A(t) and B(t) arelogarithmic functions with different coefficients. 19
17. Low-Noise SAW and BAW multiplied to 10 Gl-z (in a nonvibratingenvironment). 22
iv
18. Low-Noise SAW and BAW multiplied to 10 GHz (in a vibrating
environment). 22
19. Wristwatch accuracy as it is affected by temperature. 23
20. Effects of harmonics on f vs. T. 24
21. Activity dips in the frequency versus temperature and resistance versustemperature characteristics, with and without C,. 25
22. Warmup characteristics of AT-cut and SC-cut crystal oscillators (OCXOs). 26
23. Temperature-compensated crystal oscillator (TCXO) thermal hysteresisshowing that the f vs. T characteristic upon increasing temperaturediffers from the characteristic upon decreasing temperature. 27
24. Oven-controlled crystal oscillator (OCXO) retrace example, showing thatupon restarting the oscillator after a 14 day off-period, the frequencywas about 7x10'9 lower than it was just before turn-off, and that theaging rate had increased significantly upon the restart. About a monthelapsed before the pre-turn-off aging rate was reached again. (Figureshows AM/f in parts in 109 vs. time in days.) 28
25. 2-g tipover test (Af vs. attitude about three axes). 30
26. Vibration-induced "sidebands" (i.e., spectral lines). 30
27. Resonance in the acceleration sensitivity vs. vibration frequencycharacteristic. 31
28. Random-vibration-induced phase-noise degradation. 31
29. Coherent radar probability of detection as a function of referenceoscillator phase noise. 33
30. The effect of a shock at t = t, on oscillator frequency. 34
31. Crystal oscillator's response to a pulse of ionizing radiation: f. = originalpreirradiation frequency, Af, = steady-state frequency offset (0.2 hoursto 24 hours after exposure), f, = instantaneous frequency at time t. 35
v
32. Change in compensating frequency versus temperature due to CL
change. 38
33. Temperature-compensated crystal oscillator (TCXO) trim effect. 38
34. Relationship between accuracy and power requirements (XO = simplecrystal oscillator; TCXO = temperature-compensated crystal oscillator;OCXO = oven-controlled crystal oscillator; Rb = rubidium frequencystandard; Cs = cesium beam frequency standard). 39
35. Stability as a function of averaging time comparison of frequencystandards. 41
36. Phase instability comparison of frequency standards. 42
Tables
Table Page
Table 1. Comparison of frequency standards' salient characteristics. 40
Table 2. Comparison of frequency standards' weaknesses and wearoutmechanisms. 42
vi
I_. Introduction
More than one billion (i.e., 1 0 9) quartz crystal oscillators are produced annually forapplications ranging from inexpensive watches and clocks to radionavigation andspacecraft tracking systems. The fundamentals of quartz oscillators are reviewed in thisreport, with emphasis on quartz frequency standards (as opposed to inexpensive clockoscillators). The subjects discussed include: crystal resonators and oscillators, oscillatortypes, and the characteristics and limitations of temperature-compensated crystaloscillators (TCXO) and oven-controlled crystal oscillators (OCXO). The oscillatorinstabilities discussed include: aging, noise, frequency vs. temperature, warmup,acceleration effects, magnetic field effects, atmospheric pressure effects, radiation effects,and interactions among the various effects. Guidelines are provided for oscillatorcomparison and selection. Discussions of specifications are also included, as arereferences and suggestions for further reading.
I1. Crystal Oscillators
A. Generalized Crystal Oscillator
1. Oscillator Basics
Figure 1 is a greatly simplified circuit diagram that shows the basic elements of acrystal oscillator [1-3]. The amplifier of a crystal oscillator consists of at least one activedevice, the necessary biasing networks; and may include other elements for band limiting,impedance matching, and gain control. The feedback network consists of the crystalresonator, and may contain other elements, such as a variable capacitor for tuning.
The frequency of oscillation is determined by the requirement that the closed loopphase shift = 2nn, where n is an integer, usually 0 or 1. When the oscillator is initiallyenergized, the only signal in the circuit is noise. That component of noise, the frequencyof which satisfies the phase condition for oscillation, is propagated around the loop withincreasing amplitude. The rate of increase depends on the excess loop gain and on thebandwidth of the crystal network. The amplitude continues to increase until the amplifiergain is reduced, either by the nonlinearities of the active elements (in which case it is selflimiting) or by an external level-control method.
At steady state, the closed-loop gain = 1. If a phase perturbation A¢ occurs, thefrequency of oscillation must shift by a Af in order to maintain the 2nn phase condition.It can be shown that for a series-resonance oscillator
Af A.f 20 L
where OL is the loaded Q of the crystal in the network [1]. ("Crystal" and "resonator" are
TuningVoltage
CrystalResonator
-- JL Output
Frequency
Amplifier
Figure 1. Crystal oscillator - simplified circuit diagram.
often used interchangeably with "crystal unit," although "crystal unit" is the official name.See references 3 to 6 for further information about crystal units.) Crystal oscillator designinformation can be found in references 1, 2, 5 and 7. The abbreviation for crystaloscillator is XO.
2. Crystal Unit Equivalent Circuit
A quartz crystal unit is a quartz wafer to which electrodes have been applied, andwhich is hermetically sealed in a holder structure. (The wafer is often referred to as the"blank," or the "crystal plate".) Although the design and fabrication of crystal unitscomprise a complex subject, the oscillator designer can treat the crystal unit as a circuitcomponent and just deal with the crystal unit's equivalent circuit.
The mechanically vibrating system and the circuit shown in Figure 2 are"equivalent," because each can be described by the same differential equation [6]. Themass, spring, and damping element (i.e., the dashpot) correspond to the inductor,capacitor and resistor. The driving force corresponds to the voltage, the displacementof the mass to the charge on the capacitor, and the velocity to the current.
A crystal resonator is a mechanically vibrating system that is linked, via thepiezoelectric effect, to the electrical world. Figure 3 shows a (simplified) equivalent circuit(of one mode of vibration) of a resonator, together with the circuit symbol for a crystal
2
Spring C
Mass L
Dashpot R
Figure 2. Equivalent circuit of a mechanically vibrating system.
Symbol for crystal unit
Co
I I(
0-- --- o-- -o- I$-CL
C1 L1 R1
Figure 3. Equivalent circuit of crystal unit with load capacitor.
3
unit. A load capacitor CL is shown in series with the crystal. Co, called the "shunt"capacitance, is the capacitance due to the electrodes on the crystal plate plus the straycapacitances due to the crystal enclosure. The R1, L1, C1 portion of the circuit is the"motional arm" which arises from the mechanical vibrations of the crystal.
The C, to C1 ratio is a measure of the interconversion between electrical andmechanical energy stored in the crystal, i.e., of the piezoelectric coupling factor, k. CO/Clincreases with the square of the overtone number; the relationship of CO/CI to k and Nis 2CO/C 1 = [icN2/2k], where N is the overtone number. When a dc voltage is applied tothe electrodes of a resonator, the capacitance ratio CO/C l is also a measure of the ratioof electrical energy stored in the capacitor formed by the electrodes to the energy storedelastically in the crystal due to the lattice strains produced by the piezoelectric effect.Figure 4 shows the reactance versus frequency characteristic of the crystal unit. TheCO/C1 is also inversely proportional to the antiresonance-resonance frequency separation(i.e., the pole-zero spacing) which is a. especially important parameter in filterapplications. The slope of the reactance vs. frequency curve near f, is inverselyproportional to C,, i.e., AX/(Af/f) = 1/nfC, near f,, where X is the reactance. C, is,therefore, a measure of the crystal's "stiffness," i.e., its tunability - see the equation onthe next page.
f Antiresonance
Area of Usual"Parallel
+ Resonance'N>ý
S~fs
C1 SeriesFrqecSReso n a n ce F re q u e n c y
\1
2itfCoFigure 4. Reactance versus frequency of a crystal unit.
4
When the load capacitor is connected in series with the crystal, the frequency ofoperation of the oscillator is increased by a A', where Af' is given by
Af/ C1
f 2(co*CL)
When an inductor is connected in series with the crystal, the frequency of operation isdecreased. The ability to change the frequency of operation by adding or changing areactance allows for compensation of the frequency versus temperature variations ofcrystal units in TCXOs, and for tuning the output frequency of voltage controlled crystaloscillators (VCXO); in both, the frequency is changed by changing the voltage on avaractor.
For the simple RLC circuit of Figure 2, the width of the resonance curve isinversely proporiional to the quality factor 0, but in a crystal oscillator, the situation iscomplicated by the presence of Co and by the fact that the operating 0 is lower than theresonator 0. For a quartz resonator, Q = (2f1,CR 1)1. References 3, 5 and 6 containfurther details on the equivalent circuit.
Some of the numerous advantages of a quartz crystal resonator over a tank circuitbuilt from discrete R's, C's and L's are that the crystal is far stiffer and has a far higher0 than what could be built from normal discrete components. For example, a 5 MHzfundamental mode AT-cut crystal may have C1 = 0.01 pF, L, = 0.1 H, R, = 5 i, and U= 106. A 0.01 pF capacitor is not available, since the leads attached to such a capacitorwould alone probably contribute more than 0.01 pF. Similarly a 0.1 H inductor would bephysically large, it would need to include a large number of turns, and would need to besuperconducting in order to have a < 50 resistance.
3. Stability versus Tunability
In most crystal oscillator types, a variable-load capacitor is used to adjust thefrequency of oscillation to the desired value. Such oscillators operate at the parallelresonance regioi of Figure 4, where the reactance versus frequency slope (i.e., the"stiffness") is inversely proportional to C1. For maximum frequency stability with respectto reactance (or phase) perturbations in the oscillator circuit, the reactance slope (orphase slope) must be maximum. This requires that the C, be minimum. The smaller theC1, however, the more difficult it is to tune the oscillator (i.e., the smaller is Af' for a givenchange in CL). The highest stability oscillators use crystal units that have a small C, (anda high 0). Since C, decreases rapidly with overtone number, high-stability oscillatorsgenerally use third- or fifth-overtone crystn' units. Overtones higher than fifth are rarelyused, because R1 also increases rapidly with overtone number, and some tunability isusually desirable in order to allow setting the oscillator to the desired frequency.
5
Wide-tuning-range VCXOs use fundamental mode crystal units of large C,. Voltagecontrol is used for the following purposes: to frequency or phase lock two osc!'.ators; forfrequency modulation; for compensation, as in a TCXO (see below); and for calibration(i.e., for adjusting the frequency to compensate for aging). Whereas a high-stability,ovenized 10-MHz VCXO may have a frequency adjustment range of ±5 x 10-7 and anaging rate of 2 x 108 per year, a wide-tuning-range 10-MHz VCXO may have a tuningrange of ±50 parts per million (ppm) and an aging rate of 2 ppm per year.
In general, making an oscillator tunable over a wide frequency range degrades itsstability because making an oscillator susceptible to intentional tuning also makes itsusceptible to factors that result in unintentional tuning. For example, if an oven-controlled crystal oscillator (OCXO) is designed to have a stability of 1 x 1012 for aparticuiar averaging time and a tunability of 1 x 10-, then the crystal's load reactancemust be stable to 1 x 10s for that averaging time. Achieving such load-reactance stabilityis difficult because the load-reactance is affected by stray capacitances and inductances,by the stability of the varactor's capacitance versus voltage characteristic, and by thestability of the voltage on the varactor. Moreover, the 1 x 10-5 load-reactance stabilitymust be maintained not only under benign conditions, but also under changingenvironmental conditions (temperature, vibration, radiation, etc.). Therefore, the wider thetuning range of an oscillator, the more difficult it is to maintain a high stability.
4. Quartz and the Quartz Crystal Unit
A quartz crystal unit's high 0 and high stiffness (small CJ) make it the primaryfrequency and frequency-stability determining element in a crystal oscillator. The Qvalues of crystal units are much higher than those attainable with other circuit elements.In general-purpose crystal units, Os are generally in the range of 104 to 106 . Ahigh-stability 5-MHz crystal unit's Q is typically in the range of two to three million. Theintrinsic Q, limited by internal losses in the crystal, has been determined experimentallyto be inversely proport.onal to frequency (i.e., the Qf product is a constant for a givenresonator type). For AT- and SC-cut resonators, the maximum Of = 16 million when f isin MHz.
Quartz (which is a single-crystal form of SiO 2) has been the material of choice forstable resonators since shortly after piezoelectric crystals were first used in oscillators -in 1918. Although many other materials have been explored, none has been found to bebetter than quartz. Quartz is the only material known that possesses the followingcombination of properties:
1. It is piezoelectric ("pressure electric"; piezein means "to press" in Greek).2. Zero temperature coefficient resonators can be made when the
plates are cut along the proper directions with respect to thecrystallographic axes of quartz.
6
3. Of the zero temperature coefficient cuts, one, the SC-cut (seebelow), is "stress compensated."
4. It has low intrinsic losses (i.e., quartz resonators can have high Q's).5. It is easy to process because it is hard but not brittle, and, under
normal conditions, it has low solubility in everything except thefluoride etchants.
6. It is abundant in nature.7. It is easy to grow in large quantities, at low cost, and with relatively
high purity and perfection.
Of the man-grown single crystals, quartz, at more than 2000 tons per year (in 1991), issecond only to silicon in quantity grown.
The direct piezoelectric effect was discovered by the Curie brothers in 1880. Theyshowed that when a weight was placed on a quartz crystal, charges appeared on thecrystal surface; the magnitude of the charge was proportional to the weight. In 1881, theconverse piezoelectric effect was illustrated; when a voltage was applied to the crystal,the crystal deformed due to the lattice strains caused by the effect. The strains reversedwhen the voltage was reversed.
Of the 32 crystal classes, 20 exhibit the piezoelectric effect (but only a few of theseare useful). Piezoelectric crystals lack a center of symmetry. When a force deforms thelattice, the centers of gravity of the positive and negative charges in the crystal can beseparated so as to produce surface charges. The piezoelectric effect can provide acoupling between an electrical circuit and the mechanical properties of a crystal. Underthe proper conditions, a "good" piezoelectric resonator can stabilize the frequency of anoscillator circuit.
Quartz crystals are highly anisotropic, that is, the properties vary greatly withcrystallographic direction. For example, when a quartz sphere is etched in hydrofluoricacid, the etching rate is more than 100 times faster along the fastest etching ratedirection, the Z-direction, than along the slowest direction, the slow-X-direction. Theconstants of quartz, such as the thermal expansion coefficient and the temperaturecoefficients of the elastic constants, also vary with direction. That crystal units can havezero temperature coefficients of frequency is a consequence of the temperaturecoefficients of the elastic constants ranging from negative to positive values.
The locus of zero-temperature-coefficient cuts in quartz is shown in Figure 5. TheX, Y, and Z directions have been chosen to make the description of properties as simpleas possible. The Z-axis in Figure 5 is an axis of threefold symmetry in quartz; in otherwords, the physical properties repeat every 1200 as the crystal is rotated about the Z-axis.The cuts usually have two-letter names, where the "T" in the name indicates atemperature-compensated cut; for instance, the AT-cut was the first temperature-compensated cut discovered. The FC, IT, BT, and RT-cuts are other cuts along the zero-
7
temperature coefficient locus. These cuts were studied in the past (before the discoveryof the SC-cut) for some special properties, but are rarely used today. The highest-stability crystal oscillators employ SC-cut or AT-cut crystal units.
9 0 0 1 1 1 1I
60O "AT FC IT300 so:--C
STc0 LC
Z .-300 IRT.600q. . .
00 I00 200 90e
The AT, FC, rr, SC, BT. Wd R-cutsare on Uhs lod o zero Vmqerakre coectiecuts. the LC Is a "lew coegcisst ct NhWis used in a menmmeur.
Y-cut: = +90 ppnVOCx , (,kimss-shem mode)
X X-cut: = -20 ppnV/OC(extensionk mode)
Figure 5. Zero-temperature-coefficient cuts of quartz.
Because the properties of a quartz crystal unit depend strongly on the angles ofcut of the crystal plate, in the manufacture of crystal units, the plates are cut from aquartz bar along precisely controlled directions with respect to the crystallographic axes.The orientations of the plates are checked by means of X-ray diffraction. In someapplications, the orientations must be controlled with accuracies of a few seconds ofangle. After shaping to required dimensions, metal electrodes are applied to the wafer.Circular plates with circular electrodes are the most commonly used geometries, althoughthe blanks and electrodes may also be of other geometries. The electroded wafer ismounted in a holder structure [8]. Figure 6 shows the two common types of holderstructures used for resonators with frequencies greater than 1 MHz. (The 32-kHz tuningfork resonators used in quartz watches are packaged typically in small tubularenclosures.)
Because quartz is piezoelectric, a voltage applied to the electrodes causes thequartz plate to deform slightly. The amount of deformation due to an alternating voltage
8
Two-point mount package Three-and four-point mount package
QuartzBlankr BlankBlankElectodesBonding
CvrBonding Area ---CoverAreaA
SMounting MountingClips Clips --
Seal Basease PPins
-Top view of cover -
Figure 6. Typical constructions of AT-cut and SC-cut crystal units: (a) two-point mountpackage; (b) three- and four-point mount package.
depends on how close the frequency of the applied voltage is to a natural mechanicalresonance of the crystal. To describe the behavior of a resonator, the differentialequations for Newton's laws of motion for a continuum, and for Maxwell's equations, mustbe solved with the proper electrical and mechanical boundary conditions at the platesurfaces [9]. Because quartz is anisotropic and piezoelectric, with 10 independent linearconstants and numerous higher order constants, the equations are complex, and havenever been solved in closed form for physically realizable three-dimensional resonators.Nearly all theoretical works have used approximations. The nonlinear elastic constants,although small, are the source of some of the important instabilities of crystal oscillators;such as the acceleration sensitivity, the thermal-transient effect, and theamplitude-frequency effect, each of which is discussed in this report.
In an ideal resonator, the amplitude of vibration is maximum at the center of theelectrodes; it falls off exponentially outside the electrodes, as shown in the lower rightportion of Figure 7. In a properly designed resonator, a negligible amount of energy is
9
lost to the mounting and bonding structure, i.e., the edges must be inactive in order forthe resonator to be able to possess a high 0. The displacement of a point on theresonator surface is proportional to the drive current. At the typical drive currents usedin (e.g., 10 MHz) thickness shear resonators, the peak displacement is on the order ofa few atomic spacings. (The peak acceleration of a point on the electrodes is on theorder of 1 million g.)
MetallicElectrodes
ResonatorPlate Substrate Ul
(the "blank")
Conventional resonator geometryand amplitude distribution, Jul
Figure 7. Resonator vibration amplitude distribution for a circular plate with circularelectrodes.
As the drive level (the current through a crystal) increases, the crystal's amplitudeof vibration also increases, and the effects due to the nonlinearities of quartz becomemore pronounced. Among the many properties that depend on the drive level are:resonance frequency, motional resistance R1, phase-noise, and frequency vs. temperatureanomalies (called activity dips), which are discussed in another section of this report. Thedrive-level dependence of the resonance frequency, called the amplitude-frequency effect,is illustrated in Figure 8 [10]. The frequency change with drive level is proportional to thesquare of the drive current; the coefficient depends on resonator design [11]. Becauseof the drive-level dependence of frequency, the highest stability oscillators usually containsome form of automatic level control in order to minimize frequency changes due tooscillator circuitry changes. At high drive levels, the nonlinear effects also result in anincrease in the resistance [5]. Crystals can also exhibit anomalously high startingresistance when the crystal surfaces possess such imperfections as scratches andparticulate contamination. Under such conditions, the resistance at low drive levels canbe high enough for an oscillator to be unable to start when power is applied. The drive
10
level dependence of resistance is illustrated in Figure 9. In addition to the nonlineareffects, a high drive level can also cause a frequency change due to a temperatureincrease caused by the energy dissipation in the active area of the resonator.
S Nil AT
60
t:
ed 403 ipe
C.)•32 diopter
10 20 B
100 n0 o 400 N00 600 700
Crystal Current (p amps)
Figure 8. Drive level dependence of frequency.
Anomalous Normal Drive levelstarting operating effectsresistance range
,o %. I //
"• ~/
\/
I I I t JI0-, toI -, I0-, 1 10 104)
1. (mA)
Figure 9. Drive level dependence of crystal unit resistance.
11
Bulk-acoustic-wave quartz resonators are available in the frequency range of about1 kHz to 500 MHz. Surface-acoustic-wave (SAW) quartz resonators are available in therange of about 150 MHz to 1.5 GHz. To cover the wide range of frequencies, differentcuts, vibrating in a variety of modes, are used. The bulk wave modes of motion areshown in Figure 10. The AT-cut and SC-cut crystals vibrate in a thickness-shear mode.Although the desired thickness-shear mode usually exhibits the lowest resistance, themode spectrum of even properly designed crystal units exhibits unwanted modes abovethe main mode. The unwanted modes, also called "spurious modes" or "spurs," areespecially troublesome in filter crystals, in which "energy trapping rules" are employed tomaximize the suppression of unwanted modes [4]. These rules specify certain electrodegeometry to plate geometry relationships. In oscillator crystals, the unwanted modes maybe suppressed sufficiently by providing a large enough plate diameter to electrodediameter ratio, or by contouring (i.e., generating a spherical curvature on one or bothsides of the plate).
Flexure Mode Extensional Mode Face Shear Mode
Thickness Shear Fundamental Mode Third Overtone
Mode Thickness Shear Thickness Shear
Figure 10. Modes of motion of a quartz resonator.
Above 1 MHz, the AT-cut is commonly used. For high-precision applications, theSC-cut has important advantages over the AT-cut. The AT-cut and SC-cut crystals canbe manufactured for fundamental-mode operation up to a frequency of about 300 MHz.(Higher than 1 GHz units have been produced on an experimental basis.) Above 100MHz, overtone units that operate at a selected harmonic mode of vibration are generallyused, although higher than 100 MHz fundamental mode units can be manufactured bymeans of chemical polishing (etching) techniques [12]. Below 1 MHz, tuning forks, X-Yand NT bars (flexure mode), +50 X-cuts (extensional mode), or CT-cut and DT-cut units(face shear mode) can be used. Tuning forks have become the dominant type of low-
12
frequency units due to their small size and low cost. Hundreds of millions of quartz tuning
forks are produced annually for quartz watches and other applications.
B. Oscillator Categories
A crystal unit's resonance frequency varies with temperature. Typical frequencyvs. temperature (f vs. 7) characteristics for crystals used in frequency standards areshown in Figure 11. The three categories of crystal oscillators, based on the method ofdealing with the crystal unit's f vs. T characteristic, are XO, TCXO, and OCXO, (seeFigure 12). A simple XO does not contain means for reducing the crystal's f vs. Tvariation. A typical XO's f vs. T stability may be ±25 ppm for a temperature range of-55°C to +851C.
25 AT-cut . BT-cut
aa A20
0. 0
1 4-0 -3-0"SI0¶1 -r051 IE S3 54 51 55 07 0- E
an Y-bar quartzp i
-101 1
In-aTCOthe op sa fro a. tmeratue s350 20s'÷A8, o 6
•~ ~~ ,,,350., ,,,o , e, 0 - 0 for- - - - - -
Temperature (Oc)
Figure 11. Frequency versus temperature characteristics of AT-cut crystals, showing AT-
and BT-cut plates in Y-bar quartz.
In a TCXO, the output signal from a temperature sensor (a thermistor) is used to
generate a correction voltage that is applied to a voltage-variable reactance (a varactor)in the crystal network [13]. The reactance variations produce frequency changes that areequal and opposite to the frequency changes resulting from temperature changes; inother words, the reactance variations compensate for the crystal's f vs. T variations.Analog TCXOs can provide about a 20-fold improvement over the crystal's f vs. Tvariation. A good TCXO may have an f vs. Tstability of ±1 ppm for a temperature rangeof -550C to +850C.
13
Voltage f- + 10 ] 10"A
Output -4 C i _2 W T-7 T/+0, -0°
* Crystal Oscillator (XO) 10 X 10-F_-- i 0-
Compensation CX f _J __IX_107_
Temperature I4etwork orSensor Computer I %
0--450C% _101q 4 t I00C
.. .! ..0 -,,,1Temperature Compensated (TCXO)
Ovef +I(XId
XO ; •-451c _ +100 cOven [ T
ntrlemperatureemperatureIXs Sensore i -I X tOv
s Oven Controlled (OCXO)
Figure 12. Crystal oscillator categories based on the crystal unit's frequency versustemperature characteristic.
In an OCXO, the crystal unit and other temperature sensitive components of theoscillator circuit are maintained at a constant temperature in an oven [13]. The crystalis manufactured to have an f vs. T characteristic which has zero slope at the oven
temperature. To permit the maintenance of a stable oven temperature throughout theOCXO's temperature range (without an internal cooling means), the oven temperature isselected to be above the maximum operating temperature of the OCXO. OCXOs canprovide more than a 1000-fold improvement over the crystal's f vs. T variation. A goodOCXO may have an f vs. T stability of better than t5 x 10-9 for a temperature range of-550C to +851C. OCXOs require more power, are larger, and cost more than TCXOs.
A special case of a compensated oscillator is the microcomputer-compensatedcrystal oscillator (MCXO) (141. The MCXO overcomes the two major factors that limit thestabilities achievable with TCXOs: thermometry and the stability of the crystal unit.Instead of a thermometer that is external to the crystal unit, such as a thermistor, theMCXO uses a much more accurate "self-temperature sensing" method. Two modes of
14
the crystal are excited simultaneously in a dual-mode oscillator. The two modes arecombined such that the resulting beat frequency is a monotonic (and nearly linear)function of temperature. The crystal thereby senses its own temperature. To reduce thef vs. Tvariations, the MCXO uses digital compensation techniques: pulse deletion in oneimplementation, and direct digital synthesis of a compensating frequency in another. Thefrequency of the crystal is not "pulled," which allows the use of high-stability (small C1)SC-cut crystal units. A typical MCXO may have an f vs. T stability of ±2 X 10i for atemperature range of -550C to +850C.
C. Oscillator Circuit Types
Of the numerous oscillator circuit types, three of the more commonly discussedones, the Pierce, the Colpitts, and the Clapp, consist of the same circuit except that therf ground points are at different locations, as shown in Figure 13. The Butler andmodified Butler are also similar to each other; in each, the emitter current is the crystalcurrent. The gate oscillator is a Pierce-type that uses a logic gate plus a resistor in placeof the transistor in the Pierce oscillator. (Some gate oscillators use more than one gate.)
b IM• b E ' 0 Ir -- -- bE
T I -T
Pierce Colpitts Clapp
Butler Modified Butler Gate
Figure 13. Oscillator circuit types.
15
Information on designing crystal oscillators can be found in references 1, 2, 5, and7. The choice of oscillator circuit type depends on factors such as the desired frequencystability, input voltage and power, output power and waveform, tunability, designcomplexity, cost, and the crystal unit's characteristics.
In the Pierce family, the ground point location has a profound effect on theperformance. The Pierce configuration is generally superior to the others, e.g., withrespect to the effects of stray reactances and biasing resistors, which appear mostlyacross the capacitors in the circuit rather than the crystal unit. It is one of the mostwidely used circuits for high stability oscillators. In the Colpitts configuration, a larger partof the strays appears across the crystal, and the biasing resistors are also across thecrystal, which can degrade performance. The Clapp is seldom used because, since thecollector is tied directly to the crystal, it is difficult to apply a dc voltage to the collectorwithout introducing losses or spurious oscillations. The Pierce family usually operates at"parallel resonance" (see Figure 4), although it can be designed to operate at seriesresonance by connecting an inductor in series with the crystal. The Butler family usuallyoperates at (or near) series resonance. The Pierce can be designed to operate with thecrystal current above or below the emitter current. Gate oscillators are common in digitalsystems when high stability is not a major consideration. (See the references for moredetails on oscillator circuits.)
Most users require a sine wave, or a TTL-compatible, or a CMOS-compatible, oran ECL-compatible output. The latter three can be simply generated from a sine wave.The four output types are illustrated in Figure 14, with the dashed lines representing thesupply voltage inputs, and the bold solid lines, the outputs. (There is no "standard" inputvoltage for sine wave oscillators, and the input voltage for CMOS typically ranges from5V to 15V.)
+1 5V+10V - -- _ --
+IOV
+5V-- - - - - - - -
-0V
Sine TTL CMOS ECL
Figure 14. Oscillator outputs.
16
Il1. Oscillator Instabilities
A. Accuracy, Stability and Precision
Oscillators exhibit a variety of instabilities. These include aging, noise, andfrequency changes with temperature, acceleration, ionizing radiation, power supplyvoltage, etc. The terms accuracy, stability, and precision are often used in describing anoscillator's quality with respect to its instabilities. Figure 15 illustrates the meanings ofthese terms for a marksman and for a frequency source. (For the marksman, each bullethole's distance to the center of the target is the "measurement.")
Precise but Not accurate and Accurate but Accurate andnot accurate not precise not precise precise
f I. rr
r0-- -- -- -- --- - ---- ---------- - -
Time Time Time Time
Stable but Not stable and Accurate but Stable andnot accurate not accurate not stable accurate
Figure 15. Accuracy, stability and precision examples for a marksman, top, and for afrequency source, bottom.
Accuracy is the extent to which a given measurement, or the average of a set ofmeasurements for one sample, agrees with the definition of the quantity being measured.It is the degree of "correctness" of a quantity. Frequency standards have varying degreesof accuracy. The International System (SI) of units for time and frequency (second andHz, respectively) are obtained in laboratories using very accurate frequency standardscalled primary standards. A primary standard operates at a frequency calculable in terms
17
of the SI definition of the second: "the duration of 9,192,631,770 periods of the radiationcorresponding to the transition between the two hyperfine levels of the ground state ofthe cesium atom 133" [15].
Reproducibility is the ability of a single frequency standard to produce the samefrequency, without adjustment, each time it is put into operation. From the user's pointof view, once a frequency standard is calibrated, reproducibility confers the sameadvantages as accuracy. Stabilitydescribes the amount something changes as a functionof parameters such as time, tomperature, shock, and the like. Precision is the extent towhich a given set of measurements of one sample agrees with the mean of the set. (Arelated meaning of the term is used as a descriptor of the quality of an instrument, as ina "precision instrument." In that context, the meaning is usually defined as accurate andprecise, although a precision instrument can also be inaccurate and precise, in whichcase the instrument needs to be calibrated.)
B. Aging
"Aging" and "drift" have occasionally been used interchangeably in the literature.However, recognizing the "need for common terminology for the unambiguousspecification and description of frequency and time standard systems," the IntemationalRadio Consultative Committee (CCIR) adopted a glossary of terms and definitions in 1990[16]. According to this glossary, aging is "the systematic change in frequency with timedue to internal changes in the oscillator," and drift is "the systematic change in frequencywith time of an oscillator." Drift is due to aging plus changes in the environment andother factors external to the oscillator. Aging, not drift, is what one denotes in aspecification document and what one measures during oscillator evaluation. Drift is whatone observes in an application. For example, the drift of an oscillator in a spacecraftmight be due to (the algebraic sum of) aging and frequency changes due to radiation,temperature changes in the spacecraft, and power supply changes.
Aging can be positive or negative [17]. Occasionally, a reversal in aging directionis observed. At a constant temperature, aging usually has an approximately logarithmicdependence on time. Typical (computer-simulated) aging behaviors are illustrated inFigure 16, where A(t) is a logarithmic function and B(t) is the same function but withdifferent coefficients. The curve showing the reversal is the sum of the other two curves.A reversal indicates the presence of at least two aging mechanisms. The aging rate ofan oscillator is highest when it is first turned on. When the temperature of a crystal unitis changed (e.g., when an OCXO is tumed off and turned on at a later time), a new agingcycle starts. (See the section conc,3ming hysteresis and retrace below for additionaldiscussion of the effects of temperature cycling.)
The primary causes of crystal oscillator aging are stress relief in the mountingstructure of the crystal unit, mass transfer to or from the resonator's surfaces due toadsorption or desorption of contamination, changes in the oscillator circuitry, and,
18
A(t) = 5 Ln(0.5t+1)
Time
B(t) = -35 Ln(0.006t+1)
Figure 16. Computer-simulated typical aging behaviors; where A(t) and B(t) arelogarithmic functions with different coefficients.
possibly, changes in the quartz material. Because the frequency of a thickness-shearcrystal unit, such as an AT-cut or an SC-cut, is inversely proportional to the thickness ofthe crystal plate, and because a typical 5-MHz plate is on the order of 1 million atomiclayers thick, the adsorption or desorption of contamination equivalent to the mass of oneatomic layer of quartz changes the frequency by about 1 ppm. Therefore, in order toachieve low aging, crystal units must be fabricated and hermetically sealed in anultraclean, ultra-high-vacuum environment. As of 1992, the aging rates of typicalcommercially available crystal oscillators range from 5 ppm to 10 ppm per year for aninexpensive XO, to 0.5 ppm to 2 ppm per year for a TCXO, and to 0.05 ppm to 0.1 ppmper year for an OCXO. The highest precision OCXOs can age a few parts in 1012 perday, i.e., less than 0.01 ppm per year.
C. Noise In Frequency Standards
1. The Effects ot Noise
Sometimes the suitability of oscillators for an application is limited by deterministicphenomena. In other instances, stochastic (random) processes establish the perfor-mance limitations. Except for vibration, the short-term instabilities almost always resultfrom noise. Long-term performance of quartz and rubidium standards is limited primarily
19
by the temperature sensitivity and the aging, but the long-term performance of cesiumand some hydrogen standards is limited primarily by random processes.
Noise can have numerous adverse effects on system performance. Among theseeffects are the following: (1) it limits the ability to determine the current state and thepredictability of precision oscillators (e.g., the noise of an oscillator produces timeprediction errors of - cay(t) for prediction intervals of r); (2) it limits synchronization andsyntonization accuracies; (3) it can limit a receiver's useful dynamic range, channelspacing, and selectivity; (4) it can cause bit errors in digital communications systems; (5)it can cause loss of lock, and limit acquisition and reacquisition capability inphase-locked-loop systems; and (6) it can limit radar performance, especially Dopplerradar.
It is important to have appropriate statistical measures to characterize the randomcomponent of oscillator instability. The subject of noise characterization has beenreviewed [4,18] and is also the subject of an IEEE standard [19]. The two-sampledeviation, denoted by ay(t), is the measure of short-term instabilities in the time domain.The phase noise, denoted by SE(f), or the phase instability, denoted by S,(f), are measuresof instabilities in the frequency domain; Sf(f) =- 1/2S,(f) [19].
2. Noise in Crystal Oscillators
Although the causes of noise in crystal oscillators are not fully understood, severalcauses of short-term instabilities have been identified. Temperature fluctuations cancause short-term instabilities via thermal-transient effects (see the section belowconcerning dynamic f vs. Teffects), and via activity dips at the oven set point in OCXOs.Other cauc- dclude Johnson noise in the crystal unit, random vibration (see the sectionbelow concerning acceleration effects in crystal oscillators), noise in the oscillator circuitry(both the active and passive components can be significant noise sources), andfluctuations at various interfaces on the resonator (e.g., in the number of moleculesadsorbed on the resonator's surface).
In a properly designed oscillator, the resonator is the primary noise source closeto the carrier and the oscillator circuitry is the primary source far from the carrier. Thenoise close to the carrier (i.e., within the bandwidth of the resonator) has a strong inverserelationship with resonator 0, such that Sf(f) - IiQ4. In the time domain, aFy() = (2 x10-7)/Q at the noise floor. In the frequency domain, the noise floor is limited by Johnsonnoise, the noise power of which is kT = -174 dBm/Hz at 2900K. A higher signal (i.e., ahigher resonator drive current) will improve the noise floor but not the close-in noise. Infact, for reasons that are not understood fully, above a certain point, higher drive levelsusually degrade the close-in noise. For example, the maximum "safe" drive level is about100 ita for a 5-MHz fifth overtone AT-cut resonator with 0 = 2.5 million. The safe drivecurrent can be substantially higher for high-frequency SC-cut resonators. For example,Sf(f) = -180 dBc/Hz has been achieved with 100-MHz fifth overtone SC-cut resonators at
20
drive currents - 10 mA. However, such a noise capability is useful only in a vibration-freelaboratory environment. If there is even a slight amount of vibration at the offsetfrequencies of interest, the vibration-induced noise will dominate the quiescent noise ofthe oscillator (see the section below concerning acceleration effects in crystal oscillators).
When low noise is required in the microwave (or higher) frequency range, SAWoscillators and dielectric resonator oscillators (DROs) are sometimes used. Whencompared with multiplied-up (bulk-acoustic-wave) quartz oscillators, these oscillators canprovide lower noise far from the carder at the expense of poorer noise close to thecarrier, poorer aging, and poorer temperature stability. SAW oscillators and DROs canprovide lower noise far from the carrier because these devices can be operated at higherdrive levels, thereby providing higher signal-to-noise ratios, and because the devicesoperate at higher frequencies, thereby reducing the "20 log N" losses due to frequencymultiplication by N. SE(f) = -180 dBc/Hz noise floors have been achieved withstate-of-the-art SAW oscillators [20]. Of course, as is the case for high-frequencybulk-wave oscillators, such noise floors are realizable only in environments that are freeof vibrations at the offset frequencies of interest. Figures 17 and 18 show comparisonsof state-of-the-art 5 MHz and 100 MHz BAW oscillators and a 500 MHz SAW oscillator,multiplied to 10 GHz. Figure 17 shows the comparison in a quiet environment, andFigure 18 shows it in a vibrating environment.
D. Frequency versus Temperature Stability
1. Static Frequency versus Temperature Stability
As an illustration of the effects that temperature can have on frequency stability,Figure 19 shows the effects of temperature on the accuracy of a typical quartz wristwatch.Near the wrist temperature, the watch can be very accurate because the frequency of thecrystal (i.e., the clock rate) changes very little with temperature. However, when thewatch is cooled to -55 0C or heated to +1000C, it loses about 20 seconds per day,because the typical temperature coefficient of frequency of the tuning fork crystals usedin quartz watches is -0.035 ppm/°C2.
The static f vs. T characteristics of crystal units are detormined primarily by theangles of cut of the crystal plates with respect to the crystallographic axes of quartz [3-5]."Static" means that the rate of change of temperature is slow enough for the effects oftemperature gradients (explained later) to be negligible. As Figure 11 illustrates for theAT-cut, a small change in the angle of cut (seven minutes in the illustration) cansignificantly change the f vs. Tcharacteristics. The points of zero temperature coefficient,the "turnover points," can be varied over a wide range by varying the angles of cut. Thef vs. Tcharacteristics of SC-cut crystals are similar to the curves shown in Figure 11, withthe inflection temperature (T,) shifted to about 950C. (The exact value of T, depends onthe resonator's design.)
21
0
-20 BAW = bulk-acoustic waveoscillator
-40 SAW = surface acousticwave oscillator
N-60
S-8
0S_ BAWC -100 5 MHz x 2000
-120
-140 10~0 MHzx10
BAW is SAW is SAW-160 lowa noise lower noise 500 MHz x 20, ,200 , 5500,
to- o loi 102 1o3 to4 to' 10
Offset frequency in Hz
Figure 17. Low-noise SAW and BAW multiplied to 10 GHz (in a nonvibratingenvironment).
0Vibration induced phase noise dominates the phasenoise of both (whichever has lower acceleration-20 •sensitivity will have lower phase noise; currently,BAW can provide lower sensitivity than SAW.)
"-40 Illustration assumes I x iO'9/g accelerationsensitivity for both BAW and SAW, and 0.01
g2iHz random vibration power spectralN -60 -density at all vibration frequencies.
S -80•-5 MHz x 2000_
-1 00
-120 \ \
-140 N 100 MHz x 100
-160 500 MHz x 20p I I I I I a
1O-' 10 lOt 102 W WO' Ao6
Offset frequency in Hz
Figure 18. Low-noise SAW and BAW multiplied to 10 GHz (in a vibrating environment).
22
Temperature coefficient of frequency = -0.035 ppn/'C2
"0
lo-
0
20-t t t t t
-55 °C -10 °C +28 °C +49 °C +85 °CMilitary Winter Wrist Desert Military"Cold" Temp. "Hot"
Figure 19. Wristwatch accuracy as it is affected by temperature.
Other factors that can affect the f vs. T characteristics of crystal units include theovertone [21]; the geometry of the crystal plate; the size, shape, thickness, density andstresses of the electrodes; the drive level; impurities and strains in the quartz material;stresses in the mounting structure; interfering modes; ionizing radiation; the rate ofchange of temperature (i.e., thermal gradients) [22]; and thermal history. The last twofactors are important for understanding the behaviors of OCXOs and TCXOs, and are,therefore, discussed separately.
The effect of harmonics, i.e. "overtones," on f vs. Tis illustrated for AT-cut crystalsin Figure 20 [21]. This effect is important for understanding the operation of the MCXO.The MCXO contains an SC-cut resonator and a dual mode oscillator that excites both thefundamental mode and the third overtone of the resonator. The difference between thefundamental mode f vs. T and the third overtone f vs. T is due almost exclusively to thedifference between the first order temperature coefficients. Therefore, when the thirdovertone frequency is subtracted from three times the fundamental mode frequency, theresulting "beat frequency" is a monotonic and nearly linear function of temperature. Thisbeat frequency enables the resonator to sense its own temperature.
23
50- -0- 6
40 -
30-
20-
I 0 '- eOW 2
f 0o 3 5-
-10-
-20 M
-30 Reference angle-of-cut (0) is about
-40 8 minutes higher for the overtone modes.(For the overtone modes of the SC-cut,
-50 the reference 0-angle-of-cut is about 30/I minutes higher.)
-100 -80 -60 -40 -20 0 20 40 60 80 AT, 0C
Figure 20. Effects of harmonics on f vs. T.
Interfering modes can cause "activity dips" (see Figure 21), which can causeoscillator failure [23]. Near the activity dip temperature, anomalies appear in both thef vs. T and resistance (R) vs. T characteristics. When the resistance increases at theactivity dip, and the oscillator's gain margin is insufficient, the oscillation stops. Activitydips can be strongly influenced by the crystal's drive level and load reactance. Theactivity-dip temperature is a function of CL because the interfering mode usually has alarge temperature coefficient and a C1 that is different from that of the desired mode.Activity dips are troublesome in TCXOs, and also in OCXOs wheri the dip occurs at theoven temperature. The incidence of activity dips in SC-cut crystals is far lower than inAT-cut crystals.
An important factor that affects the f vs. T characteristics of crystal oscillators isthe load capacitor. When a capacitor is connected in series with the crystal, the f vs. Tcharacteristic of the combination is rotated slightly from that of the crystal alone. Thetemperature coefficient of the load capacitor can greatly magnify the rotation [241.
24
l •Al
CTi
Vk"2 RL2
I I 1 i I I I I , I-40 -20 0 20 40 60 80 100
Temperature ('C)
Figure 21. Activity dips in the frequency versus temperature and resistance versustemperature characteristics, with and without CL.
The f vs. Tof crystals can be described by a polynomial function. A cubic functionis usually sufficient to describe the f vs. T of AT-cut and SC-cut crystals to an accuracyof ±1 ppm. In the MCXO, in order to fit the f vs. Tdata to ±1 x 108, a polynomial of atleast seventh order is usually necessary [25].
2. Dynamic Frequency versus Temperature Effects
Changing the temperature surrounding a crystal unit produces thermal gradientswhen, for example, heat flows to or from the active area of the resonator plate throughthe mounting clips. The static f vs. T characteristic is modified by the thermal-transienteffect resulting from the thermal-gradient-induced stresses [223. When an OCXO isturned on, there can be a significant thermal-transient effect. Figure 22 shows whathappens to the frequency output of two OCXOs, each containing an oven that reaches
25
the equilibrium temperature in six minutes. One oven contains an AT-cut, the other, anSC-cut crystal. Thermal gradients in the AT-cut produce a large frequency undershootthat anneals out several minutes after the oven reaches equilibrium. The SC-cut crystal,being "stress-compensated" and thereby insensitive to such thermal-transient-inducedstresses, reaches the equilibrium frequency as soon as the oven stabilizes.
10-
. 10.3I o-s5
10-6 SCDeviation from static f vs. T = a•dT
1 where, for example, i z -2 x 10-7 s/K2
for a typical AT-cut resonator.
3 6 9 12 Time (rain")/•
105
-10-6
Figure 22. Warm-up characteristics of AT-cut and SC-cut crystal oscillators (OCXOs).
In addition to extending the warmup time of OCXOs, when crystals other thanSC-cuts are used, the thermal-transient effect makes it much more difficult to adjust thetemperature of OCXO ovens to the desired turnover points, and the OCXO frequenciesare much more sensitive to oven-temperature fluctuations [22].
The testing and compensation accuracies of TCXOs are also adversely affectedby the thermal-transient effect. As the temperature is changed, the thermal-transienteffect distorts the static f vs. T characteristic, which leads to apparent hysteresis [26].The faster the temperature is changed, the larger is the contribution of thethermal-transient effect to the f vs. T performance.
26
3. Thermal Hysteresis and Retrace
The f vs. T characteristics of crystal oscillators do not repeat exactly upontemperature cycling [27]. The lack of repeatability in TCXOs, "thermal hysteresis," isillustrated in Figure 23. The lack of repeatability in OCXOs, "retrace," is illustrated inFigure 24. Hysteresis is defined [281 as the difference between the up-cycle and thedown-cycle f vs. T characteristics, and is quantified by the value of the difference at thetemperature where the difference is maximum. Hysteresis is determined during at leastone complete quasistatic temperature cycle between specified temperature limits.Retrace is defined as the nonrepeatability of the f vs. T characteristic at a fixedtemperature (which is usually the oven temperature of an OCXO) upon on-off cycling anoscillator under specified conditions.
ItO
1.0
05.
40
ýTw Temperature (Ci-0.51~
-10.0
Figure 23. Temperature-compensated crystal oscillator (TCXO) thermal hysteresis,showing that the first f vs. T characteristic upon increasing temperature differs from thecharacteristic upon decreasing temperature.
Hysteresis is the major factor limiting the stability achievable with TCXOs. It isespecially so in the MCXO because, in principle, the digital compensation method usedin the MCXO would be capable of compensating for the f vs. T variations to arbitraryaccuracy if the f vs. T characteristics could be described by single-valued functions.
27
15OVN-4-14 DAYS-I"
10 OFF____
_OVEN ON
Figure 24. Oven-controlled crystal oscillator (OCXO) retrace example, showing that uponrestarting the oscillator after a 14 day off-period, the frequency was about 7x10 9 lowerthan what it was just before turn-off, and that the aging rate had increased significantlyupon the restart. About a month elapsed before the pre-turn-off aging rate was reachedagain. (Figure shows AM/f in parts in 109 vs. time in days.)
Retrace limits the accuracies achievable with OCXOs in applications where the OCXOis on-off cycled. Typical values of hysteresis in TCXOs range from 1 ppm to 0.1 ppmwhen the temperature-cycling ranges are O0C to 600C, and -550C to +850C. Hysteresisof less than 1 x 10-8 has been observed in a few SC-cut (MCXO) resonators [25]. Thetypical MCXO resonator hysteresis in early moJels of the MCXO was a few parts in 10l[14]. Typical OCXO retrace specifications, after a 24 hour off period at about 250C, rangefrom 2 x 108 to 1 x 10-. Low-temperature storage during the off period, and extendingthe off period, usually make the retrace worse 117].
The causes of hysteresis and retrace are not well understood; the experimentalevidence to date is inconclusive [27]. The mechanisms that can cause these effectsinclude strain changes, changes in the quartz, oscillator circuitry changes, contaminationredistribution in the crystal enclosure, and apparent hysteresis or retrace due to thermalgradients.
E. Warmup
When power is applied to a frequency standard, it takes a finite amount of timebefore the equilibrium frequency stability is reached. Figure 22, discussed above,illustrates the warmup of two OCXOs. The warmup time of an oscillator is a function ofthe thermal properties of the resonator, the oscillator circuit and oven construction, theinput power, and the oscillator's temperature prior to turn-on. Typical warmup timespecifications of OCXOs (e.g., from a O0C start) range from 3 minutes to 10 minutes.Even TCXOs, MCXOs, and simple XOs take a few seconds to "warm up," although theseare not ovenized. The reasons for the finite warmup, i.e., stabilization, periods are thatit takes a finite amount of time for the signal to build up in any high-C circuit, and the fewtens of milliwatts of power which are dissipated in these oscillators can change thethermal conditions within the oscillators.
28
F. Acceleration Effects
Acceleration changes a crystal oscillator's frequency [29]. The acceleration canbe a steady-state acceleration, vibration, shock, attitude change (2-g tipover), or acousticnoise. The amount of frequency change depe, is on the magnitude and direction of theacceleration A, and on the acceleration sensit.,vity of the oscillator r". The accelerationsensitivity is a vector quantity. The frequency change can be expressed as
AfrA
Typical values of Ill are in the range of 1 0 9/g to 1 01 /g. For example, when Vr = 2 x109 /g and is normal to the earth's surface, and the oscillator is tumed upside down (achange of 2 g), the frequency changes by 4 x 10-. When this oscillator is vibrated in theup-and-down direction, the time dependent acceleration modulates the oscillator's outputfrequency at the vibration frequency, with an amplitude of 2 x 10-/g.
When an oscillator is rotated 1800 about a horizontal axis, the scalar product of thegravitational field and the unit vector normal to the initial "top" of the oscillator changesfrom -1g to +lg, i.e., by 2g. Figure 25 shows actual data of the fractional frequency shiftsof an oscillator when the oscillator was rotated about three mutually perpendicular axesin the earth's gravitational field. For each curve, the axis of rotation was horizontal. Thesinusoidal shape of each curve is a consequence of the scalar product being proportionalto the cosine of the angle between the acceleration-sensitivity vector and the accelerationdue to gravity [29].
In the frequency domain, the modulation results in vibration-induced sidebands thatappear at plus and minus integer multiples of the vibration frequency from the carrierfrequency. Figure 26 shows the output of a spectrum analyzer for a 1 0-MHz, 1.4 x 109/goscillator that was vibrated at 100 Hz and 10 g. For sinusoidal vibration, the "sidebands"are spectral lines. When the frequency is multiplied, as it is in many applications, thesideband levels increase by 20 dB for each 1OX multiplication. The increased sidebandpower is extracted from the carrier. Under certain conditions of multiplication, the carrierdisappears, i.e., all the energy is then in the sidebands.
The acceleration sensitivity can be calculated from the vibration-induced sidebands.The preferred method is to measure the sensitivity at a number of vibration frequenciesin order to reveal resonances. Figure 27 shows an example of the consequence of aresonance in an OCXO, at 424 Hz. This resonance amplified the acceleration sensitivity17-fold.
The effect of random vibration is to raise the phase-noise level of the oscillator.The degradation of phase-noise can be substantial when the oscillator is on a vibratingplatform, such as on an aircraft. Figure 28 shows a typical aircraft random-vibration
29
Axis 3 - Gomo Wh
- x 0. (M• m ) .- P(r • . n -) I - 9- (ccw)f (ROnW) - F(mm)VZ - 1A63 •W (cw)
4 de TWTA -,106. de.
2
(I:•) - P~i-amy2 - 6.4 -I0 (ecu)AxiAxis 2
xVF Mý) - Rvmlw)]b2 -641 -1820 (ce.w)2 - -|(F(mm)- Km1ek)5/- CM -.0 (c
la -2
.4 Axis 3
Figure 25. 2-g tipover test (Af vs. attitude about three axes).-A xf)
g LEVEL - O0g
VIBRAI"•O SENSMTMIY - 1.4 x 10"9/g
Figure 26. Vibration-induced "sidebands" (i.e., spectral lines).
30
10-8
I ow- 1
1020 3O0 400 0 1000 2000
Vibration Frequency (Hz)
Figure 27. Resonance in the acceleration sensitivity vs. vibration frequency characteristic.
-70. -x
S .04
S-16 III
Sfrequency (Hz)
C -1204 45 dB Typical Aircraftb - 1304 "•• Random Vibration
Envelope-146
-150
-160I I I I
5 300 IK 2KOffset Frequency (Hz)
Figure 28. Random-vibration-induced phase-noise degradation.
31
specification (power spectral density [PSD] vs. vibration frequency) and the resultingvibration-induced phase-noise degradation. Acoustic noise is another source ofacceleration that can affect the frequency stability of oscillators.
The peak phase excursion, #P,,,, due to sinusoidal vibration is
Af = A 0 radians.
To some system designers, the quantity of concern is the integrated phase noisein the band f, to f2, which is
= 2f (f) df radians 2.
Upon freqLyency multiplication, both p,,k and 0b increase by the multiplication factor.For example, if r -A = 1 x 10-, fo = 10 MHz and f, = 10 Hz, then #*,,k = 1 x 10-3 radian.If this oscillator's frequency is multiplied to 10 GHz, e.g., in a radar system, then at 10GHz, *#,, = 1 radian. Such large phase excursions can be catastrophic to manysystems.
Figure 29 shows how the probability ot detection for a coherent radar systemvanes with the phase noise of the reference oscillator 130). The phase noiso requirementfor a 90% probability of detection of a 4km/hr target is -130 dBc per Hz at 70 Hz from thecarder, for a 10 MHz oscillator. Such a phase noise is well within the capability of 10MHz oscillators, provided that the oscillators are in a quiet environment. However, whenthe oscillators are on a vibrating platform, such as an airborne radar system, the phasenoise of even the best available oscillators (as of 1992) is degraded by an amount thatreduces the probability of detection to zero.
During shock, a crystal oscillator's frequency changes suddenly due to the suddenacceleration, as is illustrated in Figure 30. The frequency change follows the expressionabove for acceleration-induced frequency change except, if during the shock some elasticlimits in the crystal's support structure or electrodes are exceeded (as is almost alwaysthe case during typical shock tests), the shock will produce a permanent frequencychange.
Permanent frequency offsets due to shock can also be caused by changes in theoscillator circuitry (e.g., due to movement of a wire or circuit board), and the removal of(particulate) contamination from the resonator surfaces. Resonances in the mountingstructure will amplify the shock-induced stress.
32
To "see' 4 knVh tages, low phase noise 70 Hz from the
carrer is required. Shown is the probability of detection of rI•B• .knV targets vs. the phase noise "70 Hlz fromn the crrier of a 10
SN4HM reference oscillator. (After multiplication to 10 GHz.the phase noise will be at least 60 dB higher.) The phase
S80" noise due to platform vibration, eg., on an aircraft, reducesthe pobability of detection of slow-moving targets to wero.
S66
40
20
Low Noise High Noise
-140 -135 -130 -125 -120 -115 -110
Phase Noise (dBc/Hz)(at 70 Hz from carrier, for 4 knVh targets)
Figure 29. Coherent radar probability of detection as a function of reference oscillatorphase noise.
If the shock level is sufficiently high, the crystal will break; however, in applicationswhere high shock levels are a possibility, crystal units with chemically polished crystalplates can be used. Such crystals can survive shocks in excess of 30,000 g and havebeen fired successfully from howitzers [12,31].
G. Magnetic-Field Effects
Quartz is diamagnetic; however, magnetic fields can affect magnetic materials inthe crystal unit's mounting structure, electrodes, and enclosure. Time-varying electricfields will induce eddy currents in the metallic parts. Magnetic fields can also affectcomponents such as inductors in the oscillator circuitry. When a crystal oscillator isdesigned to minimize the effects of magnetic fields, the sensitivity can be much less than1 010 per oersted. Magnetic-field sensitivities on the order of 1012 per oersted have beenmeasured in crystal units designed specifically for low magnetic-field sensitivity [32].
33
H. Radiation Effects
-- Ionizing radiation changes a crystalt oscillator's frequency primarily because of3 -changes the radiation produces in the crystal
unit [33,341. Under certain conditions. theradiation will also produce an increase in thecrystal unit's equivalent series resistance. The
2 resistance increase can be large enough to stopthe oscillation when the oscillator is not radiation
Shock hardened.
I Figure 31 shows a crystal oscillator'sidealized frequency response to a pulse ofionizing radiation. The response consists of twoparts. Initially, there is a transient frequency
0 change that is due primarily to thethermal-transient effect caused by the suddendeposition of energy into the crystal unit. Thiseffect is a manifestation of the dynamic f vs. T
-l effect discussed earlier. The transient effect isabsent in SC-cut resonators made of high purityquartz.
-2 In the second part of the response, aftersteady state is reached, there is a permanentfrequency offset that is a function of the radiationdose and the nature of the crystal unit. The
-3 frequency change versus dose is nonlinear, ther Ichange per rad being much larger at low doses
to0 t. Ithan at large doses. At doses above 1 kilorad(SiO 2), the rate of frequency change with dose is
Figure 30. The effect of a shock at quartz-impurity-defect dependent. For example,t = t, on oscillator frequency. at a 1 megarad dose, the frequency change can
be as large as 10 ppm when the crystal unit ismade from natural quartz; it is typically 1 to a
few ppm when the crystal is made from cultured quartz, and it can be as small as 0.02ppm when the crystal is made from swept cultured quartz.
The impurity defect of major concern in quartz is the substitutional A13 defect withits associated interstitial charge compensator, which can be an H, Li+, or Na* ion, or ahole. This defect substitutes for a Si4" in the quartz lattice. Radiation can result in achange in the position of weakly bound compensators, which changes the elasticconstants of quartz and thereby leads to a frequency change. The movement of ions
34
ss to = oiginai, preirradiation
"C ffssl steady-ste frequency.ss (0.2 to 24 hours aterW ftexposure)
t. ft =instantaneous frequencyat any time (M)
Ito t Time
10-11 for natural quartz (R Increase can stop oscilation)
Afs's/rad* 10-12 for cultured quartz
10-13 for swept cultured quartz
* for 1 Mrad dose
Figure 31. Crystal oscillator's response to a pulse of ionizing radiation: f, originalpreirradiation frequency, AfL = steady-state frequency offset (0.2 hours to 24 hours afterexposure), f, = instantaneous f'requency at time t.
also results in a decrease in the crystal's 0, i.e., in an increase in the crystal's equivalentseries resistance, especially upon exposure to a pulse of ionizing radiation. If theoscillator's gain margin is insufficient, the increased resistance can stop the oscillation forperiods lasting many seconds. A high level pulse of ionizing radiation will producephotocurrents in the circuit which result in a momentary cessation of oscillation,independent of the type of quartz used in the resonator. In oscillators using properlydesigned oscillator circuitry and resonators made of swept quartz, the oscillator recoverswithin 15 lis after exposure [35,36].
Sweeping is a high-temperature, electric-field-driven, solid-state purification processin which the weakly bound alkali compensators are diffused out of the lattice and replacedby more tightly bound H÷ ions and holes [37,38]. In the typical sweeping process,conductive electrodes are applied to the Z surfaces of a quartz bar, the bar is heated toabout 5000C, and a voltage is applied so as to produce an electric field of about 1 kilovoltper centimeter along the Z direction. After the current through the bar decays (due tothe diffusion of impurities) to some constant value, the bar is cooled slowly, the voltage
35
is removed, and then the electrodes are removed. Crystal units made from swept quartzexhibit neither the radiation-induced 0 degradation nor the large radiation-inducedfrequency shifts. Swept quartz (or low aluminum content quartz) should be used ino.,cillators which are expected to be exposed to ionizing radiation.
At low doses (e.g., at a few rads) the frequency change per rad can be as high as10.9 per rad [39]. The low-dose effect is not well understood. It is not impurity-dependent, and it saturates at about 300 rads. At very high doses (i.e., at >> 1 Mrad),the impurity-dependent frequency shifts also saturate because, since the number ofdefects in the crystal are finite, the effects of the radiation interacting with the defects arealso finite.
When a fast neutron hurtles into a crystal lattice and collides with an atom, it isscattered like a billiard ball. A single such neutron can produce numerous vacancies,interstitials, and broken interatomic bonds. The effect of this "displacement damage" onoscillator frequency is dependent primarily upon the neutron fluence. The frequency ofoscillation increases nearly linearly with neutron fluence at rates of: 8 x 1021 neutronsper square centimeter (n/cm2) at a fluence range of 10'0 to 1012 n/cm2, 5 x 10 21/n/cm2 at1012 to 1013 n/cm2, and 0.7 x 1021/n/cm 2 at 1017 to 1018 n/cm2.
I. Other Effects on Stability
Ambient pressure change (as during an altitude change) can change a crystaloscillator's frequency if the pressure change produces a deformation of the crystal unit'sor the oscillator's enclosure (thus changing stray capacitances and stresses). Thepressure change can also affect the frequency indirectly through a change in heat-transferconditions inside the oscillator. Humidity changes can also affect the heat-transferconditions. In addition, moisture in the atmosphere will condense on surfaces when thetemperature falls below the dew point, and can permeate materials such as epoxies andpolyimides, and thereby affect the properties (e.g., conductivities and dielectric constants)of the oscillator circuitry. The frequency of a properly designed crystal oscillator changesless than 5 x 1 0 -9 when the environment changes from one atmosphere of air to avacuum. The medium and long term stability of some oscillators can be improved bycontrolling the pressure and humidity around the oscillators [40].
Electric fields can change the frequency of a crystal unit. An ideal AT-cut is notaffected by a DC voltage on the crystal electrodes, but "doubly rotated cuts," such as theSC-cut, are affected. For example, the frequency of a 5-MHz fundamental mode SC-cutcrystal changes 7 x 10' per volt. Direct-current voltages on the electrodes can alsocause sweeping, which can affect the frequencies of all cuts.
Power-supply and load-impedance changes affect the oscillator circuitry and,indirectly, the crystal's drive level and load reactance. A change in load impedancechanges the amplitude or phase of the signal reflected into the oscillator loop, which
36
changes the phase (and frequency) of the oscillation [41]. The effects can be minimizedthrough voltage regulation and the use of buffer amplifiers. The frequency of a "good"crystal oscillator changes less than 5 x 10.10 for a 10% change in load impedance. Thetypical sensitivity of a high-quality crystal oscillator to power-supply voltage changes is5 x 10-"N.
Gas permeation under conditions where there is an abnormally high concentrationof hydrogen or helium in the atmosphere can lead to anomalous aging rates. Forexample, hydrogen can permeate into "hermetically" sealed crystal units in metalenclosures, and helium can permeate through the walls of glass-enclosed crystal units.
J. Interactions Among the Influences on Stability
The various influences on frequency stability can interact in ways that lead toerroneous test results if the interfering influence is not recognized during testing. Forexample, building vibrations can interfere with the measurement of short-term stability.Vibration levels of 10-3 g to 10,2 g are commonly present in buildings. Therefore, if anoscillator's acceleration sensitivity is 1 x 10-9/g, then the building vibrations alone cancontribute short-term instabilities at the 1012 to 10-11 level.
The 2-g tipover test is often used to measure the acceleration sensitivity of crystaloscillators. Thermal effects can interfere with this test because, when an oscillator isturned upside down, the thermal gradients inside the oven can vary due to changes inconvection currents [29]. Other examples of interfering influences include temperatureand drive-level changes interfering with aging tests; induced voltages due to magneticfields interfering with vibration-sensitivity tests; and the thermal-transient effect, humiditychanges, and the effect of load-reactance temperature coefficient interfering with themeasurement of crystal units' static f vs. Tcharacteristics.
An important effect in TCXOs is the interaction between the frequency adjustmentduring calibration and the f vs. Tstability [42]. This phenomenon is called the trim effect.In TCXOs, a temperature-dependent signal from a thermistor is used to generate acorrection voltage that is applied to a varactor in the crystal network. The resultingreactance variations compensate for the crystal's f vs. Tvariations. During calibration,the crystal's load reactance is varied to compensate for the TCXO's aging. Since thefrequency versus reactance relationship is nonlinear, the capacitance change duringcalibration moves the operating point on the frequency versus reactance curve to a pointwhere the slope of the curve is different, which changes the compensation (i.e.,compensating for aging degrades the f vs. T stability). Figure 32 shows how, for thesame compensating CL vs. T, the compensating f vs. Tchanges when the operating pointis moved to a different CL. Figure 33 shows test results for a 0.5 ppm TCXO that had a±6 ppm frequency-adjustment range (to allow for aging compensation for the life of thedevice). When delivered, this TCXO met its 0.5 ppm f vs. Tspecification; however, when
37
the frequency was adjusted ±6 ppm during testing, the f vs. T performance degradedsignificantly.
Af Af Cl
_. fs 2(Co + CL)fs
IK Compensating f vs. T
CL
Compensating CL vs. T
Figure 32. Change in compensating frequency versus temperature due to CL change.
2
• a" u•,, "" k:7 T(-C) •
r-..6 7ppm aging adjustment
Figure 33. Temperature-compensated crystal oscillator (TCXO) trim effect.
38
IV. Oscillator Comparison and Selection
The discussion that follows applies to wide-temperature-range frequency standards(i.e., to those which are designed to operate over a temperature range that spans at least900C). Laboratory devices that operate over a much narrower temperature range canhave better stabilities than those in the comparison below.
Commercially available frequency sources cover an accuracy range of severalorders of magnitude--from the simple XO to the cesium-beam frequency standard. Asthe accuracy increases, so does the power requirement, size, and cost. Figure 34, forexample, shows the relationship between accuracy and power requirement. Accuracyversus cost would be a similar relationship, ranging from about $1 for a simple XO toabout $40,000 for a cesium standard (1991 prices). Table 1 shows a comparison ofsalient characteristics of frequency standards. Figure 35 shows the comparison of shortterm frequency stability ranges as a function of averaging time [43]. Figure 36 shows acomparison of phasa-noise characteristics, and Table 2 shows a comparison ofweaknesses and wear-out mechanisms.
10"12 Cs"
71 1 lWday
I1 s/year
10-6[I 0- s/day10-64/
0.001 0.01 0.1 1 10 100Power (W)
* Accuracy vs. size, and accuracy vs. cost have similar relationships.
Figure 34. Relationship between accuracy and power requirements (XO=simple crystaloscillator; TCXO=temperature-compensated crystal oscillator; OCXO=oven-controlledcrystal oscillator; Rb=rubidium frequency standard; Cs=cesium beam frequency standard).
39
Table 1. Comparison of frequency standards' salient characteristics.
Quartz Oscillators Atomic Oscillators
TCXO MCXO OCXO Rubidium RbXO Cesium
Accuracy* 2 x 104 6 x 104 1 x 104 5 x 10 0 7 x 110 ' 2 x 10"(per year)
Aging/Year 5 x 10-7 2 x 10- 5 x 10-9 2 x 1010 2 x 10.1 0
Temp. Stab. 5 x 10-7 3 x 10' 1 x 10.9 3 x 10" 5 x 10 V 2 x 10.11(range, °C) (-55 to +85) (-55 to +85) (-55 to +85) (-55 to +68) (-55 to +85) (-28 to +65)
Stability, a,(r) 1 x 10= 3 x 10° 1 x 10-12 3 x 10-1 5 x 1012 5 x 10-"(T= I s)
Size 10 50 20-200 800 1200 6000(cm3)
Warmup Time 0.1 0.1 4 3 3 20(min) (to 1 x 10") (to 2 x 10"') (to 1 x 10'8) (to 6 x 10"10) (to 5 x 10'10) (to 2 x 1011')
Power (W) 0.05 0.04 0.6 20 0.65 30(at lowest temp.)
Price (~$) 100 1,000 2,000 8,000 10,000 40,000
*Including environmental effects (note that the temperature ranges for Rb and Cs are
narrower than for quartz).
Characteristics are provided in Table 1 for atomic oscillators: rubidium and cesiumfrequency standards and the rubidium-crystal oscillator (RbXO). In atomic frequencystandards, the output signal frequency is determined by the energy difference betweentwo atomic states, rather than by some property of a bulk material (as it is in quartzoscillators). An introductory review of atomic frequency standards can be found inreference 44, and reference 45 is a review of the literature up to 1983. (Reference 44reviews both atomic and quartz frequency standards; the report you are reading is basedon the quartz portion ot that document.) The RbXO is a device intended for applicationswhere power availability is limited, but where atomic frequency standard accuracy isneeded [46,47]. It consists of a rubidium frequency standard, a low-power andhigh-stability crystal oscillator, and control circuitry that adjusts the crystal oscillator'sfrequency to that of the rubidium standard. The rubidium standard is turned onperiodically (e.g., once a week) for the few minutes it takes for it to warm up and correctthe frequency of the crystal oscillator. With the RbXO, one can approach the long-termstability of the rubidium standard with the low (average) power requirement of the crystaloscillator.
40
-11 0 -
-.12
0D•)-13
-14 !
Hdrogen Maser
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0
Log (r), seconds I1 day 1 month
Figure 35. Stability as a function of averaging time comparison of frequency standards.
The major questions to be answered in choosing an oscillator include:
1. What frequency accuracy or reproducibility is needed for the system tooperate properly?
2. How long must this accuracy be maintained, i.e., will the oscillator becalibrated or replaced periodically, or must the oscillator maintain therequired accuracy for the life of the system?
3. Is ample power available, or must the oscillator operate from batteries?4. What warmup time, if any, is permissible?5. What are the environmental extremes in which the oscillator must
operate?6. What is the short-term stability (phase-noise) requirement?7. What is the size constraint?
In relation to the second question, what cost is to be minimized: the initialacquisition cost or the life-cycle cost? Often, the cost of recalibration is far higher thanthe added cost of an oscillator that can provide calibration-free life. A better oscillatormay also allow simplification of the system's design.
41
-40_°
C& -00-
-19001
-3 -12 4
Log(f)
Typical One-sided Spectral Density of Phase Deviation vs. OffsetFrequency, for Various Standards, Calculated at 5 MHz.
Figure 36. Phase instability comparison of frequency standards.
Table 2. Comparison of frequency standards' weaknesses and wearout mechanisms.
Weakness Wearout Mechanisms
Quartz Aging NoneRadiation hardness
Rubidium Life Rubidium depletionPower Buffer gas depletionWeight Glass contaminants
Cesium Life Cesium supply depletionPower Spent cesium getteringWeight Ion pump capacityCost Electron multiplierTemperature range
42
The frequency of the oscillator is another important consideration, because thechoice can have a significant impact on both the cost and the performance. Everythingelse being equal, an oscillator of standard frequency, such as 5 MHz or 10 MHz, forwhich manufacturers have well established designs, will cost less than one of an unusualfrequency, such as 8.34289 MHz. Moreover, for thickness-shear crystals, such as theAT-cut and SC-cut, the lower the frequency, the lower the aging [17]. Since atfrequencies much below 5 MHz, thickness-shear crystals become too large foreconomical manufacturing, and since all the highest stability oscillators use thickness-shear crystals, the highest stability commercially available oscillator's frequency is 5 MHz.Such oscillators will also have the lowest phase-noise capability close to the carrier.There are also some excellent 10 MHz oscillators on the market; however, oscillators ofmuch higher frequency than 10 MHz have significantly higher aging rates and phase-noise levels close to the carrier than do 5 MHz oscillators. For lowest phase-noise farfrom the carrier, where the signal-to-noise ratio determines the noise level, higherfrequency crystals (e.g., 100 MHz) can provide lower noise because such crystals cantolerate higher drive levels, thereby allowing higher signal levels.
V. Specifications, Standards, Terms, and Definitions
Numerous specifications and standards exist which relate to frequency standards.The major organizations responsible for these documents are the Institute of Electricaland Electronics Engineers (IEEE), the International Electrotechnical Commission (IEC),the CCIR, and the U. S. Department of Defense, which maintains the MilitarySpecification (MIL-SPEC) system. A listing of "Specifications and Standards Relating toFrequency Control" can be found in the final pages of the Proceedings of the IEEEFrequency Control Symposium (and its predecessor, the Proceedings of the AnnualSymposium on Frequency Control). In the 1990 Proceedings, for example, 79 suchdocuments are listed [48]. Many of the documents include terms and definitions, someof which are inconsistent. Unfortunately, no single authoritative document exists for termsand definitions relating to frequency standards. The terms and definitions in the CCIRglossary [16], in IEEE Std. 1139-1988 [19], and in MIL-O-55310's section 6 [28] are themost recent; they address different aspects of the field, and together form a fairly goodset of terms and definitions for users of frequency standards.
The most comprehensive document dealing with the specification of frequencystandards is MIL-O-55310 [28]. The evolution of this document over a period of manyyears has included periodic coordinations between the government agencies thatpurchase crystal oscillators and the suppliers of those oscillators. The documentaddresses the specifications of all the oscillator parameters discussed above, plus manyothers. This specification was written for crystal oscillators. Because the outputfrequencies of atomic frequency standards originate from crystal oscillators, and becauseno comparable document exists that addresses atomic standards specifically,MIL-O-55310 can also serve as a useful guide to specifying atomic standards.
43
MIL-STD-188-115, Interoperability and Performance Standards for CommunicationsTiming and Synchronization Subsystems, specifies that the standard frequencies for nodalclocks shall be 1 MHz, 5 MHz, or 5 X 2 N MHz, where N is an integer. This standard alsospecifies a 1-pulse-per-second timing signal of amplitude 10 V, pulse width of 20 ps, risetime less than 20 ns, fall time less than 1 gs; and a 24-bit binary coded decimal (BCD)time-code that provides Coordinated Universal Time (UTC) time of day in hours, minutes,and seconds, with provisions for an additional 12 bits for day of the year, and anadditional four bits for describing the figure of merit (FOM) of the time signal. The FOMsrange from BCD Character 1 for better than 1 ns accuracy to BCD character 9 for"greater than 10 ms of fault" [49].
Vl. For Further Reading
Reference 4 contains a thorough bibliography on the subject of frequencystandards to 1983. The principal forum for reporting progress in the field has been theProceedings of the IEEE Frequency Control Symposium (which was called theProceedings of the Annual Symposium on Frequency Control prior to 1992) [48]. Otherpublications that deal with frequency standards include IEEE Transactions on Ultrasonics,Ferroelectrics and Frequency Control, IEEE Transactions on Instrumentation andMeasurement, Proceedings of the Annual Precise Time and Time Interval (PTTI)Applications and Planning Meeting [50], and Proceedings of the European Frequency andTime Forum [51]. Review articles can be found in special issues and publications [52-56].
VII. References
1. Smith, W. L., Precision Oscillators. In: Precision Frequency Control, Vol. 2 (E. A.Gerber and A. Ballato, eds.), Academic Press, New York, pp. 45-98, 1985.
2. Frerking, M. E., Crystal Oscillator Design and Temperature Compensation, VanNostrand Reinhold Company, 1978.
3. Bottom, V. E., Introduction to Quartz Crystal Unit Design, Van Nostrand Reinhold,New York, 1982.
4. Gerber, E. A. and Ballato, A. (eds.), Precision Frequency Control, Academic Press,New York, 1985.
5. Parzen, B., Design of Crystal and Other Harmonic Oscillators, Wiley, New York,1983. Chapter 3 of this book, Piezoelectric Resonators, by A. Ballato, is an oscillator-application oriented treatment of the subject.
44
6. Hafner, E., Resonator and Device Measurements. In: Precision Frequency Control,Vol. 2 (E. A. Gerber and A. Ballato, eds.), Academic Press, pp. 1-44, 1985.
7. Benjaminson, A., Computer-Aided Design of Crystal Oscillators, U. S. ArmyLaboratory Command R&D Technical Report DELET-TR-84-0386-F, August 1985, AD-B096820; Advanced Crystal Oscillator Design, U. S. Army Laboratory Command R&DTechnical Report SLCET-TR-85-0445-F, January 1988, AD-B1i21288; Advanced CrystalOscillator Design, U. S. Army Laboratory Command R&D Technical Report SLCET-TR-88-0804-1, February 1989, AD-B134514, and Advanced Crystal Oscillator Design, U. S.Army Laboratory Command R&D Technical Report SLCET-TR-88-0804-F, December,1991, AD-B163808.
8. Kusters, J. A., Resonator and Device Technology. In: Precision FrequencyControl, Vol. 1 (E. A. Gerber and A. Ballato, eds.), Academic Press, pp. 161-183, 1985.
9. Meeker, T. R., Theory and Properties of Piezoelectric Resonators and Waves. In:Precision Frequency Control, Vol. 1 (E. A. Gerber and A. Ballato, eds.), Academic Press,pp. 47-119, 1985.
10. Kusters, J. A., The SC-cut Crystal - An Overview, Proc. 1981 Ultrasonics Symp.,pp. 402-409.
11. R. L. Filler, The Amplitude-Frequency Effect in SC-cut Resonators, Proc. 39th Ann.Symp. on Frequency Control, pp. 311-316, NTIS Accession No. AD-A217404, 1985.
12. Vig, J. R., LeBus, J. W., and Filler, R. L., Chemically Polished Quartz, Proc. 31stAnn. Symp. on Frequency Control, pp. 131-143, NTIS Accession No. AD-A088221,1977.
13. Frerking, M. E., Temperature Control and Compensation. In: Precision FrequencyControl, Vol. 2 (E. A. Gerber and A. Ballato, eds.), Academic Press, New York, pp. 99-111, 1985.
14. Schodowski, S. S., et al., Microcomputer Compensated Crystal Oscillator for LowPower Clocks, Proc. 21st Ann. Precise Time & Time Interval (PTTI) Applications &Planning Meeting, pp. 445-464, 1989. Available from the U. S. Naval Observatory, TimeServices Department, 34th and Massachusetts Avenue, NW, Washington, DC 20392.Details of the MCXO are also described in a series of five papers in the Proc. 43rd Ann.Symp. Frequency Control, NTIS Accession No. AD-A235629, 1989.
15. XIIIth General Conference of Weights and Measures, Geneva, Switzerland,October 1967.
16. International Radio Consultative Committee (CCIR), Recommendation No. 686,Glossary. In: CCIR 17th Plenary Assembly, Vol. 7, Standard Frequencies and TimeSignals (Study Group 7), CCIR, Geneva, Switzerland, 1990. Copies available from
45
International Telecommunications Union, General Secretariat - Sales Section, Place desNations, CH1211 Geneva, Switzerland.
17. Vig, J. R., and Meeker, T. R., The Aging of Bulk Acoustic Wave Resonators,Filters, and Oscillators, Proc. 45th Ann. Symp. Frequency Control, IEEE Cat. No.91CH2965-2, pp. 77-101, 1991.
18. Rutman, J., and Walls, F. L., Characterization of Frequency Stability in PrecisionFrequency Sources, Proc. of the IEEE, Vol. 79, No. 6, pp. 952-960, June 1991.
19. IEEE Standard Definitions of Physical Quantities for Fundamental Frequency andTime Metrology, IEEE Std. 1139-1988. IEEE, 445 Hoes Lane, Piscataway, NJ 08854,U.S.A.
20. Parker, T. E., Characteristics and Sources of Phase Noise in Stable Oscillators,Proc. 41st Ann. Symp. on Frequency Control, pp. 99-110, NTIS Accession No. AD-A216858, 1987.
21. Ballato, A. and Lukaszek, T., Higher Order Temperature Coefficients of Frequencyof Mass-Loaded Piezoelectric Crystal Plates, Proc. 29th Ann. Symp. on FrequencyControl, pp. 10-25, NTIS Accession No. AD-AO17466, 1975.
22. Ballato, A. and Vig, J. R., Static and Dynamic Frequency-Temperature Behaviorof Singly and Doubly Rotated, Oven-Controlled Quartz Resonators, Proc. 32nd Ann.Symp. on Frequency Control, pp. 180-188, NTIS Accession No. AD-A955718, 1978.
23. Ballato, A. and Tilton, R., Electronic Activity Dip Measurement, IEEE Trans. onInstrumentation and Measurement, Vol. IM-27, pp. 59-65, 1978.
24. Ballato, A., Frequency-Temperature-Load Capacitance Behavior of Resonators forTCXO Applications, IEEE Trans.Sonics and Ultrasonics, SU-25, pp. 185-191, July 1978.
25. Filler, R. L., Frequency-Temperature Considerations for Digital TemperatureCompensation, Proc. 45th Ann. Symp. on Frequency Control, pp. 398-404, IEEE Cat. No.87CH2965-2, 1991.
26. Filler, R. L., Measurement and Analysis of Thermal Hysteresis in Resonators andTCXOs, Proc. 42nd Ann. Symp. Frequency Control, pp. 380-388, NTIS Accession No.AD-A217275, 1988.
27. Kusters, J. A., and Vig, J. R., Thermal Hysteresis in Quartz Resonators - AReview, Proc. 44th Ann. Symp. Frequency Control, pp. 165-175, IEEE Catalog No.90CH2818-3, 1990.
28. U.S. Department of Defense, Military Specification, Oscillators, Crystal, General
46
28. U.S. Department of Defense, Military Specification, Oscillators, Crystal, GeneralSpecification for, MIL-O-55310. The latest revision is available from Military Specificationsand Standards, 700 Robbins Ave., Bldg. 4D, Philadelphia, PA 19111-5094.
29. Vig, J. R., et al., Acceleration, Vibration and Shock Effects - IEEE StandardsProject Pl193, Proc. 1992 IEEE Frequency Control Symposium, IEEE Cat. No.92CH3083-3, 1992; also, Vig, J. R., et al., The Effects of Acceleration on PrecisionFrequency Sources (Proposed for IEEE Standards Project P1193), U.S. Army LaboratoryCommand Research and Development Technical Report SLCET-TR-91 -3, March 1991.Copies available from National Technical Information Service, 5285 Port Royal Road, SillsBuilding, Springfield, VA 22161; NTIS Accession No. AD-A235470.
30. Taylor, J., Effects of Crystal Reference Oscillator Phase Noise ir a VibratoryEnvironment, Technical Memorandum 2799-1011, Motorola, SOTAS EngineeringDevelopment Section, Radar Operations, August 8, 1980. The Stand-Off TargetAcquisition System (SOTAS) was a helicopter-borne coherent radar system that wasbeing developed for the U.S. Army; the program was canceled before completion. Tomeet the 90% probability of detection goal for 4 km/h targets while operating from ahelicopter, the system required a reference oscillator acceleration sensitivity of 4 x 10.12per g, which was about 100-fold beyond the state-of-the-art at the time.
31. Filler, R. L., et al., Ceramic Flatpack Enclosed AT and SC-cut Resonators, Proc.1980 IEEE Ultrasonic Symp., pp. 81 9-824, 1980.
32. Brendel, R., et al., Influence of Magnetic Field on Quartz Crystal Oscillators, Proc.43rd Ann. Symp. Frequency Control, pp. 268-274, NTIS Accession No. AD-A235629,1989.
33. King, J. C., and Koehler, D. R., Radiation Effects on Resonators. In: PrecisionFrequency Control, Vol. 2 (E. A. Gerber and A. Ballato, eds.), Academic Press, New York,pp. 147-159, 1985.
34. Suter, J. J., et al., The Effects of Ionizing and Particle Radiation on PrecisionFrequency Sources, Proc. 1992 IEEE Frequency Control Symposium, IEEE Cat. No.92CH3083-3, 1992.
35. King, J. C. and Sander, H. H., Rapid Annealing of Frequency Change in HighFrequency Crystal Resonators Following Pulsed X-irradiation at Room Temperature, Proc.27th Ann. Symp. Frequency Control, pp. 117-119, NTIS Accession No. AD-771 042, 1973.
36. Paradysz, R. E. and Smith W. L., Crystal Controlled Oscillators for RadiationEnvironments, Proc. 27th Ann. Symp. Frequency Control, pp. 120-123, NTIS AccessionNo. AD-771 042, 1973.
47
37. Martin, J. J., Electrodiffusion (Sweeping) of Ions in Quartz, IEEE Transactions onUltrasonics, Ferroelectrics, and Frequency Control, Vol. 35, No. 3, pp. 228-296, May IEEECatalog 88CH2588-2, 1988.
38. Gualtier, J. G., Sweeping Quartz Crystals, Proc. 1989 IEEE Ultrasonics Symp., pp.381-391, 1989.
39. Flanagan, T. M., Leadon, R. E., and Shannon, D. L., Evaluation of Mechanismsfor Low-Dose Frequency Shifts in Crystal Oscillators, Proc. 40th Ann. Symp. FrequencyControl, pp. 127-133, NTIS Accession No. AD-A235435, 1986.
40. Walls, F. L., The Influence of Pressure and Humidity on the Medium and Long-Term Frequency Stability of Quartz Oscillators, Proc. 42nd Ann. Symp. on FrequencyControl, pp. 279-283, NTIS Accession No. AD-A217725, 1988.
41. Walls, F. L., Environmental Sensitivities of Quartz Crystal Oscillators, Proc. 22ndAnn. Precise Time and Time Interval (PTTI) Applications and Planning Meeting, pp. 465-477, NTIS Accession No. AD-A239372, 1990.
42. Filler, et al., Specification and Measurement of the Frequency Versus TemperatureCharacteristics of Crystal Oscillators, Proc. 43rd Ann. Symp. Frequency Control, pp.253-256, NTIS Accession No. AD-A235629, 1989.
43. The graphs in Figures 34 and 35 were prepared in 1989 for a CCIR document byRichard Sydnor, Jet Propulsion Laboratories.
44. Stein, S. R. and Vig, J. R., Communications Frequency Standards, in: TheFroelich/Kent Encyclopedia of Telecommunications, Vol. 3 (Froehlich, F. E. and Kent, A.eds.), Marcel Dekker, Inc., New York, 1992, pp. 445-500. A reprint of this chapter isavailable under the title "Frequency Standards for Communications," as U. S. ArmyLaboratory Command Technical Report SLCET-TR-91-2 (Rev. 1), October 1991, NTISAccession No. AD-A24321 1.
45. Hellwig, H., Microwave Time and Frequency Standards, In: Precision FrequencyControl, Vol. 2 (E. A. Gerber and A. Ballato, eds.), Academic Press, New York, 1985,pp. 113-176.
46. Vig, J. R. and V. J. Rosati, The Rubidium-Crystal Oscillator Hybrid DevelopmentProgram, Proceedings of the 16th Annual PTTI Applications and Planning Meeting, 1984,pp. 157-165.
47. Riley, W. J. arid Vaccaro, J R., A Rubidium-Crystal Oscillator (RbXO), IEEE Trans.on Ultrasonics, Ferroelectrics and Frequency Control, Vol. UFFC-34, pp. 612-618, 1987.
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48. The Proceedings of the IEEE Frequency Control Symposium, and its predecessor,the Proceedings of the Annual Sympos;,jm on Frequency Control, have been publishedsince the tenth symposium in 1956. The latest volumes are available from the IEEE, 445Hoes Lane, Piscataway, NJ 08854. The earlier volumes are available from the NationalTechnical Information 3ervice, 5285 Port Royal Road, Sills Building, Springfield, VA22161, USA. Ordering information for all the Proceedings can be found in the back ofthe latest volumes (e.g., the Proceedings of the 45th Annual Symposium on FrequencyControl 1991 is available from the IEEE, Cat. No. 91 CH2965-2, and the Proceedings ofthe 1992 IEEE Frequency Control Symposium is Cat. No. 92CH3083-3).
49. U.S. Department of Defense, Military Standard, MIL-STD-1 88-115, Interoperabilityand Performance Standards for Communications Timing and SynchronizationSubsystems. The latest revision is available from Military Specifications and Standards,700 Robbins Avenue, Building 4D, Philadelphia, PA 19111-5094.
50. The Proceedings of the Annual Precise Time and Time Interval (PTTI) Applicationsand Planning Meeting are available from the U. S. Naval Observatory, Time ServicesDepartment, 34th and Massachusetts Ave., N.W., Washington, DC 20392-5100. Thelatest volumes are also available from the National Technical Information Service, 5285Port Royal Road, Sills Building, Springfield, VA 22161, USA.
51. The Proceedings of the European Frequency and Time Forum are available fromthe Swiss Foundation for Research in Metrology (FSRM), Rue de I'Orangerie 8, CH-2000Neuchatel, Switzerland.
52. IEEE Trans. Ultrasonics, Ferroelectrics and Frequency Control, UFFC-34,November 1987.
53. IEEE Trans. Ultrasonics, Ferroelectrics and Frequency Control, UFFC-35, May1988.
54. Kroupa, V. F. (ed.), Frequency Stability. Fundamentals and Measurement, IEEEPress, New York, 1983.
55. Sullivan, D. B., et al. (eds.), Characterization of Clocks and Oscillators, NationalInstitute of Standards and Technology Technical Note 1337, National Institute ofStandards and Technology, Boulder, CO 80303-3328.
56. Proceedings of the IEEE, Special Issue on Time and Frequency, Vol. 79, No. 7,July 1991.
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