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Slide1: 

John R. Vig Consultant. Most of this Tutorial was prepared while the author was employed by the US Army Communications-Electronics Research, Development & Engineering Center Fort Monmouth, NJ, USA J.Vig@IEEE.org Approved for public release. Distribution is unlimited Quartz Crystal Resonators and Oscillators For Frequency Control and Timing Applications - A Tutorial January 2007 Rev. 8.5.3.6

Disclaimer: 

NOTICES The citation of trade names and names of manufacturers in this report is not to be construed as official Government endorsement or consent or approval of commercial products or services referenced herein. Disclaimer

Table of Contents: 

iii Table of Contents Preface………………………………..……………………….. v 1. Applications and Requirements………………………. 1 2. Quartz Crystal Oscillators………………………………. 2 3. Quartz Crystal Resonators……………………………… 3 4. Oscillator Stability………………………………………… 4 5. Quartz Material Properties……………………………... 5 6. Atomic Frequency Standards…………………………… 6 7. Oscillator Comparison and Specification…………….. 7 8. Time and Timekeeping…………………………………. 8 9. Related Devices and Applications……………………… 9 10. FCS Proceedings Ordering, Website, and Index………….. 10

Preface Why This Tutorial?: 

“Everything should be made as simple as possible - but not simpler,” said Einstein. The main goal of this “tutorial” is to assist with presenting the most frequently encountered concepts in frequency control and timing, as simply as possible. I have often been called upon to brief visitors, management, and potential users of precision oscillators, and have also been invited to present seminars, tutorials, and review papers before university, IEEE, and other professional groups. In the beginning, I spent a great deal of time preparing these presentations. Much of the time was spent on preparing the slides. As I accumulated more and more slides, it became easier and easier to prepare successive presentations. I was frequently asked for “hard-copies” of the slides, so I started organizing, adding some text, and filling the gaps in the slide collection. As the collection grew, I began receiving favorable comments and requests for additional copies. Apparently, others, too, found this collection to be useful. Eventually, I assembled this document, the “Tutorial”. This is a work in progress. I plan to include additional material, including additional notes. Comments, corrections, and suggestions for future revisions will be welcome. John R. Vig iv Preface Why This Tutorial?

Notes and References: 

v Notes and references can be found in the “Notes” of most of the pages. To view the notes, use the “Notes Page View” icon (near the lower left corner of the screen), or select “Notes Page” in the View menu. In PowerPoint 2000 (and, presumably, later versions), the notes also appear in the “Normal view”. To print a page so that it includes the notes, select Print in the File menu, and, near the bottom, at “Print what:,” select “Notes Pages”. Many of the references are to IEEE publications which are available online in the IEEE UFFC-S digital archive, www.ieee-uffc.org/archive, or in IEEE Xplore, www.ieee.org/ieeexplore . Notes and References

In all pointed sentences [and tutorials], some degree of accuracy must be sacrificed to conciseness. Samuel Johnson: 

In all pointed sentences [and tutorials], some degree of accuracy must be sacrificed to conciseness. Samuel Johnson

CHAPTER 1Applications and Requirements: 

1 CHAPTER 1 Applications and Requirements

Electronics Applications of Quartz Crystals: 

Military & Aerospace Communications Navigation IFF Radar Sensors Guidance systems Fuzes Electronic warfare Sonobouys Research & Metrology Atomic clocks Instruments Astronomy & geodesy Space tracking Celestial navigation Industrial Communications Telecommunications Mobile/cellular/portable radio, telephone & pager Aviation Marine Navigation Instrumentation Computers Digital systems CRT displays Disk drives Modems Tagging/identification Utilities Sensors Consumer Watches & clocks Cellular & cordless phones, pagers Radio & hi-fi equipment TV & cable TV Personal computers Digital cameras Video camera/recorder CB & amateur radio Toys & games Pacemakers Other medical devices Other digital devices Automotive Engine control, stereo, clock, yaw stability control, trip computer, GPS 1-1 Electronics Applications of Quartz Crystals

Frequency Control Device Market: 

1-2 (estimates, as of ~2006) Frequency Control Device Market

Navigation: 

Navigation

Commercial Two-way Radio: 

Commercial Two-way Radio

Digital Processing of Analog Signals: 

1-5 The Effect of Timing Jitter Analog* input Analog output Digital output Digitized signal V t Time Analog signal (A) (B) (C) V(t) V(t) * e.g., from an antenna Digital Processing of Analog Signals

Digital Network Synchronization: 

Synchronization plays a critical role in digital telecommunication systems. It ensures that information transfer is performed with minimal buffer overflow or underflow events, i.e., with an acceptable level of "slips." Slips cause problems, e.g., missing lines in FAX transmission, clicks in voice transmission, loss of encryption key in secure voice transmission, and data retransmission. In AT&T's network, for example, timing is distributed down a hierarchy of nodes. A timing source-receiver relationship is established between pairs of nodes containing clocks. The clocks are of four types, in four "stratum levels." 1-6 Digital Network Synchronization

Phase Noise in PLL and PSK Systems: 

Phase Noise in PLL and PSK Systems

Utility Fault Location: 

1-8 When a fault occurs, e.g., when a "sportsman" shoots out an insulator, a disturbance propagates down the line. The location of the fault can be determined from the differences in the times of arrival at the nearest substations: x=1/2[L - c(tb-ta)] = 1/2[L - ct] where x = distance of the fault from substation A, L = A to B line length, c = speed of light, and ta and tb= time of arrival of disturbance at A and B, respectively. Fault locator error = xerror=1/2(cterror); therefore, if terror  1 microsecond, then xerror  150 meters  1/2 of high voltage tower spacings, so, the utility company can send a repair crew directly to the tower that is nearest to the fault. Insulator Sportsman X L Zap! ta tb Utility Fault Location

Space Exploration: 

1-9 (t)  Wavefront Mean wavelength   t Local Time & Frequency Standard Schematic of VLBI Technique Microwave mixer Recorder Microwave mixer Local Time & Frequency Standard Recorder Correlation and Integration Data tape Data tape Amplitude Interference Fringes Space Exploration

Military Requirements: 

1-10 Military needs are a prime driver of frequency control technology. Modern military systems require oscillators/clocks that are: Stable over a wide range of parameters (time, temperature, acceleration, radiation, etc.) Low noise Low power Small size Fast warmup Low life-cycle cost Military Requirements

Impacts of Oscillator Technology Improvements: 

1-11 Higher jamming resistance & improved ability to hide signals Improved ability to deny use of systems to unauthorized users Longer autonomy period (radio silence interval) Fast signal acquisition (net entry) Lower power for reduced battery consumption Improved spectrum utilization Improved surveillance capability (e.g., slow-moving target detection, bistatic radar) Improved missile guidance (e.g., on-board radar vs. ground radar) Improved identification-friend-or-foe (IFF) capability Improved electronic warfare capability (e.g., emitter location via TOA) Lower error rates in digital communications Improved navigation capability Improved survivability and performance in radiation environment Improved survivability and performance in high shock applications Longer life, and smaller size, weight, and cost Longer recalibration interval (lower logistics costs) Impacts of Oscillator Technology Improvements

Spread Spectrum Systems: 

Spread Spectrum Systems

Clock for Very Fast Frequency Hopping Radio: 

1-13 Example Let R1 to R2 = 1 km, R1 to J =5 km, and J to R2 = 5 km. Then, since propagation delay =3.3 s/km, t1 = t2 = 16.5 s, tR = 3.3 s, and tm < 30 s. Allowed clock error  0.2 tm  6 s. For a 4 hour resynch interval, clock accuracy requirement is: 4 X 10-10 To defeat a “perfect” follower jammer, one needs a hop-rate given by: tm < (t1 + t2) - tR where tm  message duration/hop  1/hop-rate Jammer J Radio R1 Radio R2 t1 t2 tR Clock for Very Fast Frequency Hopping Radio

Clocks and Frequency Hopping C3 Systems: 

1-14 Slow hopping ‹-------------------------------›Good clock Fast hopping ‹------------------------------› Better clock Extended radio silence ‹-----------------› Better clock Extended calibration interval ‹----------› Better clock Othogonality ‹-------------------------------› Better clock Interoperability ‹----------------------------› Better clock Clocks and Frequency Hopping C3 Systems

Identification-Friend-Or-Foe (IFF): 

1-15 F-16 AWACS FAAD PATRIOT STINGER FRIEND OR FOE? Air Defense IFF Applications Identification-Friend-Or-Foe (IFF)

Effect of Noise in Doppler Radar System: 

1-16 Echo = Doppler-shifted echo from moving target + large "clutter" signal (Echo signal) - (reference signal) --› Doppler shifted signal from target Phase noise of the local oscillator modulates (decorrelates) the clutter signal, generates higher frequency clutter components, and thereby degrades the radar's ability to separate the target signal from the clutter signal. Transmitter fD Receiver Stationary Object Moving Object f fD Doppler Signal Decorrelated Clutter Noise A Effect of Noise in Doppler Radar System

Bistatic Radar: 

1-17 Conventional (i.e., "monostatic") radar, in which the illuminator and receiver are on the same platform, is vulnerable to a variety of countermeasures. Bistatic radar, in which the illuminator and receiver are widely separated, can greatly reduce the vulnerability to countermeasures such as jamming and antiradiation weapons, and can increase slow moving target detection and identification capability via "clutter tuning” (receiver maneuvers so that its motion compensates for the motion of the illuminator; creates zero Doppler shift for the area being searched). The transmitter can remain far from the battle area, in a "sanctuary." The receiver can remain "quiet.” The timing and phase coherence problems can be orders of magnitude more severe in bistatic than in monostatic radar, especially when the platforms are moving. The reference oscillators must remain synchronized and syntonized during a mission so that the receiver knows when the transmitter emits each pulse, and the phase variations will be small enough to allow a satisfactory image to be formed. Low noise crystal oscillators are required for short term stability; atomic frequency standards are often required for long term stability. Receiver Illuminator Target Bistatic Radar

Doppler Shifts: 

1-18 Doppler Shift for Target Moving Toward Fixed Radar (Hz) 5 0 10 15 20 25 30 40 10 100 1K 10K 100K 1M Radar Frequency (GHz) 4km/h - Man or Slow Moving Vechile 100km/h - Vehicle, Ground or Air 700km/h - Subsonic Aircraft 2,400 km/h - Mach 2 Aircraft X-Band RADAR Doppler Shifts

CHAPTER 2Quartz Crystal Oscillators: 

3 CHAPTER 2 Quartz Crystal Oscillators

Crystal Oscillator: 

Tuning Voltage Crystal resonator Amplifier Output Frequency 2-1 Crystal Oscillator

Oscillation: 

2-2 At the frequency of oscillation, the closed loop phase shift = 2n. When initially energized, the only signal in the circuit is noise. That component of noise, the frequency of which satisfies the phase condition for oscillation, is propagated around the loop with increasing amplitude. The rate of increase depends on the excess; i.e., small-signal, loop gain and on the BW of the crystal in the network. The amplitude continues to increase until the amplifier gain is reduced either by nonlinearities of the active elements ("self limiting") or by some automatic level control. At steady state, the closed-loop gain = 1. Oscillation

Oscillation and Stability: 

Oscillation and Stability

Tunability and Stability: 

Tunability and Stability

Oscillator Acronyms: 

2-5 Most Commonly Used: XO…………..Crystal Oscillator VCXO………Voltage Controlled Crystal Oscillator OCXO………Oven Controlled Crystal Oscillator TCXO………Temperature Compensated Crystal Oscillator Others: TCVCXO..…Temperature Compensated/Voltage Controlled Crystal Oscillator OCVCXO.….Oven Controlled/Voltage Controlled Crystal Oscillator MCXO………Microcomputer Compensated Crystal Oscillator RbXO……….Rubidium-Crystal Oscillator Oscillator Acronyms

Crystal Oscillator Categories: 

2-6 The three categories, based on the method of dealing with the crystal unit's frequency vs. temperature (f vs. T) characteristic, are: XO, crystal oscillator, does not contain means for reducing the crystal's f vs. T characteristic (also called PXO-packaged crystal oscillator). TCXO, temperature compensated crystal oscillator, in which, e.g., the output signal from a temperature sensor (e.g., a thermistor) is used to generate a correction voltage that is applied to a variable reactance (e.g., a varactor) in the crystal network. The reactance variations compensate for the crystal's f vs. T characteristic. Analog TCXO's can provide about a 20X improvement over the crystal's f vs. T variation. OCXO, oven controlled crystal oscillator, in which the crystal and other temperature sensitive components are in a stable oven which is adjusted to the temperature where the crystal's f vs. T has zero slope. OCXO's can provide a >1000X improvement over the crystal's f vs. T variation. Crystal Oscillator Categories

Crystal Oscillator Categories: 

2-7 Temperature Sensor Compensation Network or Computer XO  Temperature Compensated (TCXO) -450C +1 ppm -1 ppm Oven control XO Temperature Sensor Oven  Oven Controlled (OCXO) Voltage Tune Output  Crystal Oscillator (XO) -450C -10 ppm +10 ppm 250C T +1000C Crystal Oscillator Categories

Hierarchy of Oscillators: 

2-8 Oscillator Type* Crystal oscillator (XO) Temperature compensated crystal oscillator (TCXO) Microcomputer compensated crystal oscillator (MCXO) Oven controlled crystal oscillator (OCXO) Small atomic frequency standard (Rb, RbXO) High performance atomic standard (Cs) Typical Applications Computer timing Frequency control in tactical radios Spread spectrum system clock Navigation system clock & frequency standard, MTI radar C3 satellite terminals, bistatic, & multistatic radar Strategic C3, EW Accuracy** 10-5 to 10-4 10-6 10-8 to 10-7 10-8 (with 10-10 per g option) 10-9 10-12 to 10-11 * Sizes range from <5cm3 for clock oscillators to > 30 liters for Cs standards Costs range from <$5 for clock oscillators to > $50,000 for Cs standards. ** Including environmental effects (e.g., -40oC to +75oC) and one year of aging. Hierarchy of Oscillators

Oscillator Circuit Types: 

2-9 Of the numerous oscillator circuit types, three of the more common ones, the Pierce, the Colpitts and the Clapp, consist of the same circuit except that the rf ground points are at different locations. The Butler and modified Butler are also similar to each other; in each, the emitter current is the crystal current. The gate oscillator is a Pierce-type that uses a logic gate plus a resistor in place of the transistor in the Pierce oscillator. (Some gate oscillators use more than one gate). Pierce Colpitts Clapp Gate Modified Butler Butler b c  b c  b c  b c  b c  Oscillator Circuit Types

OCXO Block Diagram: 

 Output Oven 2-10 Each of the three main parts of an OCXO, i.e., the crystal, the sustaining circuit, and the oven, contribute to instabilities. The various instabilities are discussed in the rest of chapter 3 and in chapter 4. OCXO Block Diagram

Oscillator Instabilities - General Expression: 

2-11 where QL = loaded Q of the resonator, and d(ff) is a small change in loop phase at offset frequency ff away from carrier frequency f. Systematic phase changes and phase noise within the loop can originate in either the resonator or the sustaining circuits. Maximizing QL helps to reduce the effects of noise and environmentally induced changes in the sustaining electronics. In a properly designed oscillator, the short-term instabilities are determined by the resonator at offset frequencies smaller than the resonator’s half-bandwidth, and by the sustaining circuit and the amount of power delivered from the loop for larger offsets. Oscillator Instabilities - General Expression

Instabilities due to Sustaining Circuit: 

2-12 Load reactance change - adding a load capacitance to a crystal changes the frequency by Example: If C0 = 5 pF, C1 = 14fF and CL = 20pF, then a CL = 10 fF (= 5 X 10-4) causes 1 X 10-7 frequency change, and a CL aging of 10 ppm per day causes 2 X 10-9 per day of oscillator aging. Drive level changes: Typically 10-8 per ma2 for a 10 MHz 3rd SC-cut. DC bias on the crystal also contributes to oscillator aging. Instabilities due to Sustaining Circuit

Oscillator Instabilities - Tuned Circuits: 

2-13 Many oscillators contain tuned circuits - to suppress unwanted modes, as matching circuits, and as filters. The effects of small changes in the tuned circuit's inductance and capacitance is given by: where BW is the bandwidth of the filter, ff is the frequency offset of the center frequency of the filter from the carrier frequency, QL is the loaded Q of the resonator, and Qc, Lc and Cc are the tuned circuit's Q, inductance and capacitance, respectively. Oscillator Instabilities - Tuned Circuits

Oscillator Instabilities - Circuit Noise: 

2-14 Flicker PM noise in the sustaining circuit causes flicker FM contribution to the oscillator output frequency given by: where ff is the frequency offset from the carrier frequency f, QLis the loaded Q of the resonator in the circuit, Lckt (1Hz) is the flicker PM noise at ff = 1Hz, and  is any measurement time in the flicker floor range. For QL = 106 and Lckt (1Hz) = -140dBc/Hz, y() = 8.3 x 10-14. ( Lckt (1Hz) = -155dBc/Hz has been achieved.) Oscillator Instabilities - Circuit Noise

Oscillator Instabilities - External Load: 

2-15 If the external load changes, there is a change in the amplitude or phase of the signal reflected back into the oscillator. The portion of that signal which reaches the oscillating loop changes the oscillation phase, and hence the frequency by where  is the VSWR of the load, and  is the phase angle of the reflected wave; e.g., if Q ~ 106, and isolation ~40 dB (i.e., ~10-4), then the worst case (100% reflection) pulling is ~5 x 10-9. A VSWR of 2 reduces the maximum pulling by only a factor of 3. The problem of load pulling becomes worse at higher frequencies, because both the Q and the isolation are lower. Oscillator Instabilities - External Load

Oscillator Outputs: 

2-16 Most users require a sine wave, a TTL-compatible, a CMOS-compatible, or an ECL-compatible output. The latter three can be simply generated from a sine wave. The four output types are illustrated below, with the dashed lines representing the supply voltage inputs, and the bold solid lines, the outputs. (There is no “standard” input voltage for sine wave oscillators. The input voltages for CMOS typically range from 1V to 10V.) +15V +10V +5V 0V -5V Sine TTL CMOS ECL Oscillator Outputs

Silicon Resonator & Oscillator: 

Silicon Resonator & Oscillator Resonator (Si): 0.2 x 0.2 x 0.01 mm3 5 MHz; f vs. T: -30 ppm/oC Oscillator (CMOS): 2.0 x 2.5 x 0.85 mm3 www.SiTime.com ±50 ppm, ±100 ppm; -45 to +85 oC (±5 ppm demoed, w. careful calibration) 1 to 125 MHz <2 ppm/y aging; <2 ppm hysteresis ±200 ps peak-to-peak jitter, 20-125 MHz 2-17

Resonator Self-Temperature Sensing: 

172300 171300 170300 -35 -15 5 25 45 65 85 Temperature (oC) f (Hz) f  3f1 - f3 2-18 Resonator Self-Temperature Sensing

Thermometric Beat Frequency Generation: 

LOW PASS FILTER X3 MULTIPLIER M=1 M=3 f1 f3 DUAL MODE OSCILLATOR f = 3f1 - f3 2-19 Mixer Thermometric Beat Frequency Generation

Microcomputer Compensated Crystal Oscillator(MCXO): 

2-20 Dual-mode XO x3 Reciprocal Counter com-puter Correction Circuit N1 N2 f1 f 3 f f0 Mixer Microcomputer Compensated Crystal Oscillator (MCXO)

MCXO Frequency Summing Method: 

CRYSTAL 3rd OVERTONE DUAL-MODE OSCILLATOR FUNDAMENTAL MODE Divide by 3 COUNTER Clock N1 out NON-VOLATILE MEMORY MICRO- COMPUTER DIRECT DIGITAL SYNTHESIZER Divide by 4000 Divide by 2500 PHASE- LOCKED LOOP VCXO 10 MHz output F F T 1 PPS output T = Timing Mode F = Frequency Mode f3 = 10 MHz - fd f1 Mixer fb N2 Clock Clock T fd Block Diagram 2-21 MCXO Frequency Summing Method

MCXO - Pulse Deletion Method: 

SC-cut crystal Digital circuitry (ASIC) Microprocessor circuitry f output fc output f0 corrected output for timing MCXO - Pulse Deletion Method

MCXO - TCXO Resonator Comparison: 

MCXO - TCXO Resonator Comparison

Opto-Electronic Oscillator (OEO): 

2-24 Optical fiber Bias Optical out "Pump Laser" Optical Fiber Photodetector RF Amplifier Filter RF driving port Electrical injection RF coupler Electrical output Optical Injection Optical coupler Piezoelectric fiber stretcher Opto-Electronic Oscillator (OEO)

CHAPTER 3Quartz Crystal Resonators: 

3 CHAPTER 3 Quartz Crystal Resonators

Why Quartz?: 

Why Quartz?

The Piezoelectric Effect: 

3-2 The piezoelectric effect provides a coupling between the mechanical properties of a piezoelectric crystal and an electrical circuit. Undeformed lattice X + + + + + + + + + + + + + + + + + + + + + _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Strained lattice + + + + + + + + + + + + + + + + + + + + + _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ X   - + Y Y _ _ The Piezoelectric Effect

The Piezoelectric Effect in Quartz: 

X Y Z The Piezoelectric Effect in Quartz

Modes of Motion(Click on the mode names to see animation.): 

3-4 Flexure Mode Extensional Mode Face Shear Mode Thickness Shear Mode Fundamental Mode Thickness Shear Third Overtone Thickness Shear Modes of Motion (Click on the mode names to see animation.)

Motion Of A Thickness Shear Crystal: 

Motion Of A Thickness Shear Crystal CLICK ON FIGURE TO START MOTION

Resonator Vibration Amplitude Distribution: 

Metallic electrodes Resonator plate substrate (the “blank”) u Conventional resonator geometry and amplitude distribution, u Resonator Vibration Amplitude Distribution

Resonant Vibrations of a Quartz Plate: 

3-6 X-ray topographs (21•0 plane) of various modes excited during a frequency scan of a fundamental mode, circular, AT-cut resonator. The first peak, at 3.2 MHz, is the main mode; all others are unwanted modes. Dark areas correspond to high amplitudes of displacement. Resonant Vibrations of a Quartz Plate

Overtone Response of a Quartz Crystal: 

0 jX -jX Reactance Fundamental mode 3rd overtone 5th overtone Frequency Spurious responses Spurious responses 3-7 Spurious responses Overtone Response of a Quartz Crystal

Unwanted Modes vs. Temperature: 

Unwanted Modes vs. Temperature

Mathematical Description of a Quartz Resonator: 

3-9 In piezoelectric materials, electrical current and voltage are coupled to elastic displacement and stress: {T} = [c] {S} - [e] {E} {D} = [e] {S} + [] {E} where {T} = stress tensor, [c] = elastic stiffness matrix, {S} = strain tensor, [e] = piezoelectric matrix {E} = electric field vector, {D} = electric displacement vector, and [] = is the dielectric matrix For a linear piezoelectric material c11 c12 c13 c14 c15 c16 e11 e21 e31 c21 c22 c23 c24 c25 c26 e12 e22 e32 c31 c32 c33 c34 c35 c36 e13 e23 e33 c41 c42 c43 c44 c45 c46 e14 e24 e34 c51 c52 c53 c54 c55 c56 e15 e25 e35 c61 c62 c63 c64 c65 c66 e16 e26 e36 e11 e12 e13 e14 e15 e16 11 12 13 e21 e22 e23 e24 e25 e26 21 22 23 e31 e32 e33 e34 e35 e36 31 32 33 T1 T2 T3 T4 T5 T6 D1 D2 D3 = where T1 = T11 S1 = S11 T2 = T22 S2 = S22 T3 = T33 S3 = S33 T4 = T23 S4 = 2S23 T5 = T13 S5 = 2S13 T6 = T12 S6 = 2S12 S1 S2 S3 S4 S5 S6 E1 E2 E3 Elasto-electric matrix for quartz S1 S2 S3 S4 S5 S6 -E1 -E2 -E3 et T1 T2 T3 T4 T5 T6 D1 D2 D3 e X S LINES JOIN NUMERICAL EQUALITIES EXCEPT FOR COMPLETE RECIPROCITY ACROSS PRINCIPAL DIAGONAL INDICATES NEGATIVE OF INDICATES TWICE THE NUMERICAL EQUALITIES INDICATES 1/2 (c11 - c12) X  Mathematical Description of a Quartz Resonator

Mathematical Description - Continued: 

3-10 Number of independent non-zero constants depend on crystal symmetry. For quartz (trigonal, class 32), there are 10 independent linear constants - 6 elastic, 2 piezoelectric and 2 dielectric. "Constants” depend on temperature, stress, coordinate system, etc. To describe the behavior of a resonator, the differential equations for Newton's law of motion for a continuum, and for Maxwell's equation* must be solved, with the proper electrical and mechanical boundary conditions at the plate surfaces. Equations are very "messy" - they have never been solved in closed form for physically realizable three- dimensional resonators. Nearly all theoretical work has used approximations. Some of the most important resonator phenomena (e.g., acceleration sensitivity) are due to nonlinear effects. Quartz has numerous higher order constants, e.g., 14 third-order and 23 fourth-order elastic constants, as well as 16 third-order piezoelectric coefficients are known; nonlinear equations are extremely messy. * Magnetic field effects are generally negligible; quartz is diamagnetic, however, magnetic fields can affect the mounting structure and electrodes. Mathematical Description - Continued

Infinite Plate Thickness Shear Resonator: 

3-11 Where fn = resonant frequency of n-th harmonic h = plate thickness  = density cij = elastic modulus associated with the elastic wave being propagated where Tf is the linear temperature coefficient of frequency. The temperature coefficient of cij is negative for most materials (i.e., “springs” become “softer” as T increases). The coefficients for quartz can be +, - or zero (see next page). Infinite Plate Thickness Shear Resonator

Quartz is Highly Anisotropic: 

Quartz is Highly Anisotropic

Zero Temperature Coefficient Quartz Cuts: 

90o 60o 30o 0 -30o -60o -90o 0o 10o 20o 30o AT FC IT LC SC SBTC BT   Singly Rotated Cut Doubly Rotated Cut Zero Temperature Coefficient Quartz Cuts

Comparison of SC and AT-cuts: 

3-14 Advantages of the SC-cut Thermal transient compensated (allows faster warmup OCXO) Static and dynamic f vs. T allow higher stability OCXO and MCXO Better f vs. T repeatability allows higher stability OCXO and MCXO Far fewer activity dips Lower drive level sensitivity Planar stress compensated; lower f due to edge forces and bending Lower sensitivity to radiation Higher capacitance ratio (less f for oscillator reactance changes) Higher Q for fundamental mode resonators of similar geometry Less sensitive to plate geometry - can use wide range of contours Disadvantage of the SC-cut : More difficult to manufacture for OCXO (but is easier to manufacture for MCXO than is an AT-cut for precision TCXO) Other Significant Differences B-mode is excited in the SC-cut, although not necessarily in LFR's The SC-cut is sensitive to electric fields (which can be used for compensation) Comparison of SC and AT-cuts

Mode Spectrograph of an SC-cut: 

Attenuation Normalized Frequency (referenced to the fundamental c-mode) 0 -20 -10 -30 -40 0 1 2 3 4 5 6 1.10 c(1) b(1) a(1) c(3) b(3) c(5) b(5) a(3) 3-15 a-mode: quasi-longitudinal mode b-mode: fast quasi-shear mode c-mode: slow quasi-shear mode Mode Spectrograph of an SC-cut

SC- cut f vs. T for b-mode and c-mode: 

400 200 0 -200 -400 -600 -800 -1000 -1200 0 10 20 30 40 50 60 70 b-Mode (Fast Shear) -25.5 ppm/oC c-Mode (Slow Shear) Temperature (OC) FREQUENCY DEVIATION (PPM) 3-16 SC- cut f vs. T for b-mode and c-mode

B and C Modes Of A Thickness Shear Crystal: 

B and C Modes Of A Thickness Shear Crystal C MODE B MODE CLICK ON FIGURES TO START MOTION 3-17

Singly Rotated and Doubly Rotated Cuts’Vibrational Displacements: 

Singly Rotated Cut Doubly Rotated Cut X X’ Y q q j Z 3-18 Singly Rotated and Doubly Rotated Cuts’ Vibrational Displacements Singly rotated resonator Doubly rotated resonator

Resistance vs. Electrode Thickness: 

RS (Ohms) -Df (kHz) [fundamental mode] 0 20 40 60 100 1000 10 AT-cut; f1=12 MHz; polished surfaces; evaporated 1.2 cm (0.490”) diameter silver electrodes 5th 3rd Fundamental 3-19 Resistance vs. Electrode Thickness

Resonator Packaging: 

3-20 Base Mounting clips Bonding area Electrodes Quartz blank Cover Seal Pins Quartz blank Bonding area Cover Mounting clips Seal Base Pins Two-point Mount Package Three- and Four-point Mount Package Top view of cover Resonator Packaging

Equivalent Circuits: 

C L R Spring Mass Dashpot Equivalent Circuits

Equivalent Circuit of a Resonator: 

3-22 { 1. Voltage control (VCXO) 2. Temperature compensation (TCXO) Symbol for crystal unit CL C1 L1 R1 C0 CL Equivalent Circuit of a Resonator

Crystal Oscillator f vs. T Compensation: 

3-23 Compensated frequency of TCXO Compensating voltage on varactor CL Frequency / Voltage Uncompensated frequency T Crystal Oscillator f vs. T Compensation

Resonator Reactance vs. Frequency: 

3-24 0 + - Reactance Area of usual operation in an oscillator Antiresonance, fa Frequency Resonance, fr Resonator Reactance vs. Frequency

Equivalent Circuit Parameter Relationships: 

3-25 n: Overtone number C0: Static capacitance C1: Motional capacitance C1n: C1 of n-th overtone L1: Motional inductance L1n: L1 of n-th overtone R1: Motional resistance R1n: R1 of n-th overtone : Dielectric permittivity of quartz 40 pF/m (average) A: Electrode area t: Plate thickness r: Capacitance ratio r’: fn/f1 fs: Series resonance frequency fR fa: Antiresonance frequency Q; Quality factor 1: Motional time constant : Angular frequency = 2f : Phase angle of the impedance k; Piezoelectric coupling factor =8.8% for AT-cut, 4.99% for SC Equivalent Circuit Parameter Relationships

What is Q and Why is it Important?: 

3-26 Q is proportional to the decay-time, and is inversely proportional to the linewidth of resonance (see next page). The higher the Q, the higher the frequency stability and accuracy capability of a resonator (i.e., high Q is a necessary but not a sufficient condition). If, e.g., Q = 106, then 10-10 accuracy requires ability to determine center of resonance curve to 0.01% of the linewidth, and stability (for some averaging time) of 10-12 requires ability to stay near peak of resonance curve to 10-6 of linewidth. Phase noise close to the carrier has an especially strong dependence on Q (L(f)  1/Q4 for quartz oscillators). What is Q and Why is it Important?

Decay Time, Linewidth, and Q: 

3-27 Oscillation Exciting pulse ends TIME Decaying oscillation of a resonator td Max. intensity BW Maximum intensity FREQUENCY Resonance behavior of a resonator ½ Maximum intensity Decay Time, Linewidth, and Q

Factors that Determine Resonator Q: 

Factors that Determine Resonator Q

Resonator Fabrication Steps: 

3-29 SEAL BAKE PLATE FINAL CLEAN FREQUENCY ADJUST CLEAN INSPECT BOND MOUNT PREPARE ENCLOSURE DEPOSIT CONTACTS ORIENT IN MASK CLEAN ETCH (CHEMICAL POLISH) CONTOUR ANGLE CORRECT X-RAY ORIENT ROUND LAP CUT SWEEP GROW QUARTZ DESIGN RESONATORS TEST OSCILLATOR Resonator Fabrication Steps

X-ray Orientation of Crystal Plates: 

3-30 S Copper target X-ray source Shielding Monochromator crystal Detector Crystal under test Double-crystal x-ray diffraction system Goniometer X-ray beam X-ray Orientation of Crystal Plates

Contamination Control: 

3-31 Contamination control is essential during the fabrication of resonators because contamination can adversely affect: Stability (see chapter 4) - aging - hysteresis - retrace - noise - nonlinearities and resistance anomalies (high starting resistance, second-level of drive, intermodulation in filters) - frequency jumps? Manufacturing yields Reliability Contamination Control

Crystal Enclosure Contamination: 

The enclosure and sealing process can have important influences on resonator stability. A monolayer of adsorbed contamination contains ~ 1015 molecules/cm2 (on a smooth surface) An enclosure at 10-7 torr contains ~109 gaseous molecules/cm3 Therefore: In a 1 cm3 enclosure that has a monolayer of contamination on its inside surfaces, there are ~106 times more adsorbed molecules than gaseous molecules when the enclosure is sealed at 10-7 torr. The desorption and adsorption of such adsorbed molecules leads to aging, hysteresis, retrace, noise, etc. 3-32 Crystal Enclosure Contamination

What is an “f-squared”?: 

What is an “f-squared”?

Milestones in Quartz Technology: 

Milestones in Quartz Technology

Quartz Resonators for Wristwatches: 

3-35 Requirements: Small size Low power dissipation (including the oscillator) Low cost High stability (temperature, aging, shock, attitude) These requirements can be met with 32,768 Hz quartz tuning forks Quartz Resonators for Wristwatches

Why 32,768 Hz?: 

Why 32,768 Hz?

Quartz Tuning Fork: 

3-37 Z Y X Y’ 0~50 Y Z X base arm a) natural faces and crystallographic axes of quartz b) crystallographic orientation of tuning fork c) vibration mode of tuning fork Quartz Tuning Fork

Watch Crystal: 

3-38 Watch Crystal

Lateral Field Resonator: 

3-39 In lateral field resonators (LFR): 1. the electrodes are absent from the regions of greatest motion, and 2. varying the orientation of the gap between the electrodes varies certain important resonator properties. LFRs can also be made with electrodes on only one major face. Advantages of LFR are: Ability to eliminate undesired modes, e.g., the b-mode in SC-cuts Potentially higher Q (less damping due to electrodes and mode traps) Potentially higher stability (less electrode and mode trap effects, smaller C1) Lateral Field Thickness Field Lateral Field Resonator

Electrodeless (BVA) Resonator: 

C D1 D2 Side view of BVA2 resonator construction Side and top views of center plate C C Quartz bridge Electrodeless (BVA) Resonator

CHAPTER 4Oscillator Stability: 

4 CHAPTER 4 Oscillator Stability

The Units of Stability in Perspective: 

4-1 What is one part in 1010 ? (As in 1 x 10-10/day aging.) ~1/2 cm out of the circumference of the earth. ~1/4 second per human lifetime (of ~80 years). Power received on earth from a GPS satellite, -160 dBW, is as “bright” as a flashlight in Los Angeles would look in New York City, ~5000 km away (neglecting earth’s curvature). What is -170 dB? (As in -170 dBc/Hz phase noise.) -170 dB = 1 part in 1017  thickness of a sheet of paper out of the total distance traveled by all the cars in the world in a day. The Units of Stability in Perspective

Accuracy, Precision, and Stability: 

4-2 Precise but not accurate Not accurate and not precise Accurate but not precise Accurate and precise Time Time Time Time Stable but not accurate Not stable and not accurate Accurate (on the average) but not stable Stable and accurate 0 f f f f Accuracy, Precision, and Stability

Influences on Oscillator Frequency: 

Influences on Oscillator Frequency

Idealized Frequency-Time-Influence Behavior: 

4-4 3 2 1 0 -1 -2 -3 t0 t1 t2 t3 t4 Temperature Step Vibration Shock Oscillator Turn Off & Turn On 2-g Tipover Radiation Time t5 t6 t7 t8 Aging Off On Short-Term Instability Idealized Frequency-Time-Influence Behavior

Aging and Short-Term Stability: 

4-5 5 10 15 20 25 Time (days) Short-term instability (Noise) f/f (ppm) 30 25 20 15 10 Aging and Short-Term Stability

Aging Mechanisms: 

4-6  Mass transfer due to contamination Since f  1/t, f/f = -t/t; e.g., f5MHz Fund  106 molecular layers, therefore, 1 quartz-equivalent monolayer  f/f  1 ppm  Stress relief in the resonator's: mounting and bonding structure, electrodes, and in the quartz (?)  Other effects  Quartz outgassing  Diffusion effects  Chemical reaction effects  Pressure changes in resonator enclosure (leaks and outgassing)  Oscillator circuit aging (load reactance and drive level changes)  Electric field changes (doubly rotated crystals only)  Oven-control circuitry aging Aging Mechanisms

Typical Aging Behaviors: 

4-7 f/f A(t) = 5 ln(0.5t+1) Time A(t) +B(t) B(t) = -35 ln(0.006t+1) Typical Aging Behaviors

Stresses on a Quartz Resonator Plate: 

4-8 Causes: Thermal expansion coefficient differences Bonding materials changing dimensions upon solidifying/curing Residual stresses due to clip forming and welding operations, sealing Intrinsic stresses in electrodes Nonuniform growth, impurities & other defects during quartz growing Surface damage due to cutting, lapping and (mechanical) polishing Effects: In-plane diametric forces Tangential (torsional) forces, especially in 3 and 4-point mounts Bending (flexural) forces, e.g., due to clip misalignment and electrode stresses Localized stresses in the quartz lattice due to dislocations, inclusions, other impurities, and surface damage Stresses on a Quartz Resonator Plate

Thermal Expansion Coefficients of Quartz: 

4-9 XXl ZZl 13.71 11.63 9.56 00 100 200 300 400 500 600 700 800 900 14 13 12 11 10 9 Radial Tangential  (Thickness) = 11.64 Orientation, , With Respect To XXl Thermal Expansion Coefficient, , of AT-cut Quartz, 10-6/0K Thermal Expansion Coefficients of Quartz

Force-Frequency Coefficient: 

* 10-15 m  s / N AT-cut quartz Z’ F X’ F 30 25 20 15 10 5 0 -5 -10 -15 00 100 200 300 400 500 600 700 800 900  Kf ()  Force-Frequency Coefficient

Strains Due To Mounting Clips: 

4-11 X-ray topograph of an AT-cut, two-point mounted resonator. The topograph shows the lattice deformation due to the stresses caused by the mounting clips. Strains Due To Mounting Clips

Strains Due To Bonding Cements: 

4-12 X-ray topographs showing lattice distortions caused by bonding cements; (a) Bakelite cement - expanded upon curing, (b) DuPont 5504 cement - shrank upon curing (a) (b) Strains Due To Bonding Cements

Mounting Force Induced Frequency Change: 

4-13 The force-frequency coefficient, KF (), is defined by Maximum KF (AT-cut) = 24.5 x 10-15 m-s/N at  = 0o Maximum KF (SC-cut) = 14.7 x 10-15 m-s/N at  = 44o As an example, consider a 5 MHz 3rd overtone, 14 mm diameter resonator. Assuming the presence of diametrical forces only, (1 gram = 9.81 x 10-3 newtons), 2.9 x 10-8 per gram for an AT-cut resonator 1.7 x 10-8 per gram for an SC-cut resonator 0 at  = 61o for an AT-cut resonator, and at  = 82o for an SC-cut. { F F X’ Z’  Mounting Force Induced Frequency Change

Bonding Strains Induced Frequency Changes: 

4-14 When 22 MHz fundamental mode AT-cut resonators were reprocessed so as to vary the bonding orientations, the frequency vs. temperature characteristics of the resonators changed as if the angles of cut had been changed. The resonator blanks were 6.4 mm in diameter plano-plano, and were bonded to low-stress mounting clips by nickel electrobonding. Bonding orientation,  Apparent angle shift (minutes)  Blank No. 7 Blank No. 8 Z’ X’ 6’ 5’ 4’ 3’ 2’ 1’ 0’ -1’ -2’ 300 600 900  Bonding Strains Induced Frequency Changes

Bending Force vs. Frequency Change: 

AT-cut resonator SC-cut resonator 4-15 5gf fo = 10Mz fo = 10Mz 5gf Frequency Change (Hz) Frequency Change (Hz) 30 20 10 0 240 120 180 60 300 360 240 120 180 60 300 360 +10 -10 Azimuth angle  (degrees) Azimuth angle  (degrees) Frequency change for symmetrical bending, SC-cut crystal. Frequency change for symmetrical bending, AT-cut crystal. • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Bending Force vs. Frequency Change

Short Term Instability (Noise): 

4-16 Stable Frequency (Ideal Oscillator) Unstable Frequency (Real Oscillator) Time (t) Time (t) V 1 -1 1 -1 V(t) = V0 sin(20t) V(t) =[V0 + (t)] sin[20t + (t)] (t) = 20t (t) = 20t + (t) V(t) = Oscillator output voltage, V0 = Nominal peak voltage amplitude (t) = Amplitude noise, 0 = Nominal (or "carrier") frequency (t) = Instantaneous phase, and (t) = Deviation of phase from nominal (i.e., the ideal) V Short Term Instability (Noise)

Instantaneous Output Voltage of an Oscillator: 

4-17 Amplitude instability Frequency instability Phase instability - Voltage + 0 Time Instantaneous Output Voltage of an Oscillator

Impacts of Oscillator Noise: 

Limits the ability to determine the current state and the predictability of oscillators Limits syntonization and synchronization accuracy Limits receivers' useful dynamic range, channel spacing, and selectivity; can limit jamming resistance Limits radar performance (especially Doppler radar's) Causes timing errors [~y( )] Causes bit errors in digital communication systems Limits number of communication system users, as noise from transmitters interfere with receivers in nearby channels Limits navigation accuracy Limits ability to lock to narrow-linewidth resonances Can cause loss of lock; can limit acquisition/reacquisition capability in phase-locked-loop systems 4-18 Impacts of Oscillator Noise

Time Domain - Frequency Domain: 

4-19 (b) A(t) A(f) (c) Amplitude - Time Amplitude - Frequency t A (a) f Time Domain - Frequency Domain

Causes of Short Term Instabilities: 

Causes of Short Term Instabilities

Short-Term Stability Measures: 

Short-Term Stability Measures

Allan Deviation: 

4-22 Also called two-sample deviation, or square-root of the "Allan variance," it is the standard method of describing the short term stability of oscillators in the time domain. It is denoted by y(), where The fractional frequencies, are measured over a time interval, ; (yk+1 - yk) are the differences between pairs of successive measurements of y, and, ideally, < > denotes a time average of an infinite number of (yk+1 - yk)2. A good estimate can be obtained by a limited number, m, of measurements (m100). y() generally denotes i.e., Allan Deviation

Why y()?: 

4-23  Classical variance: diverges for some commonly observed noise processes, such as random walk, i.e., the variance increases with increasing number of data points.  Allan variance: • Converges for all noise processes observed in precision oscillators. • Has straightforward relationship to power law spectral density types. • Is easy to compute. • Is faster and more accurate in estimating noise processes than the Fast Fourier Transform. Why y()?

Frequency Noise and y(): 

4-24 0.1 s averaging time 100 s 1.0 s averaging time 3 X 10-11 0 -3 X 10-11 100 s 0.01 0.1 1 10 100 Averaging time, , s 10-10 10-11 10-12 y() Frequency Noise and y()

Time Domain Stability: 

4-25 *For y() to be a proper measure of random frequency fluctuations, aging must be properly subtracted from the data at long ’s. y() Frequency noise Aging* and random walk of frequency Short-term stability Long-term stability 1 s 1 m 1 h Sample time  Time Domain Stability

Power Law Dependence of y(): 

y() -1 -1 0 Noise type: White phase Flicker phase White freq. Flicker freq. Random walk freq. -1/2 1/2 to 1 Power Law Dependence of y()

Pictures of Noise: 

4-27 Plots show fluctuations of a quantity z(t), which can be,e.g., the output of a counter (f vs. t) or of a phase detector ([t] vs. t). The plots show simulated time-domain behaviors corresponding to the most common (power-law) spectral densities; h is an amplitude coefficient. Note: since Sf = f 2S, e.g. white frequency noise and random walk of phase are equivalent. Sz(f) = hf  = 0  = -1  = -2  = -3 Noise name White Flicker Random walk Plot of z(t) vs. t Pictures of Noise

Spectral Densities: 

Spectral Densities

Mixer Functions: 

4-29 V0 Filter V1V2 Trigonometric identities: sin(x)sin(y) = ½cos(x-y) - ½cos(x+y) cos(x/2) = sin(x) Phase detector: AM detector: Frequency multiplier: When V1 = V2 and the filter is bandpass at 21 Mixer Functions

Phase Detector: 

~ ~ fO V(t) VR(t)  = 900 VO(t) LPF * Or phase-locked loop V(t) Low-Noise Amplifier Spectrum Analyzer S(f) Reference DUT 4-30 Phase Detector

Phase Noise Measurement: 

4-31 RF Source Phase Detector V(t) = k(t) V(t) RF Voltmeter Oscilloscope (t) RMS(t) in BW of meter S(f) vs. f Phase Noise Measurement

Frequency - Phase - Time Relationships: 

The five common power-law noise processes in precision oscillators are: (White PM) (Flicker PM) (White FM) (Flicker FM) (Random-walk FM) 4-32 Frequency - Phase - Time Relationships

S(f) to SSB Power Ratio Relationship: 

Consider the “simple” case of sinusoidal phase modulation at frequency fm. Then, (t) = o(t)sin(2fmt), and V(t) = Vocos[2fct + (t)] = Vocos[2fct + 0(t)sin(fmt)], where o(t)= peak phase excursion, and fc=carrier frequency. Cosine of a sine function suggests a Bessel function expansion of V(t) into its components at various frequencies via the identities: After some messy algebra, SV(f) and S(f) are as shown on the next page. Then, S(f) to SSB Power Ratio Relationship

S(f), Sv(f) and L (f): 

4-34 0 fm f SV(f) fC-3fm fC-2fm fC-fm fC fC+fm fC+2fm fC+3fm f S(f), Sv(f) and L (f)

Types of Phase Noise: 

4-35 L(ff) 40 dB/decade (ff-4) Random walk of frequency 30 dB/decade (ff-3) Flicker of frequency 20 dB/decade (ff-2) White frequency; Random walk of phase 10 dB/decade (ff-1) Flicker of phase 0 dB/decade (ff0) White phase ff ~BW of resonator Offset frequency (also, Fourier frequency, sideband frequency, or modulation frequency) Types of Phase Noise

Noise in Crystal Oscillators: 

4-36  The resonator is the primary noise source close to the carrier; the oscillator sustaining circuitry is the primary source far from the carrier.  Frequency multiplication by N increases the phase noise by N2 (i.e., by 20log N, in dB's).  Vibration-induced "noise" dominates all other sources of noise in many applications (see acceleration effects section, later).  Close to the carrier (within BW of resonator), Sy(f) varies as 1/f, S(f) as 1/f3, where f = offset from carrier frequency, . S(f) also varies as 1/Q4, where Q = unloaded Q. Since Qmax = const., S(f)  4. (Qmax)BAW = 1.6 x 1013 Hz; (Qmax)SAW = 1.05 x 1013 Hz.  In the time domain, noise floor is y()  (2.0 x 10-7)Q-1  1.2 x 10-20,  in Hz. In the regions where y() varies as -1 and -1/2 (-1/2 occurs in atomic frequency standards), y()  (QSR)-1, where SR is the signal-to-noise ratio; i.e., the higher the Q and the signal- to-noise ratio, the better the short term stability (and the phase noise far from the carrier, in the frequency domain). It is the loaded Q of the resonator that affects the noise when the oscillator sustaining circuitry is a significant noise source. Noise floor is limited by Johnson noise; noise power, kT = -174 dBm/Hz at 290K. Resonator amplitude-frequency effect can contribute to amplitude and phase noise. Higher signal level improves the noise floor but not the close-in noise. (In fact, high drive levels generally degrade the close-in noise, for reasons that are not fully understood.)  Low noise SAW vs. low noise BAW multiplied up: BAW is lower noise at f < ~1 kHz, SAW is lower noise at f > ~1 kHz; can phase lock the two to get the best of both. Noise in Crystal Oscillators

Low-Noise SAW and BAW Multiplied to 10 GHz(in a nonvibrating environment): 

4-37 Offset frequency in Hz 0 -20 -40 -60 -80 -100 -120 -140 -160 10-1 100 101 102 103 104 105 106 L(f) in dBc/Hz BAW = bulk-acoustic wave oscillator SAW = surface acoustic wave oscillator BAW is lower noise SAW is lower noise 200 5500 BAW 5 MHz x 2000 BAW 100 MHz x 100 SAW 500 MHz x 20 Low-Noise SAW and BAW Multiplied to 10 GHz (in a nonvibrating environment)

Low-Noise SAW and BAW Multiplied to 10 GHz(in a vibrating environment): 

Low-Noise SAW and BAW Multiplied to 10 GHz (in a vibrating environment)

Effects of Frequency Multiplication: 

4-39 Note that y = , Sy(f), and y() are unaffected by frequency multiplication. Noiseless Multiplier Effects of Frequency Multiplication

TCXO Noise: 

4-40 The short term stabilities of TCXOs are temperature (T) dependent, and are generally worse than those of OCXOs, for the following reasons:  The slope of the TCXO crystal’s frequency (f) vs. T varies with T. For example, the f vs. T slope may be near zero at ~20oC, but it will be ~1ppm/oC at the T extremes. T fluctuations will cause small f fluctuations at laboratory ambient T’s, so the stability can be good there, but millidegree fluctuations will cause ~10-9 f fluctuations at the T extremes. The TCXO’s f vs. T slopes also vary with T; the zeros and maxima can be at any T, and the maximum slopes can be on the order of 1 ppm/oC.  AT-cut crystals’ thermal transient sensitivity makes the effects of T fluctuations depend not only on the T but also on the rate of change of T (whereas the SC-cut crystals typically used in precision OCXOs are insensitive to thermal transients). Under changing T conditions, the T gradient between the T sensor (thermistor) and the crystal will aggravate the problems.  TCXOs typically use fundamental mode AT-cut crystals which have lower Q and larger C1 than the crystals typically used in OCXOs. The lower Q makes the crystals inherently noisier, and the larger C1 makes the oscillators more susceptible to circuitry noise.  AT-cut crystals’ f vs. T often exhibit activity dips (see “Activity Dips” later in this chapter). At the T’s where the dips occur, the f vs. T slope can be very high, so the noise due to T fluctuations will also be very high, e.g., 100x degradation of y() and 30 dB degradation of phase noise are possible. Activity dips can occur at any T. TCXO Noise

Quartz Wristwatch Accuracy vs. Temperature: 

Temperature coefficient of frequency = -0.035 ppm/0C2 Time Error per Day (seconds) -550C Military “Cold” -100C Winter +280C Wrist Temp. +490C Desert +850C Military “Hot” 0 10 20 Quartz Wristwatch Accuracy vs. Temperature

Frequency vs. Temperature Characteristics: 

Inflection Point Temperature Lower Turnover Point (LTP) Upper Turnover Point (UTP) f (UTP) f (LTP) Frequency Frequency vs. Temperature Characteristics

Resonator f vs. T Determining Factors: 

Resonator f vs. T Determining Factors

Frequency-Temperature vs. Angle-of-Cut, AT-cut: 

4-44 r m R R R R r m Y Z AT-cut BT-cut 49o 35¼o -1’ 0’ 1’ 2’ 3’ 4’ 5’ 6’ 7’ 8’ -1’ 0’ 1’ 2’ 3’ 4’ 5’ 6’ 7’ 8’  Y-bar quartz Z 25 20 15 10 5 0 -5 -10 -15 -20 -25 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 f f (ppm) Temperature (oC)  = 35o 20’ + ,  = 0 for 5th overtone AT-cut  = 35o 12.5’+ ,  = 0 for fundamental mode plano-plano AT-cut Frequency-Temperature vs. Angle-of-Cut, AT-cut

Desired f vs. T of SC-cut Resonatorfor OCXO Applications: 

4-45 Frequency Offset (ppm) Frequency remains within  1 ppm over a  250C range about Ti Temperature (0C) 20 15 10 5 0 -5 -10 -15 -20 20 40 60 80 100 120 140 160 Desired f vs. T of SC-cut Resonator for OCXO Applications

OCXO Oven’s Effect on Stability: 

4-46 A comparative table for AT and other non-thermal-transient compensated cuts of oscillators would not be meaningful because the dynamic f vs. T effects would generally dominate the static f vs. T effects. Oven Parameters vs. Stability for SC-cut Oscillator Assuming Ti - TLTP = 100C 100 10 1 0.1 0 TURNOVER POINT OVEN SET POINT TURNOVER POINT OVEN OFFSET 2 To OVEN CYCLING RANGE Typical f vs. T characteristic for AT and SC-cut resonators Frequency Temperature OCXO Oven’s Effect on Stability

Oven Stability Limits: 

Oven Stability Limits

Warmup of AT- and SC-cut Resonators: 

4-48 { Deviation from static f vs. t = , where, for example, -2 x 10-7 s/K2 for a typical AT-cut resonator Time (min) Oven Warmup Time Fractional Frequency Deviation From Turnover Frequency 3 6 9 12 15 10-3 10-4 10-5 -10-6 10-7 10-8 -10-8 -10-7 10-6 0 Warmup of AT- and SC-cut Resonators

TCXO Thermal Hysteresis: 

Temperature (0C) TCXO = Temperature Compensated Crystal Oscillator Fractional Frequency Error (ppm) 0.5 1.0 0.0 -0.5 -1.0 -25 -5 15 35 55 75 TCXO Thermal Hysteresis

Apparent Hysteresis: 

4-50 Temperature (C) -55 -45 -35 -25 -15 -5 5 15 25 35 45 55 65 75 85 45 40 35 30 25 20 15 10 5 0 Normalized frequency change (ppm) Apparent Hysteresis

OCXO Retrace: 

4-51 In (a), the oscillator was kept on continuously while the oven was cycled off and on. In (b), the oven was kept on continuously while the oscillator was cycled off and on. OVEN OFF (a) 14 days 14 days OSCILLATOR OFF OSCILLATOR ON (b) OVEN ON 15 10 5 0 15 5 0 10 X 10-9 OCXO Retrace

TCXO Trim Effect: 

4-52 In TCXO’s, temperature sensitive reactances are used to compensate for f vs. T variations. A variable reactance is also used to compensate for TCXO aging. The effect of the adjustment for aging on f vs. T stability is the “trim effect”. Curves show f vs. T stability of a “0.5 ppm TCXO,” at zero trim and at 6 ppm trim. (Curves have been vertically displaced for clarity.) 2 1 0 -1 -25 -5 15 35 55 75 -6 ppm aging adjustment +6 ppm aging adjustment T (0C) TCXO Trim Effect

Why the Trim Effect?: 

CL Compensated f vs. T Compensating CL vs. T Why the Trim Effect?

Effects of Load Capacitance on f vs. T: 

T DEGREES CELSIUS SC-cut r = Co/C1 = 746  = 0.130 12 8 4 0 -4 -8 -12 -50 200 450 700 950 1200 1450 1700 1950 * 10-6 Effects of Load Capacitance on f vs. T

Effects of Harmonics on f vs. T: 

4-55 (ppm) 5 3 M T, 0C 50 40 30 20 10 0 -10 -20 -30 -50 -100 -80 -40 -20 -0 20 40 60 80 AT-cut Reference angle-of-cut () is about 8 minutes higher for the overtone modes. (for the overtone modes of the SC-cut, the reference -angle-of-cut is about 30 minutes higher) 1 -60 -40  Effects of Harmonics on f vs. T

Amplitude - Frequency Effect: 

4-56 At high drive levels, resonance curves become asymmetric due to the nonlinearities of quartz. Normalized current amplitude Frequency 10 -6 10  W 100  W 400  W 4000  W Amplitude - Frequency Effect

Frequency vs. Drive Level: 

Frequency Change (parts in 109) 80 60 40 20 0 -20 100 200 300 400 500 600 700 5 MHz AT 3 diopter 10 MHz SC 2 diopter 10 MHz SC 1 diopter 10 MHz SC 10 MHz BT Crystal Current (microamperes) Frequency vs. Drive Level

Drive Level vs. Resistance: 

4-58 10-3 10-2 10-1 1 10 100 Resistance R1 IX (mA) Anomalous starting resistance Normal operating range Drive level effects Drive Level vs. Resistance

Second Level of Drive Effect: 

4-59 O A B C D Drive level (voltage) Activity (current) Second Level of Drive Effect

Activity Dips: 

4-60 Activity dips in the f vs. T and R vs. T when operated with and without load capacitors. Dip temperatures are a function of CL, which indicates that the dip is caused by a mode (probably flexure) with a large negative temperature coefficient. Frequency Resistance Temperature (0C) -40 -20 0 20 40 60 80 100 RL2 RL1 R1 fL1 fL2 fR 10 X10-6 Activity Dips

Frequency Jumps: 

4-61 0 2 4 6 8 10 No. 2 No. 3 No. 4 Frequency deviation (ppb) Elapsed time (hours) 2.0 x 10-11 30 min. Frequency Jumps

Acceleration vs. Frequency Change: 

A1 A2 A3 A5 A6 A2 A6 A4 A4 A3 A5 A1 Crystal plate Supports X’ Y’ Z’ G O Acceleration vs. Frequency Change

Acceleration Is Everywhere: 

4-63 Environment Buildings**, quiesent Tractor-trailer (3-80 Hz) Armored personnel carrier Ship - calm seas Ship - rough seas Propeller aircraft Helicopter Jet aircraft Missile - boost phase Railroads Spacecraft Acceleration typical levels*, in g’s 0.02 rms 0.2 peak 0.5 to 3 rms 0.02 to 0.1 peak 0.8 peak 0.3 to 5 rms 0.1 to 7 rms 0.02 to 2 rms 15 peak 0.1 to 1 peak Up to 0.2 peak f/f x10-11, for 1x10-9/g oscillator 2 20 50 to 300 2 to 10 80 30 to 500 10 to 700 2 to 200 1,500 10 to 100 Up to 20 * Levels at the oscillator depend on how and where the oscillator is mounted Platform resonances can greatly amplify the acceleration levels. ** Building vibrations can have significant effects on noise measurements Acceleration Is Everywhere

Acceleration Affects “Everything”: 

4-634 Acceleration Force Deformation (strain) Change in material and device properties - to some level Examples: - Quartz resonator frequency - Amplifier gain (strain changes semiconductor band structure) - Laser diode emission frequencies - Optical properties - fiber index of refraction (acoustooptics) - Cavity frequencies - DRO frequency (strain changes dielectric constants) - Atomic clock frequencies - Stray reactances - Clock rates (relativistic effects) Acceleration Affects “Everything”

2-g Tipover Test(f vs. attitude about three axes): 

4-65 Axis 3 Axis 2 Axis 1 g 10.000 MHz oscillator’s tipover test (f(max) - f(min))/2 = 1.889x10-09 (ccw) (f(max) - f(min))/2 = 1.863x10-09 (cw) delta  = 106.0 deg. (f(max) - f(min))/2 = 6.841x10-10 (ccw) (f(max) - f(min))/2 = 6.896x10-10 (cw) delta  = 150.0 deg. (f(max) - f(min))/2 = 1.882x10-09 (ccw) (f(max) - f(min))/2 = 1.859x10-09 (cw) delta  = 16.0 deg. Axis 1 Axis 2 4 2 0 45 90 135 180 225 270 315 360 2 0 45 90 135 180 225 270 315 360 2 0 45 90 135 180 225 270 315 360 4 4 2-g Tipover Test (f vs. attitude about three axes)

Sinusoidal Vibration Modulated Frequency: 

Time f0 - f f0 + f f0 - f f0 + f f0 - f f0 + f f0 - f f0 + f f0 - f f0 + f Acceleration Time Time Voltage Sinusoidal Vibration Modulated Frequency

Acceleration Sensitivity Vector: 

4-67 Axis 1 Axis 2 Axis 3 1 2 3 Acceleration Sensitivity Vector

Vibration-Induced Allan Deviation Degradation: 

0.001 0.01 0.1 1 10-9 10-10 10-11 10-12 Vibration-Induced Allan Deviation Degradation

Vibration-Induced Phase Excursion: 

4-69 Vibration-Induced Phase Excursion

Vibration-Induced Sidebands: 

4-70 L(f) 0 -10 -20 -30 -40 -50 -60 -70 -80 -90 -100 -250 -200 -150 -100 -50 0 50 100 150 200 250 f NOTE: the “sidebands” are spectral lines at fV from the carrier frequency (where fV = vibration frequency). The lines are broadened because of the finite bandwidth of the spectrum analyzer. Vibration-Induced Sidebands

Vibration-Induced SidebandsAfter Frequency Multiplication: 

4-71 0 -10 -20 -30 -40 -50 -60 -70 -80 -90 -100 -250 -200 -150 -100 -50 0 50 100 150 200 250 f L(f) Each frequency multiplication by 10 increases the sidebands by 20 dB. 10X 1X Vibration-Induced Sidebands After Frequency Multiplication

Sine Vibration-Induced Phase Noise: 

4-72 Sinusoidal vibration produces spectral lines at fv from the carrier, where fv is the vibration frequency. e.g., if  = 1 x 10-9/g and f0 = 10 MHz, then even if the oscillator is completely noise free at rest, the phase “noise” i.e., the spectral lines, due solely to a sine vibration level of 1g will be; Vibr. freq., fv, in Hz 1 10 100 1,000 10,000 -46 -66 -86 -106 -126 L’(fv), in dBc Sine Vibration-Induced Phase Noise

Random Vibration-Induced Phase Noise: 

4-73 Random vibration’s contribution to phase noise is given by: e.g., if  = 1 x 10-9/g and f0 = 10 MHz, then even if the oscillator is completely noise free at rest, the phase “noise” i.e., the spectral lines, due solely to a vibration of power spectral density, PSD = 0.1 g2/Hz will be: Offset freq., f, in Hz 1 10 100 1,000 10,000 L’(f), in dBc/Hz -53 -73 -93 -113 -133 Random Vibration-Induced Phase Noise

Random-Vibration-Induced Phase Noise: 

4-74 -70 -80 -90 -100 -110 -120 -130 -140 -150 -160 L (f) (dBc) 45 dB L(f) without vibration L(f) under the random vibration shown 5 300 1K 2K PSD (g2/Hz) .04 .07 Frequency (Hz) Typical aircraft random vibration envelope Random-Vibration-Induced Phase Noise

Acceleration Sensitivity vs. Vibration Frequency: 

Spectrum analyzer dynamic range limit Vibration Sensitivity (/g) 10-8 10-9 10-10 100 200 300 400 500 1000 Vibration Frequency (Hz) Acceleration Sensitivity vs. Vibration Frequency

Acceleration Sensitivity of Quartz Resonators: 

4-76 Resonator acceleration sensitivities range from the low parts in 1010 per g for the best commercially available SC-cuts, to parts in 107 per g for tuning-fork-type watch crystals. When a wide range of resonators were examined: AT, BT, FC, IT, SC, AK, and GT-cuts; 5 MHz 5th overtones to 500 MHz fundamental mode inverted mesa resonators; resonators made of natural quartz, cultured quartz, and swept cultured quartz; numerous geometries and mounting configurations (including rectangular AT-cuts); nearly all of the results were within a factor of three of 1x10-9 per g. On the other hand, the fact that a few resonators have been found to have sensitivities of less than 1x10-10 per g indicates that the observed acceleration sensitivities are not due to any inherent natural limitations. Theoretical and experimental evidence indicates that the major variables yet to be controlled properly are the mode shape and location (i.e., the amplitude of vibration distribution), and the strain distribution associated with the mode of vibration. Theoretically, when the mounting is completely symmetrical with respect to the mode shape, the acceleration sensitivity can be zero, but tiny changes from this ideal condition can cause a significant sensitivity. Until the acceleration sensitivity problem is solved, acceleration compensation and vibration isolation can provide lower than 1x10-10 per g, for a limited range of vibration frequencies, and at a cost. Acceleration Sensitivity of Quartz Resonators

Phase Noise Degradation Due to Vibration: 

4-77 OFFSET FROM CARRIER (Hz) Required to “see” 4km/hr target “Good’ oscillator at rest “Good’ oscillator on vibrating platform (1g) Radar oscillator specification -50 -100 -150 53 dB dBc/Hz 100K 10K 1K 100 10 1 1 10 100 1K 10K 100K Impacts on Radar Performance  Lower probability of detection  Lower probability of identification  Shorter range  False targets Data shown is for a 10 MHz, 2 x 10-9 per g oscillator Radar spec. shown is for a coherent radar (e.g., SOTAS) Phase Noise Degradation Due to Vibration

Coherent Radar Probability of Detection: 

4-78 To “see” 4 km/h targets, low phase noise 70 Hz from the carrier is required. Shown is the probability of detection of 4 km/h targets vs. the phase noise 70 Hz from the carrier of a 10 MHz reference oscillator. (After multiplication to 10 GHz the phase noise will be at least 60 dB higher.) The phase noise due to platform vibration, e.g., on an aircraft, reduces the probability of detection of slow-moving targets to zero. 100 80 60 40 20 -140 -135 -130 -125 -120 -115 -110 High Noise Low Noise Phase Noise (dBc/Hz) at 70 Hz from carrier, for 4 km/h targets Probability of Detection (%) Coherent Radar Probability of Detection

Vibration Isolation: 

4-79 Limitations Poor at low frequencies Adds size, weight and cost Ineffective for acoustic noise Region of Amplification 1 0.2 1 Forcing Freq./Resonant Freq. Transmissibility Region of Isolation Vibration Isolation

Vibration Compensation: 

4-80 Stimulus OSC. DC Voltage on Crystal OSC. fv AC Voltage on Crystal OSC. fv Crystal Being Vibrated Response f 7 x 10-9 /Volt V 5 MHz fund. SC OSC. Compensated Oscillator AMP Vibration Compensated Oscillator ACC = accelerometer Response to Vibration Vibration Compensation

Vibration Sensitivity Measurement System: 

Controller Signal Generator fV Spectrum Analyzer Plotter or Printer Vibration Level Controller Power Amplifier Shake Table Test Oscillator Accelerometer Frequency Multiplier (x10) Synthesizer (Local Oscillator) Vibration Sensitivity Measurement System

Shock: 

4-82 The frequency excursion during a shock is due to the resonator’s stress sensitivity. The magnitude of the excursion is a function of resonator design, and of the shock induced stresses on the resonator (resonances in the mounting structure will amplify the stresses.) The permanent frequency offset can be due to: shock induced stress changes, a change in (particulate) contamination on the resonator surfaces, and changes in the oscillator circuitry. Survival under shock is primarily a function of resonator surface imperfections. Chemical-polishing-produced scratch-free resonators have survived shocks up to 36,000 g in air gun tests, and have survived the shocks due to being fired from a 155 mm howitzer (16,000 g, 12 ms duration). Shock 3 2 1 0 -1 -2 -3 tO t1 Shock

Radiation-Induced Frequency Shifts: 

4-83 Idealized frequency vs. time behavior for a quartz resonator following a pulse of ionizing radiation. t0 t Time Frequency fO ft fSS fSS fO = original, preirradiation frequency fSS = steady-state frequency (0.2 to 24 hours after exposure) fSS = steady-state frequency offset fT = frequency at time t 10-11 for natural quartz (and R increase can stop the oscillation) fSS/rad* = 10-12 for cultured quartz 10-13 for swept cultured quartz * for a 1 megarad dose (the coefficients are dose dependent) { Radiation-Induced Frequency Shifts

Effects of Repeated Radiations: 

Fractional Frequency, ppb 10 0 -10 -20 -30 -40 10 102 103 104 105 106 Dose, rad(SiO2) 1. Initial irradiation 2. Reirradiation (after 2.5 x 104 rad) 3. Reirradiation (after >106 rad) Five irradiations; responses during the 4th and 5th irradiations repeated the results of the 3rd. At least 2 days elapsed between successive irradiations. Initial slopes: 1st: -1 x 10-9/rad 2nd: +1 x 10-11/rad 3rd: +3 x 10-12/rad 4th: +3 x 10-12/rad 5th: +5 x 10-12/rad Effects of Repeated Radiations

Radiation Induced f vs. Dose and Quartz Type: 

4-85 10 MeV electrons, 5 MHz 5th overtone AT-cut resonators Z-growth cultured Swept Z-growth cultured Natural Frequency Change (Hz) Reds (Si) 104 5 105 5 106 5 107 50 30 10 0 -10 -30 -50 Radiation Induced f vs. Dose and Quartz Type

Annealing of Radiation Induced f Changes: 

4-86 For a 4 MHz AT-cut resonator, X-ray dose of 6 x 106 rads produced f = 41 Hz. Activiation energies were calculated from the temperature dependence of the annealing curves. The experimental results can be reproduced by two processes, with activation energies E1 = 0.3  0.1 eV and E2 = 1.3  0.3eV. Annealing was complete in less than 3 hours at > 2400C. x x x x x x x x x x x x -f 40 20 0 Frequency change, Hz 100 200 300 x fS = 41 Hz X T= 4330K (1600C) X T= 4540K X T= 4680K X T= 4880K (2150C) Annealing time, minutes T = 5130K(2400C) Annealing of Radiation Induced f Changes

Transient f After a Pulse of  Radiation: 

4 0 -4 -8 -12 -16 -20 -24 f/f (pp 108) Time (seconds after event) 0.1 1.0 10 100 1000 X X X X X X X X X X X X X X X X X X X X X X X X X X X X Experimental data, dose = 1.3 x 104 rads, SC-cut Experimental data, dose = 2.3 x 104 rads, AT-cut Model Calculation: AT-cut X Transient f After a Pulse of  Radiation

Effects of Flash X-rays on RS: 

4-88 The curves show the series resonance resistance, RS, vs. time following a 4 x 104 rad pulse. Resonators made of swept quartz show no change in RS from the earliest measurement time (1 ms) after exposure, at room temperature. Large increases in RS (i.e., large decrease in the Q) will stop the oscillation. RS in Ohms 14 13 12 11 10 9 8 7 6 5 80 70 60 50 40 30 0.001 0.01 0.1 1.0 10 100 1000 Value of Q-1 x 106 Time following exposure (seconds) 32 MHz AT-cut resonators Preirradiation value RS C-22 C-7 N-4 N-4 (Natural) 4.5 x 104 R C-7 (Unswept synthetic) 4 x 104 R C-22 (Unswept synthetic) 3.5 x 104 R S-25 Swept synthetic) 4 x 104 R S-26 Swept synthetic) 4 x 104 R Effects of Flash X-rays on RS

Frequency Change due to Neutrons: 

4-89 Fast Neutron Exposure (nvt) x1017 0 1 2 3 4 5 6 7 8 9 10 11 12 1000 900 800 700 600 500 400 300 200 100 0 5 MHz AT-cut Slope = 0.7 x 10-21/n/cm2 Frequency Change due to Neutrons

Neutron Damage: 

4-90 A fast neutron can displace about 50 to 100 atoms before it comes to rest. Most of the damage is done by the recoiling atoms. Net result is that each neutron can cause numerous vacancies and interstitials. (1) (2) (3) (4) Neutron Damage

Summary - Steady-State Radiation Results: 

Summary - Steady-State Radiation Results

Summary - Pulse Irradiation Results: 

4-92  For applications requiring circuits hardened to pulse irradiation, quartz resonators are the least tolerant element in properly designed oscillator circuits.  Resonators made of unswept quartz or natural quartz can experience a large increase in Rs following a pulse of radiation. The radiation pulse can stop the oscillation.  Natural, cultured, and swept cultured AT-cut quartz resonators experience an initial negative frequency shift immediately after exposure to a pulse of X-rays (e.g., 104 to 105 Rad of flash X-rays), f/f is as large as -3ppm at 0.02sec after burst of 1012 Rad/sec.  Transient f offset anneals as t-1/2; the nonthermal-transient part of the f offset is probably due to the diffusion and retrapping of hydrogen at the Al3+ trap.  Resonators made of properly swept quartz experience a negligibly small change in Rs when subjected to pulsed ionizing radiation (therefore, the oscillator circuit does not require a large reserve of gain margin).  SC-cut quartz resonators made of properly swept high Q quartz do not exhibit transient frequency offsets following a pulse of ionizing radiation.  Crystal oscillators will stop oscillating during an intense pulse of ionizing radiation because of the large prompt photoconductivity in quartz and in the transistors comprising the oscillator circuit. Oscillation will start up within 15sec after a burst if swept quartz is used in the resonator and the oscillator circuit is properly designed for the radiation environment. Summary - Pulse Irradiation Results

Summary - Neutron Irradiation Results: 

4-93  When a fast neutron (~MeV energy) hurtles into a crystal lattice and collides with an atom, it is scattered like a billiard ball. The recoiling atom, having an energy (~104 to 106 eV) that is much greater than its binding energy in the lattice, leaves behind a vacancy and, as it travels through the lattice, it displaces and ionizes other atoms. A single fast neutron can thereby produce numerous vacancies, interstitials, and broken interatomic bonds. Neutron damage thus changes both the elastic constants and the density of quartz. Of the fast neutrons that impinge on a resonator, most pass through without any collisions, i.e., without any effects on the resonator. The small fraction of neutrons that collide with atoms in the lattice cause the damage.  Frequency increases approximately linearly with fluence. For AT- and SC-cut resonators, the slopes range from +0.7 x 10-21/n/cm2, at very high fluences (1017 to 1018n/cm2) to 5 x 10-21/n/cm2 at 1012 to 1013n/cm2, and 8 x 10-21/n/cm2at 1010 to 1012n/cm2. Sensitivity probably depends somewhat on the quartz defect density and on the neutron energy distribution. (Thermonuclear neutrons cause more damage than reactor neutrons.)  Neutron irradiation also rotates the frequency vs. temperature characteristic.  When a heavily neutron irradiated sample was baked at 500C for six days, 90% of the neutron-induced frequency shift was removed (but the 10% remaining was still 93 ppm). Summary - Neutron Irradiation Results

Other Effects on Stability: 

4-94  Electric field - affects doubly-rotated resonators; e.g., a voltage on the electrodes of a 5 MHz fundamental mode SC-cut resonator results in a f/f = 7 x 10-9 per volt. The voltage can also cause sweeping, which can affect the frequency (of all cuts), even at normal operating temperatures.  Magnetic field - quartz is diamagnetic, however, magnetic fields can induce Eddy currents, and will affect magnetic materials in the resonator package and the oscillator circuitry. Induced ac voltages can affect varactors, AGC circuits and power supplies. Typical frequency change of a "good" quartz oscillator is <<10-10 per gauss.  Ambient pressure (altitude) - deformation of resonator and oscillator packages, and change in heat transfer conditions affect the frequency.  Humidity - can affect the oscillator circuitry, and the oscillator's thermal properties, e.g., moisture absorbed by organics can affect dielectric constants.  Power supply voltage, and load impedance - affect the oscillator circuitry, and indirectly, the resonator's drive level and load reactance. A change in load impedance changes the amplitude or phase of the signal reflected into the oscillator loop, which changes the phase (and frequency) of the oscillation. The effects can be minimized by using a (low noise) voltage regulator and buffer amplifier.  Gas permeation - stability can be affected by excessive levels of atmospheric hydrogen and helium diffusing into "hermetically sealed" metal and glass enclosures (e.g., hydrogen diffusion through nickel resonator enclosures, and helium diffusion through glass Rb standard bulbs). Other Effects on Stability

Interactions Among Influences: 

Interactions Among Influences

CHAPTER 5Quartz Material Properties: 

5 CHAPTER 5 Quartz Material Properties

Hydrothermal Growth of Quartz: 

5-1 The autoclave is filled to some predetermined factor with water plus mineralizer (NaOH or Na2CO3). The baffle localizes the temperature gradient so that each zone is nearly isothermal. The seeds are thin slices of (usually) Z-cut single crystals. The nutrient consists of small (~2½ to 4 cm) pieces of single-crystal quartz (“lascas”). The temperatures and pressures are typically about 3500C and 800 to 2,000 atmospheres; T2 - T1 is typically 40C to 100C. The nutrient dissolves slowly (30 to 260 days per run), diffuses to the growth zone, and deposits onto the seeds. Cover Closure area Autoclave Seeds Baffle Solute- nutrient Nutrient dissolving zone, T2 T2 > T1 Growth zone, T1 Nutrient Hydrothermal Growth of Quartz

Deeply Dissolved Quartz Sphere: 

Anisotropic Etching 5-2 Z +X Looking along Y-axis Looking along Z-axis Deeply Dissolved Quartz Sphere

Etching & Chemical Polishing: 

5-3 Etchant Must: 1. Diffuse to Surface 2. Be Adsorbed 3. React Chemically Reaction Products Must: 4. Be Desorbed 5. Diffuse Away Diffusion Controlled Etching: Lapped surface Chemically polished surface Etching & Chemical Polishing

Left-Handed and Right-Handed Quartz: 

5-4 Y X r z z r Y X r r z z m m m m r r z z Left-Handed Right-Handed Y Z Left-Handed and Right-Handed Quartz

The Quartz Lattice: 

5-5 Si Si Si Si O O O O Si 109o Z Y 144.2o The Quartz Lattice

Quartz Properties’ Effects on Device Properties: 

Quartz Properties’ Effects on Device Properties

Ions in Quartz - Simplified Model: 

5-7 = Oxygen = Si4+ Al H Axis of channel Al H Al Li 0.089 eV Al Na 0.143 eV 0.055 eV Al K 0.2 eV A) E) D) C) B) a Ions in Quartz - Simplified Model

Aluminum Associated Defects: 

Ox Ox Ox Ox Ox Ox Ox Ox H+ M+ Al3+ Al3+ Al3+ Ox Ox Ox Al-OH center OH molecule Al-M+ center Interstitial Alkali 5-8 Hole trapped in nonbonding oxygen p orbital h+ Al-hole center Aluminum Associated Defects

Sweeping: 

High voltage power supply Thermometer Ammeter Z Cr-Au Oven T = 500OC E = 1000 V/cm 5-9 I Time 0.5 a/cm2 Sweeping

Quartz Quality Indicators: 

Quartz Quality Indicators

Infrared Absorption of Quartz: 

5-11 Transmission (%) Wave number (cm-1) 20 40 60 80 100 0 2.5 3.0 3.5 4.0 3500 3585 3300 3200 3410 4000 3500 3000 2500 E parallel to Z E parallel to X Infrared Absorption of Quartz

Infrared Absorption Coefficient: 

Infrared Absorption Coefficient

Quartz Twinning: 

Electrical twinning Optical Twinning The X-axes of quartz, the electrical axes, are parallel to the line bisecting adjacent prism faces; the +X-direction is positive upon extension due to tension. Electric twinning (also called Dauphiné twinning) consists of localized reversal of the X-axes. It usually consists of irregular patches, with irregular boundaries. It can be produced artificially by inversion from high quartz, thermal shock, high local pressure (even at room temperature), and by an intense electric field. In right-handed quartz, the plane of polarization is rotated clockwise as seen by looking toward the light source; in left handed, it is counterclockwise. Optically twinned (also called Brazil twinned) quartz contains both left and right-handed quartz. Boundaries between optical twins are usually straight. Etching can reveal both kinds of twinning. 5-13 > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >                                                                                                Quartz Twinning

Twinning - Axial Relationships: 

5-14 The diagrams illustrate the relationship between the axial system and hand of twinned crystals. The arrows indicate the hand. Electrical (Dauphine) Combined Optical (Brazil) + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z r r r r r r r r r r r r r r r r r r Twinning - Axial Relationships

Quartz Lattice and Twinning: 

5-15 Z-axis projection showing electric (Dauphiné) twins separated by a twin wall of one unit cell thickness. The numbers in the atoms are atom heights expressed in units of percent of a unit cell height. The atom shifts during twinning involve motions of <0.03 nm. 33 45 67 21 21 00 79 67 45 12 21 45 67 33 88 55 79 00 88 79 00 88 Silicon Oxygen Domain Wall Quartz Lattice and Twinning

Quartz Inversion: 

Quartz Inversion

Phase Diagram of Silica (SiO2): 

5-17 Low or -quartz High or -quartz Cristobalite Tridymite Liquid Coesite Stishovite P(gpa) 12 10 8 6 4 2 0 0 500 1000 1500 2000 2500 T(oC) Phase Diagram of Silica (SiO2)

Internal Friction (i.e., the Q) of Quartz: 

5-18 Empirically determined Q vs. frequency curves indicate that the maximum achievable Q times the frequency is a constant, e.g., 16 million for AT-cut resonators, when f is in MHz. 100 60 40 20 10 8 6 4 2 1 0.8 0.6 0.4 0.2 0.1 0.1 0.2 0.4 0.6 1.0 2 4 6 8 10 20 40 60 100 Value of Q, in millions Frequency in MHz Most probable internal friction curve for quartz; excluding mounting losses Diameter of shaped quartz plates, in vacuum 90 mm 30 mm 15 mm Flat quartz plates, in air Internal Friction (i.e., the Q) of Quartz

Langasite and Its Isomorphs: 

5-19 La3Ga5SiO14 Langasite (LGS) La3Ga5.5Nb0.5O14 Langanite (LGN) La3Ga5.5Ta0.5O14 Langatate (LGT) Lower acoustic attenuation than quartz (higher Qf than AT- or SC-cut quartz) No phase transition (melts at ~1,400 oC vs. phase transition at 573 oC for quartz) Higher piezoelectric coupling than quartz Temperature-compensated Gallium phosphate is another promising high-Q, temperature-compensated material Langasite and Its Isomorphs

CHAPTER 6Atomic Frequency Standards*: 

* There are two important reasons for including this chapter: 1. atomic frequency standards are one of the most important applications of precision quartz oscillators, and 2. those who study or use crystal oscillators ought to be aware of what is available in case they need an oscillator with better long-term stability than what crystal oscillators can provide. 6 CHAPTER 6 Atomic Frequency Standards*

Precision Frequency Standards: 

6-1 Quartz crystal resonator-based (f ~ 5 MHz, Q ~ 106) Atomic resonator-based Rubidium cell (f0 = 6.8 GHz, Q ~ 107) Cesium beam (f0 = 9.2 GHz, Q ~ 108) Hydrogen maser (f0 = 1.4 GHz, Q ~ 109) Trapped ions (f0 > 10 GHz, Q > 1011) Cesium fountain (f0 = 9.2 GHz, Q ~ 5 x 1011) Precision Frequency Standards

Atomic Frequency Standard Basic Concepts: 

6-2 When an atomic system changes energy from an exited state to a lower energy state, a photon is emitted. The photon frequency  is given by Planck’s law where E2 and E1 are the energies of the upper and lower states, respectively, and h is Planck’s constant. An atomic frequency standard produces an output signal the frequency of which is determined by this intrinsic frequency rather than by the properties of a solid object and how it is fabricated (as it is in quartz oscillators). The properties of isolated atoms at rest, and in free space, would not change with space and time. Therefore, the frequency of an ideal atomic standard would not change with time or with changes in the environment. Unfortunately, in real atomic frequency standards: 1) the atoms are moving at thermal velocities, 2) the atoms are not isolated but experience collisions and electric and magnetic fields, and 3) some of the components needed for producing and observing the atomic transitions contribute to instabilities. Atomic Frequency Standard Basic Concepts

Hydrogen-Like Atoms: 

Hydrogen-like (or alkali) atoms Hyperfine structure of 87Rb, with nuclear spin I=3/2, 0=W/h=6,834,682,605 Hz and X=[(-J/J) +(I/I)]H0/W calibrated in units of 2.44 x 103 Oe. S N Nuclear spin and dipole Electron spin and dipole N Closed electronic shell Electron S 3 2 1 -1 -2 -3 2 3 4 X MF = 2 1 0 -1 MF = -2 -1 0 1 F=2 F=1 W Nucleus Electron Hydrogen-Like Atoms

Atomic Frequency Standard*Block Diagram: 

6-4 Atomic Resonator Feedback Multiplier Quartz Crystal Oscillator 5 MHz Output Atomic Frequency Standard* Block Diagram * Passive microwave atomic standard (e.g., commercial Rb and Cs standards)

Generalized Microwave Atomic Resonator: 

6-5 Prepare Atomic State Apply Microwaves Detect Atomic State Change Tune Microwave Frequency For Maximum State Change B A Generalized Microwave Atomic Resonator

Atomic Resonator Concepts: 

Atomic Resonator Concepts

Rubidium Cell Frequency Standard: 

6-7 Energy level diagrams of 85Rb and 87Rb F = 3 F = 2 363 MHz 816 MHz F = 2 F = 1 52P1/2 85Rb 87Rb 795 nm 795 nm F = 3 F = 2 F = 2 3.045 GHz 52S1/2 F = 1 6.834,682,608 GHz Rubidium Cell Frequency Standard

Rubidium Cell Frequency Standard: 

6-8 Atomic resonator schematic diagram Magnetic shield “C-Field” Absorption cell 87Rb lamp rf lamp exciter Power supplies for lamp, filter and absorption cell thermostats Filter Cell 85Rb + buffer gas Cavity Photo cell Detector output C-field power supply Frequency input 6.834,685 GHz Rb-87 + buffer gas Light Rubidium Cell Frequency Standard

Cs Hyperfine Energy Levels: 

6-9 9.2 0 Energy (Frequency) (GHz) Magnetic Field HO Energy states at H = HO (F, mF) (4,4) (4,3) (4,2) (4,1) (4,0) (4,-1) (4,-2) (4,-3) (4,-4) (3,-3) (3,-2) (3,-1) (3,0) (3,1) (3,2) (3,3) 9.192,631,770 GHz Cs Hyperfine Energy Levels

Cesium-Beam Frequency Standard: 

ATOMIC BEAM SOURCE ATOMIC BEAM Cs VAPOR, CONTAINING AN EQUAL AMOUNT OF THE TWO KINDS OF Cs ATOMS VACUUM CHAMBER MAGNET (STATE SELECTOR) N S KIND 1 - ATOMS (LOWER STATE) KIND 2 - ATOMS (UPPER STATE) DETECTOR DETECTOR MAXIMUM SIGNAL NO SIGNAL S S N N MAGNET MAGNET MICROWAVE CAVITY MICROWAVE CAVITY MICROWAVE SIGNAL (OF ATOMIC RESONANCE FREQUENCY) STATE SELECTED ATOMIC BEAM STATE SELECTED ATOMIC BEAM NO SIGNAL 6-10 Cesium-Beam Frequency Standard

Cesium-Beam Frequency Standard: 

Cs atomic resonator schematic diagram 6-11 HOT WIRE IONIZER B-MAGNET GETTER ION COLLECTOR PUMP DETECTOR SIGNAL PUMP POWER SUPPLY DETECTOR POWER SUPPLY C-FIELD POWER SUPPLY DC MAGNETIC SHIELD “C-FIELD” Cs-BEAM CAVITY FREQUENCY INPUT 9,192,631,770 Hz VACUUM ENVELOPE OVEN HEATER POWER SUPPLY A-MAGNET GETTER Cesium-Beam Frequency Standard

Atomic Hydrogen Energy Levels: 

6-12 W H’ (F, mF) (1, +1) (1, 0) (1, -1) (0, 0) Ground state energy levels of atomic hydrogen as a function of magnetic field H’. 1.42040…GHz Atomic Hydrogen Energy Levels

Passive H-Maser Schematic Diagram: 

6-13 Microwave output Teflon coated storage bulb Microwave cavity Microwave input State selector Hydrogen atoms Passive H-Maser Schematic Diagram

Laser Cooling of Atoms: 

Atom Direction of motion Light Light 1 2 3 4 Direction of force 6-14 Laser Cooling of Atoms

Cesium Fountain: 

Cesium Fountain 6-15 Click here for animation Accuracy ~1 x 10-15 or 1 second in 30 million years 1 x 10-16 is achievable

Atomic Resonator Instabilities: 

6-16 Noise - due to the circuitry, crystal resonator, and atomic resonator. (See next page.) Cavity pulling - microwave cavity is also a resonator; atoms and cavity behave as two coupled oscillators; effect can be minimized by tuning the cavity to the atomic resonance frequency, and by maximizing the atomic resonance Q to cavity Q ratio. Collisions - cause frequency shifts and shortening of oscillation duration. Doppler effects - 1st order is classical, can be minimized by design; 2nd order is relativistic; can be minimized by slowing the atoms via laser cooling - see “Laser Cooling of Atoms” later in this chapter. Magnetic field - this is the only influence that directly affects the atomic resonance frequency. Microwave spectrum - asymmetric frequency distribution causes frequency pulling; can be made negligible through proper design. Environmental effects - magnetic field changes, temperature changes, vibration, shock, radiation, atmospheric pressure changes, and He permeation into Rb bulbs. Atomic Resonator Instabilities

Noise in Atomic Frequency Standards: 

6-17 If the time constant for the atomic-to-crystal servo-loop is to, then at  < to, the crystal oscillator determines y(), i.e., y () ~ -1. From  > to to the  where the "flicker floor" begins, variations in the atomic beam intensity (shot-noise) determine y(), and y() ~ (i)-1/2, where i = number of signal events per second. Shot noise within the feedback loop shows up as white frequency noise (random walk of phase). Shot noise is generally present in any electronic device (vacuum tube, transistor, photodetector, etc.) where discrete particles (electrons, atoms) move across a potential barrier in a random way. In commercial standards, to ranges from 0.01 s for a small Rb standard to 60 s for a high-performance Cs standard. In the regions where y() varies as  -1 and  -1/2, y()  (QSR)-1, where SR is the signal-to-noise ratio, i.e., the higher the Q and the signal-to-noise ratio, the better the short term stability (and the phase noise far from the carrier, in the frequency domain). Noise in Atomic Frequency Standards

Short-Term Stability of a Cs Standard: 

STANDARD TUBE 0 = 1 SECOND 0 = 60 SECONDS* OPTION 004 TUBE 0 = 1 SECOND SYSTEM BW = 100 kHz y() 10-9 10-10 10-11 10-12 10-13 10-14 10-15 10-16 10-3 10-2 10-1 100 101 102 103 104 105 106 AVERAGING TIME  (SECONDS) * The 60 s time constant provides better short- term stability, but it is usable only in benign environments. Short-Term Stability of a Cs Standard

Short-Term Stability of a Rb Standard: 

6-19 .001 .01 .1 1 10 100 (seconds) 10-9 10-10 10-11 10-12 y() fL (LOOP BW) = fL = 100 Hz (STANDARD) OTHERS OPTIONAL fL = 0.01 Hz fL = 1 Hz VCXO RUBIDIUM - WORST CASE fL = 100 Hz Short-Term Stability of a Rb Standard

Acceleration Sensitivity of Atomic Standards: 

6-20 Let the servo loop time constant = t0, let the atomic standard's  = A, and the crystal oscillator’s (VCXO's)  = O. Then, For fast acceleration changes (fvib >> 1/2t0), A = O For slow acceleration changes, (fvib << 1/2t0), A << O For fvib  fmod, 2fmod, servo is confused, A  O, plus a frequency offset For small fvib, (at Bessel function null), loss of lock, A  O Atomic Resonator Feedback Multiplier Quartz Crystal Oscillator 5 MHz Output Acceleration Sensitivity of Atomic Standards

Atomic Standard Acceleration Effects: 

6-21 In Rb cell standards, high acceleration can cause f due to light shift, power shift, and servo effects: Location of molten Rb in the Rb lamp can shift Mechanical changes can deflect light beam Mechanical changes can cause rf power changes In Cs beam standards, high acceleration can cause f due to changes in the atomic trajectory with respect to the tube & microwave cavity structures: Vibration modulates the amplitude of the detected signal. Worst when fvib = f mod. Beam to cavity position change causes cavity phase shift effects Velocity distribution of Cs atoms can change Rocking effect can cause f even when fvib < f mod In H-masers, cavity deformation causes f due to cavity pulling effect Atomic Standard Acceleration Effects

Magnetic Field Sensitivities of Atomic Clocks: 

6-22 Magnetic Field Sensitivities of Atomic Clocks

Crystal’s Influences on Atomic Standard: 

6-23 Short term stability - for averaging times less than the atomic-to- crystal servo loop time constant, L, the crystal oscillator determines y(). Loss of lock - caused by large phase excursions in t < L (due to shock, attitude change, vibration, thermal transient, radiation pulse). At a Rb standard's 6.8 GHz, for a f = 1 x 10-9 in 1s, as in a 2g tipover in 1s,  ~ 7. Control voltage sweeping during reacquisition attempt can cause the phase and frequency to change wildly. Maintenance or end of life - when crystal oscillator frequency offset due to aging approaches EFC range (typically ~ 1 to 2 x 10-7). Long term stability - noise at second harmonic of modulation f causes time varying f's; this effect is significant only in the highest stability (e.g., H and Hg) standards. Crystal’s Influences on Atomic Standard

Optically Pumped Cs Standard: 

6-24 The proper atomic energy levels are populated by optical pumping with a laser diode. This method provides superior utilization of Cs atoms, and provides the potential advantages of: higher S/N, longer life, lower weight, and the possibility of trading off size for accuracy. A miniature Cs standard of 1 x 10-11 accuracy, and <<1 liter volume, i.e., about 100x higher accuracy than a Rb standard, in a smaller volume (but not necessarily the same shape factor) seems possible. Fluorescence Detector  Detection laser Pump laser(s) Oven Essential Elements of an Optically Pumped Cesium Beam Standard 62 P 3/2 62 S 1/2 F = 5 F = 4 F = 3 F = 4 F = 3 State selection State detection Tuned laser diode pumps Spontaneous decays 453 MHz 852 nm (~350 THz) 9.192631770 GHz Atomic Energy Levels Optically Pumped Cs Standard

Rubidium - Crystal Oscillator (RbXO): 

6-25 Rubidium Frequency Standard (25W @ -550C) RbXO Interface Low-power Crystal Oscillator Rubidium - Crystal Oscillator (RbXO)

RbXO Principle of Operation: 

6-26 Rb Reference Power Source RF Sample Control Signals Rb Reference OCXO Tuning Memory Output OCXO and Tuning Memory Power Source Control Voltage RbXO Principle of Operation

Rubidium Crystal Oscillator: 

Rubidium Crystal Oscillator 6-27

CHAPTER 7Oscillator Comparisons andSpecifications: 

7 CHAPTER 7 Oscillator Comparisons and Specifications

Oscillator Comparison: 

7-1 * Including environmental effects (note that the temperature ranges for Rb and Cs are narrower than for quartz). Quartz Oscillators Atomic Oscillators Accuracy * (per year) Aging/Year Temp. Stab. (range, 0C) Stability,y() ( = 1s) Size (cm3) Warmup Time (min) Power (W) (at lowest temp.) Price (~$) TCXO 2 x 10-6 5 x 10-7 5 x 10-7 (-55 to +85) 1 x 10-9 10 0.03 (to 1 x 10-6) 0.04 10 - 100 MCXO 5 x 10-8 2 x 10-8 3 x 10-8 (-55 to +85) 3 x 10-10 30 0.03 (to 2 x 10-8) 0.04 <1,000 OCXO 1 x 10-8 5 x 10-9 1 x 10-9 (-55 to +85) 1 x 10-12 20-200 4 (to 1 x 10-8) 0.6 200-2,000 Rubidium 5 x 10-10 2 x 10-10 3 x 10-10 (-55 to +68) 3 x 10-12 200-800 3 (to 5 x 10-10) 20 2,000-8,000 RbXO 7 x 10-10 2 x 10-10 5 x 10-10 (-55 to +85) 5 x 10-12 1,000 3 (to 5 x 10-10) 0.65 <10,000 Cesium 2 x 10-11 0 2 x 10-11 (-28 to +65) 5 x 10-11 6,000 20 (to 2 x 10-11) 30 50,000 Oscillator Comparison

Clock Accuracy vs. Power Requirement*: 

* Accuracy vs., size, and accuracy vs. cost have similar relationships 10-12 10-10 10-8 10-6 10-4 Accuracy Power (W) 0.01 0.1 1 10 100 0.001 XO TCXO OCXO Rb Cs 1s/day 1ms/year 1ms/day 1s/year 1s/day Clock Accuracy vs. Power Requirement* 7-2

Clock Accuracy vs. Power Requirement*: 

(Goal of R&D is to move technologies toward the upper left) 7-3 * Accuracy vs., size, and accuracy vs. cost have similar relationships 10-12 10-10 10-8 10-6 10-4 Accuracy Power (W) = in production = developmental 0.01 0.1 1 10 100 0.001 XO TCXO OCXO Rb Cs MCXO TMXO RbXO Mini-Rb/Cs 1s/day 1ms/year 1ms/day 1s/year 1s/day Clock Accuracy vs. Power Requirement*

Battery Life vs. Oscillator Power: 

Oscillator Power (Watts) Operation at –30oC. The oscillators are assumed to consume ½ of the battery capacity. Batteries (except alkaline) are derated for temperature. Days of Battery Life 1 Year 6 Months 1 Month 1 Week 1 Day 0.001 0.01 0.1 1 10 XO TCXO MCXO Mini Rb/Cs Small OCXO Small RB Std 1000 100 10 1 0.1 BA 5567, 9.2 cm3 AA Alkaline, 8 cm3, 25°C Li Ion (Cell Phone), 135 cm3 BA 5093, 621 cm3 BA 5800, 127 cm3 BA 5590, 883 cm3 7-4 Battery Life vs. Oscillator Power

Short Term Stability Ranges of Various Frequency Standards: 

7-5 Log (y()) Log (), seconds -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 1 day 1 month -9 -10 -11 -12 -13 -14 -15 -16 Hydrogen Maser Rubidium Quartz Cesium Short Term Stability Ranges of Various Frequency Standards

Phase Instabilities of Various Frequency Standards: 

7-6 Typical one-sided spectral density of phase deviation vs. offset frequency, for various standards, calculated at 5 MHz. L(f) = ½ S -30 -40 -50 -60 -70 -80 -90 -100 -110 -120 -130 -140 -150 -160 -3 -2 -1 0 1 2 3 4 10*Log(S(f)) Log (f) Cesium Quartz Hydrogen Maser Rubidium Phase Instabilities of Various Frequency Standards

Weaknesses and Wearout Mechanisms: 

7-7 Weaknesses and Wearout Mechanisms

Why Do Crystal Oscillators Fail?: 

7-8 Crystal oscillators have no inherent failure mechanisms. Some have operated for decades without failure. Oscillators do fail (go out of spec.) occasionally for reasons such as: Poor workmanship & quality control - e.g., wires come loose at poor quality solder joints, leaks into the enclosure, and random failure of components Frequency ages to outside the calibration range due to high aging plus insufficient tuning range TCXO frequency vs. temperature characteristic degrades due to aging and the “trim effect”. OCXO frequency vs. temperature characteristic degrades due to shift of oven set point. Oscillation stops, or frequency shifts out of range or becomes noisy at certain temperatures, due to activity dips Oscillation stops or frequency shifts out of range when exposed to ionizing radiation - due to use of unswept quartz or poor choice of circuit components Oscillator noise exceeds specifications due to vibration induced noise Crystal breaks under shock due to insufficient surface finish Why Do Crystal Oscillators Fail?

Oscillator Selection Considerations: 

7-9  Frequency accuracy or reproducibility requirement  Recalibration interval  Environmental extremes  Power availability - must it operate from batteries?  Allowable warmup time  Short term stability (phase noise) requirements  Size and weight constraints  Cost to be minimized - acquisition or life cycle cost Oscillator Selection Considerations

Crystal Oscillator Specification: MIL-PRF-55310: 

7-10 MIL-PRF-55310D 15 March 1998 ----------------------- SUPERSEDING MIL-0-55310C 15 Mar 1994 PERFORMANCE SPECIFICATION OSCILLATOR, CRYSTAL CONTROLLED GENERAL SPECIFICATION FOR This specification is approved for use by all Departments and Agencies of the Department of Defense. 1. SCOPE 1.1 Statement of scope. This specification covers the general requirements for quartz crystal oscillators used in electronic equipment. ---------------------------------- Full text version is available via a link from <http:\\www.ieee.org/uffc/fc> Crystal Oscillator Specification: MIL-PRF-55310

CHAPTER 8Time and Timekeeping: 

8 CHAPTER 8 Time and Timekeeping

What Is Time?: 

What Is Time?

Dictionary Definition of “Time”: 

(From The Random House Dictionary of the English Language 1987) 8-2 Dictionary Definition of “Time”

The Second: 

The Second

Frequency and Time: 

8-4 where f = frequency (= number of “events” per unit time), and  = period (= time between “events”) Frequency source + counting mechanism  clock Examples of frequency sources: the rotating earth, pendulum, quartz crystal oscillator, and atomic frequency standard. Frequency and Time

Typical Clock System: 

t = t0 +  Where t is the time output, t0 is the initial setting, and  is the time interval being counted. 8-5 Frequency Source Counting Mechanism Setting Mechanism Synchronization Mechanism Display or Time code Typical Clock System

Evolution of Clock Technologies: 

Evolution of Clock Technologies

Progress in Timekeeping: 

8-7 Progress in Timekeeping

Clock Errors: 

8-8 T(t) = T0 + R(t)dt + (t) = T0 + (R0t + 1/2At2 + …) + Ei(t)dt +(t) Where, T(t) = time difference between two clocks at time t after synchronization T0 = synchronization error at t = 0 R(t) = the rate (i.e., fractional frequency) difference between the two clocks under comparison; R(t) = R0 + At + …Ei(t) (t) = error due to random fluctuations = y() R0 = R(t) at t = 0 A = aging term (higher order terms are included if the aging is not linear) Ei(t) = rate difference due to environmental effects (temperature, etc.) - - - - - - - - - - - - - - Example: If a watch is set to within 0.5 seconds of a time tone (T0 = 0.5 s), and the watch initially gains 2 s/week (R0 = 2 s/week), and the watch rate ages -0.1 s per week2, (A = -0.1 s/week2), then after 10 weeks (and assuming Ei(t) = 0): T (10 weeks) = 0.5 (2 x 10) + 1/2(-0.1 x (10)2) = 15.5 seconds. Clock Errors

Frequency Error vs. Time Error: 

8-9 fr = reference (i.e., the “correct”) frequency Frequency t Time Error 1 2 3 t 1 2 3 fr t Frequency Time Error t fr Frequency Time Error t t fr 3 t Time Error 1 2 t fr 1 2 3 Frequency Frequency Error vs. Time Error

Clock Error vs. Resynchronization Interval: 

8-10 Avg. Temp. Stab. Aging/Day Resynch Interval* (A/J & security) Recalibr. Interval * (Maintenance cost) TCXO 1 x 10-6 1 x 10-8 10 min 10 yrs 4 hrs 80 days OCXO 2 x 10-8 1 x 10-10 6 hours 50 years 4 days 1.5 yrs MCXO 2 x 10-8 5 x 10-11 4 days 3 yrs 6 hours 94 yrs RbXO 2 x 10-8 5 x 10-13 6 hours None needed 4 days 300 yrs * Calculated for an accuracy requirement of 25 milliseconds. Many modern systems need much better. 25 20 15 10 5 0 10 20 30 40 50 60 70 80 90 100 Days Since Calibration Time Error (ms) Aging/Day = 5 x 10-10 Temp Stability = 2 x 10-8 Resync Interval = 4 days Clock Error vs. Resynchronization Interval

Time Error vs. Elapsed Time: 

8-11 10 s 1 s 100 ms 10 ms 1 ms 100 s 10 s 1 s 10 30 1 2 4 8 16 1 2 3 4 5 6 1 2 3 1 2 4 1 minutes hour day week MONTH YEAR Elapsed Time Accumulated Time Error Aging rates are per day OFFSET 1 X 10-5 OFFSET 1 X 10-6 OFFSET 1 X 10-7 OFFSET 1 X 10-8 OFFSET 1 X 10-9 OFFSET 1 X 10-10 OFFSET 1 X 10-11 AGING 1 X 10-5 AGING 1 X 10-6 AGING 1 X 10-7 AGING 1 X 10-8 AGING 1 X 10-9 AGING 1 X 10-10 AGING 1 X 10-11 AGING 1 X 10-12 AGING 1 X 10-4 Time Error vs. Elapsed Time

Synchronization, Syntonization: 

8-12 Clocks are synchronized* when - They are in agreement as to the time, or - Output signals or data streams agree in phase, or - Sync patterns are in alignment   Clocks/oscillators are syntonized** when - Oscillators have the “same” frequency (the output signals need not be in phase) - Clocks run at the same rate (the internal oscillators need not be of the same frequency) * Chron  time ** Tone  frequency Synchronization, Syntonization

On Using Time for Clock Rate Calibration: 

8-13 It takes time to measure the clock rate (i.e., frequency) difference between two clocks. The smaller the rate difference between a clock to be calibrated and a reference clock, the longer it takes to measure the difference (t/t  f/f). For example, assume that a reference timing source (e.g., Loran or GPS) with a random time uncertainty of 100 ns is used to calibrate the rate of a clock to 1 x 10-11 accuracy. A frequency offset of 1 x 10-11 will produce1 x 10-11 x 3600 s/hour = 36 ns time error per hour. Then, to have a high certainty that the measured time difference is due to the frequency offset rather than the reference clock uncertainty, one must accumulate a sufficient amount (100 ns) of time error. It will take hours to perform the calibration. (See the next page for a different example.) If one wishes to know the frequency offset to a ±1 x 10-12 precision, then the calibration will take more than a day. Of course, if one has a cesium standard for frequency reference, then, for example, with a high resolution frequency counter, one can make frequency comparisons of the same precision much faster. On Using Time for Clock Rate Calibration

Calibration With a 1 pps Reference: 

Calibration With a 1 pps Reference

Time Transfer Methods: 

Time Transfer Methods

Global Positioning System (GPS): 

8-16 GPS Nominal Constellation: 24 satellites in 6 orbital planes, 4 satellites in each plane, 20,200 km altitude, 55 degree inclinations Global Positioning System (GPS)

GPS: 

GPS

Oscillator’s Impact on GPS: 

Oscillator’s Impact on GPS

Time Scales: 

Time Scales

Clock Ensembles and Time Scales: 

Clock Ensembles and Time Scales

Relativistic Time: 

Relativistic Time

Relativistic Time Effects: 

8-22 Transporting "perfect" clocks slowly around the surface of the earth along the equator yields t = -207 ns eastward and t = +207 ns westward (portable clock is late eastward). The effect is due to the earth's rotation. At latitude 40o, for example, the rate of a clock will change by 1.091 x 10-13 per kilometer above sea level. Moving a clock from sea level to 1km elevation makes it gain 9.4 nsec/day at that latitude. In 1971, atomic clocks flown eastward then westward around the world in airlines demonstrated relativistic time effects; eastward t = -59 ns, westward t = +273 ns; both values agreed with prediction to within the experimental uncertainties. Spacecraft Examples: For a space shuttle in a 325 km orbit, t = tspace - tground = -25 sec/day For GPS satellites (12 hr period circular orbits), t = +38.5 sec/day In precise time and frequency comparisons, relativistic effects must be included in the comparison procedures. Relativistic Time Effects

Relativistic Time Corrections: 

Relativistic Time Corrections

Some Useful Relationships: 

8-24 Propagation delay = 1 ns/30 cm = 1 ns/ft = 3.3 s/km  5 s/mile 1 day = 86,400 seconds; 1 year = 31.5 million seconds Clock accuracy: 1 ms/day  1 x 10-8 At 10 MHz: period = 100 ns; phase deviation of 1° = 0.3 ns of time deviation Doppler shift* = f/f = 2v/c -------------------------------------- * Doppler shift example: if v = 4 km/h and f = 10 GHz (e.g., a slow-moving vehicle approaching an X-band radar), then f = 74 Hz, i.e., an oscillator with low phase noise at 74Hz from the carrier is necessary in order to "see" the vehicle. Some Useful Relationships

One Pulse-Per-Second Timing Signal(MIL-STD-188-115): 

8-25 "The leading edge of the BCD code (negative going transitions after extended high level) shall coincide with the on-time (positive going transition) edge of the one pulse-per-second signal to within ±1 millisecond." See next page for the MIL-STD BCD code. 10 Volts ( 10%) 0 Volts ( 1 Volt Rise Time < 20 Nanoseconds Fall Time < 1 Microseconds 20 sec  5% One Pulse-Per-Second Timing Signal (MIL-STD-188-115)

BCD Time Code(MIL-STD-188-115): 

Level Held Hi Until Start of Next Code- Word Example: Selected Time is 12:34:56 Level Held Hi Until Start of Code- Word 20 msec LLLH 8421 LLHL 8421 LLHH 8421 LHLL 8421 LHLH 8421 LHHL 8421 Hours Minutes Seconds 1 2 3 4 5 6 Rate: 50 Bits per Second Bit Pulse Width: 20 msec H = +6V dc  1V L = -6V dc  1V 8 4 2 1 BCD Time Code (MIL-STD-188-115)

Time and Frequency Subsystem: 

8-27 Oscillator and Clock Driver Power Source Time Code Generator Frequency Distribution f1 f2 f3 TOD 1 pps Time and Frequency Subsystem

The MIFTTI SubsystemMIFTTI = Modular Intelligent Frequency, Time and Time Interval: 

8-28 * The microcomputer compensates for systematic effects (after filtering random effects), and performs: automatic synchronization and calibration when an external reference is available, and built-in-testing. External Reference Oscillator/ Clock-Driver Microcomputer Compensation and Control Frequency Distribution Clock and Time code Generator Battery DC-DC Converter > Vin V1 V2 f1 f2 f3 TOD 1pps The MIFTTI Subsystem MIFTTI = Modular Intelligent Frequency, Time and Time Interval

"Time" Quotations: 

8-29  3 o'clock is always too late or too early for anything you want to do..................Jean-Paul Sartre  Time ripens all things. No man's born wise............Cervantes.  Time is the rider that breaks youth............George Herbert  Time wounds all heels..................Jane Ace  Time heals all wounds..................Proverb  The hardest time to tell: when to stop.....Malcolm Forbes  Time is on our side..................William E. Gladstone  It takes time to save time.............Joe Taylor  Time, whose tooth gnaws away everything else, is powerless against truth..................Thomas H. Huxley  Time has a wonderful way of weeding out the trivial..................Richard Ben Sapir  Time is a file that wears and makes no noise...........English proverb  The trouble with life is that there are so many beautiful women - and so little time..................John Barrymore  Life is too short, and the time we waste yawning can never be regained..................Stendahl  Time goes by: reputation increases, ability declines..................Dag Hammarskjöld  Remember that time is money...............Benjamin Franklin  Time is money - says the vulgarest saw known to any age or people. Turn it around, and you get a precious truth - Money is time..................George (Robert) Gissing  The butterfly counts not months but moments, and has time enough..................Rabindranath Tagore  Everywhere is walking distance if you have the time..................Steven Wright  The only true time which a man can properly call his own, is that which he has all to himself; the rest, though in some sense he may be said to live it, is other people's time, not his..................Charles Lamb  It is familiarity with life that makes time speed quickly. When every day is a step in the unknown, as for children, the days are long with gathering of experience..................George Gissing  Time is a great teacher, but unfortunately it kills all its pupils..................Hector Berlioz  To everything there is a season, and a time to every purpose under the heaven..................Ecclesiastes 3:1  Time goes, you say? Ah no! Time stays, we go..................Henry Austin Dobson "Time" Quotations

Units of Measurement Having Special Namesin the International System of Units (SI): 

SI Base Units Mass kilogram Length meter Time second Electric Current ampere Luminous Intensity candela kg m s A Temperature kelvin K cd Amount of Substance mole mol SI Derived Units kg m2s-2 Energy joule J kg m s-3 Power watt W s-1 Activity becquerel Bq m2s-1 Absorbed Dose gray Gy m2s-2 Dose Equivalent sievert Sv kg m s-2 Force newton N kg m-1s-2 Pressure pascal Pa kg m2s-3 A-1 Electric Potential volt V kg-1 m2s4 A2 Capacitance farad F kg-1 m2s3 A2 Conductance siemens S kg s-2 A-1 Conductance siemens S S Coordinated Time international atomic time TAI s-1 Frequency hertz Hz S A Electric charge coulomb C kg m2s-3A-2 Resistance ohm  kg m2s-2A-1 Magnetic Flux weber Wb kg m2s-2A-2 Inductance henry H K Celsius Temperature 0Celsius 0C cd sr Luminous Flux lumen lm m-2cd sr Illuminance lux lx sr: the steradian is the supplementary SI unit of solid angle (dimensionless) rad: the radian is the supplementary SI unit of plane angle (dimensionless) Electromagnetic measurement units Health related measurement units Non-SI units recognized for use with SI day: 1 d = 86400 s hour: 1 h = 3600 s minute: 1 min = 60 s liter: 1 l = 10-3 m3 ton: 1 t = 103 kg degree: 10 = (/180) rad minute: 1’ = (/10800)rad second: 1” = (/648000)rad electronvolt: 1 eV  1.602177 x 10-19 J unified atomic mass unit: 1 u  1.660540 x 10-27 kg 8-30 Units of Measurement Having Special Names in the International System of Units (SI)

Units of Measurement Having Special Names in the SI Units, NOT Needing Standard Uncertainty in SI Average Frequency: 

8-31 Units of Measurement Having Special Names in the SI Units, NOT Needing Standard Uncertainty in SI Average Frequency

CHAPTER 9Related Devices and Application: 

9 CHAPTER 9 Related Devices and Application

Discrete-Resonator Crystal FilterA Typical Six-pole Narrow-band Filter: 

Layout Circuit Discrete-Resonator Crystal Filter A Typical Six-pole Narrow-band Filter

Monolithic Crystal Filters: 

25.0 20.0 15.0 10.0 5.0 0 Frequency Attenuation (dB) Four-pole filter electrode arrangement Two-pole filter and its response Monolithic Crystal Filters

Surface Acoustic Wave (SAW) Devices: 

9-3 BAW SAW, One-port SAW, Two-port Simplified Equivalent Circuits BAW and One-port SAW C0 C1 L1 R1 Two-port SAW C0 L1 C1 R1 C0 Surface Acoustic Wave (SAW) Devices

Quartz Bulk-Wave Resonator Sensors: 

Quartz Bulk-Wave Resonator Sensors

Tuning Fork Resonator Sensors: 

9-5 Photolithographically produced tuning forks, single- and double-ended (flexural-mode or torsional-mode), can provide low-cost, high-resolution sensors for measuring temperature, pressure, force, and acceleration. Shown are flexural-mode tuning forks. Tine Motion Force Force Beam Motion Tuning Fork Resonator Sensors

Dual Mode SC-cut Sensors: 

Dual Mode SC-cut Sensors Advantages - Self temperature sensing by dual mode operation allows separation/compensation of temp. effects - Thermal transient compensated - Isotropic stress compensated - Fewer activity dips than AT-cut - Less sensitive to circuit reactance changes - Less sensitive to drive level changes Disadvantage - Severe attenuation in a liquid - Fewer SC-cut suppliers than AT-cut suppliers 9-6

Separation of Mass and Temperature Effects: 

Separation of Mass and Temperature Effects Frequency changes Mass: adsorption and desorption Temperature/beat frequency 9-7

Dual-Mode Pressure Sensor: 

End Caps Electrode Resonator 9-8 Dual-Mode Pressure Sensor

Sensor Uncertainty (“Limit of Detection”): 

Sensor Uncertainty (“Limit of Detection”) 2-Sample Statistics: 2 * Allan Variance for continuous measurements (no dead-time) √2 * Allan Deviation for continuous measurements “Signal” “Limit of Detection” = Signal required for a desired SNR √2 * ADev  ~68% of the measurements have SNR >1 2*√2*ADev  ~95% of the measurements have SNR >1 3*√2*ADev  ~99% of the measurements have SNR >1 (i.e., ~1% probability that the “signal” is noise) 9-9

Sensor Stability in the Time Domain : 

9-10 In region 1, the white noise region, additional averaging (more data) improves the limit of detection. In region 2, flicker noise, it does not. In region 3, it makes it worse. For y() to be a proper measure of random frequency fluctuations, aging must be properly subtracted from the data at long ’s. y() Frequency noise Aging and random walk of frequency Short-term stability Long-term stability 1 s 1 m 1 h Sample time  Sensor Stability in the Time Domain 1 2 3

CHAPTER 10Proceedings Ordering Information, Standards, Website, and Index: 

10 CHAPTER 10 Proceedings Ordering Information, Standards, Website, and Index

IEEE International Frequency Control SymposiumPROCEEDINGS ORDERING INFORMATION: 

10-1 Please check with NTIS or IEEE for current pricing. IEEE members may order IEEE proceedings at half-price. *NTIS - National Technical Information Service *IEEE - Inst. of Electrical & Electronics Engineers 5285 Port Royal Road, Sills Building 445 Hoes Lane Springfield, VA 22161, U.S.A. Piscataway, NJ 08854, U.S.A. Tel: 703-487-4650 Fax: 703-321-8547 Tel: 800-678-4333 or 908-981-0060 E-mail: info@NTIS.fedworld.gov E-mail: customer.services@ieee.org http://www.fedworld.gov/ntis/search.htm http://www.ieee.org/ieeestore/ordinfo.html ______________________________________________________________________________ Prior to 1992, the Symposium’s name was the “Annual Symposium on Frequency Control,” and in 1992, the name was IEEE Frequency Control Symposium (i.e., without the “International”). NO. YEAR DOCUMENT NO. SOURCE* 10 1956 AD-298322 NTIS 11 1957 AD-298323 NTIS 12 1958 AD-298324 NTIS 13 1959 AD-298325 NTIS 14 1960 AD-246500 NTIS 15 1961 AD-265455 NTIS 16 1962 AD-285086 NTIS 17 1963 AD-423381 NTIS 18 1964 AD-450341 NTIS 19 1965 AD-471229 NTIS 20 1966 AD-800523 NTIS 21 1967 AD-659792 NTIS 22 1968 AD-844911 NTIS 23 1969 AD-746209 NTIS 24 1970 AD-746210 NTIS 25 1971 AD-746211 NTIS 26 1972 AD-771043 NTIS 27 1973 AD-771042 NTIS 28 1974 AD-A011113 NTIS 29 1975 AD-A017466 NTIS 30 1976 AD-A046089 NTIS 31 1977 AD-A088221 NTIS 32 1978 AD-A955718 NTIS 33 1979 AD-A213544 NTIS 34 1980 AD-A213670 NTIS 35 1981 AD-A110870 NTIS 36 1982 AD-A130811 NTIS 37 1983 AD-A136673 NTIS NO. YEAR DOCUMENT NO. SOURCE* 38 1984 AD-A217381 NTIS 39 1985 AD-A217404 NTIS 40 1986 AD-A235435 NTIS 41 1987 AD-A216858 NTIS 42 1988 AD-A217275 NTIS 43 1989 AD-A235629 NTIS 44 1990 AD-A272017 NTIS 45 1991 AD-A272274 NTIS 46 1992 92CH3083-3 IEEE 47 1993 93CH3244-1 IEEE 48 1994 94CH3446-2 IEEE 49 1995 95CH3575-2 IEEE 50 1996 96CH35935 IEEE 51 1997 97CH36016 IEEE 52 1998 98CH36165 IEEE 53 1999 99CH36313 IEEE 54 2000 00CH37052 IEEE 55 2001 01CH37218 IEEE 56 2002 02CH37234 IEEE 57 2003 03CH37409 IEEE 58 2004 04CH37553C IEEE 59 2005 05CH37664 IEEE 60 2006 06CH37752 IEEE 61 2007 IEEE 62 2008 IEEE 63 2009 IEEE 64 2010 IEEE 65 2011 IEEE IEEE International Frequency Control Symposium PROCEEDINGS ORDERING INFORMATION

Specifications And Standards Relating To Frequency Control - 1: 

10-2  Institute Of Electrical & Electronic Engineers (IEEE)   Order from: IEEE Service Center 445 Hoes Lane Piscataway, NJ 08854 Telephone: (732) 981-0060 http://standards.ieee.org/catalog/contents.html   176-1987 (ANSI/IEEE) Standard on Piezoelectricity   177-1966 Standard Definitions & Methods of Measurements of Piezoelectric Vibrators   180-1986 (ANSI/IEEE) Definitions of Primary Ferroelectric Crystal Terms (SH10553)   319-1971 (Reaff 1978) Piezomagnetic Nomenclature (SH02360)   1139-1988 Standard Definitions of Physical Quantities for Fundamental Frequency & Time Metrology (SH12526) IEEE Std 1193-1994 (ANSI) IEEE Guide for Measurement of Environmental Sensitivities of Standard Frequency Generators Department of Defense (DOD)   Order from: Naval Pubs & Form Center 5801 Tabor Avenue Philadelphia, PA 19120 Telephone: (215) 697-2000 http://www.dscc.dla.mil/Programs/MilSpec/default.asp http://stinet.dtic.mil/str/dodiss4_fields.html     General Specs for:   MIL-C-3098 Crystal Unit, Quartz   MIL-C-24523 (SHIPS) Chronometer, Quartz Crystal MIL-F-15733 Filters & Capacitors, Radio Interference   MIL-F-18327 Filters, High Pass, Band Pass Suppression and Dual Processing   MIL-F-28861 Filters and Capacitors, Radio Frequency Electro-magnetic Interference Suppression   MIL-F-28811 Frequency Standard, Cesium Beam Tube   MIL-H-10056 Holders (Encl), Crystal   MIL-O-55310 Oscillators, Crystal MIL-O-39021 Oven   MIL-S-4933(ER) Surface Acoustic Wave Devices   MIL-STD-683 Crystal Units, Quartz/Holders, Crystal   MIL-STD-188-115 Interoperability & Performance Standards for Communications, Timing & Synchron­ization Subsystems   MIL-STD-1395 Filters & Networks, Selection & Use   MIL-T-28816(EC) Time Frequency Standard, Disciplined AN/URQ-23   MIL-W-46374D Watch, wrist: General purpose   MIL-W-87967 Watch, wrist: Digital   Specifications And Standards Relating To Frequency Control - 1

Specifications And Standards Relating To Frequency Control - 2: 

10-3 US Government Standards     FED-STD-1002 Time & Frequency Reference Information in Telecommunication Systems   Federal Standard 1037C: Glossary of Telecommunications Terms http://www.its.bldrdoc.gov/fs-1037/   IRIG Stdrd 200-98 - IRIG Serial Time Code Formats http://tecnet0.jcte.jcs.mil/RCC/manuals/200/index.htm l   A source of many standards:   American National Standards Institute (ANSI) 1819 L Street, NW Suite 600 Washington, DC 20036 http://webstore.ansi.org/ansidocstore/default.asp Electronic Industries Association (EIA)   Order from: Electronic Industries Assoc. 2001 Eye Street, NW Washington, DC 20006 Telephone: (202) 457-4900   (a) Holders and Sockets   EIA-192-A, Holder Outlines and Pin Connections for Quartz Crystal Units (standard dimensions for holder types)   EIA-367, Dimensional & Electrical Characteristics Defining Receiver Type Sockets (including crystal sockets)   EIA-417, Crystal Outlines (standard dimensions and pin connections for current quartz crystal units, 1974)   (b) Production Tests   EIA-186-E, (All Sections) Standard Test Methods for Electronic Component Parts EIA-512, Standard Methods for Measurement of Equivalent Electrical Parameters of Quartz Crystal Units, 1 kHz to 1 GHz, 1985   EIA-IS-17-A, Assessment of Outgoing Non­conforming Levels in Parts per Million (PPM)   EIA-IS-18, Lot Acceptance Procedure for Verifying Compliance with Specified Quality Level in PPM   (c) Application Information   EIA Components Bulletin No. CB6-A, Guide for the Use of Quartz Crystal Units for Frequency Control, Oct. 1987   (d) EIA-477, Cultured Quartz (Apr. 81)   EIA-477-1, Quartz Crystal Test Methods (May 1985) International Electro-Technical Commission (IEC)   Order from: American Nat'l. Standard Inst. (ANSI) 1430 Broadway New York NY 1001 Telephone: (212) 354-3300 http://webstore.ansi.org/ansidocstore/default.asp     IEC Publications Prepared by TC 49: Specifications And Standards Relating To Frequency Control - 2

Specifications And Standards Relating To Frequency Control - 3: 

10-4 122: Quartz crystal units for frequency control and selection   122-2 (1983) Part 2: Guide to the use of quartz crystal units for frequency control and selection   122-2-1 (1991) Section One: Quartz crystal units for microprocessor clock supply (Amendment 1 - 1993)   122-3 (1977) Part 3: Standard outlines and pin connection (Amendment 2 -1991, Amendment 3 - 1992, Amendment 4 - 1993)   283 (1986) Methods for the measurement of frequency and equivalent resistance of unwanted resonances of filter crystal units   302 (1969) Standard definitions and methods of measurement for piezoelectric vibrators operating over the frequency range up to 30 MHz   314 (1970) Temperature control devices for quartz crystal units (Amendment 1 - 1979)   314A (1971) First supplement   368: Piezoelectric Filters   368-l (1992) Part 1: General information, standard values and test conditions   368-2 (1973) Part 2: Guide to the use of piezoelectric filters   368-2-1 (1988) Section One - Quartz crystal filters   368B (1975) Second supplement   368-3 (1991) Part 3: Standard Outlines   444: Measurement of quartz crystal unit parameters   444-1 (1986) Part 1: Basic method for the measurement of resonance frequency and resonance resistance of quartz crystal units by zero phase technique in a  - network with compensation of the parallel capacitance Co   444-4 (1988) Part 4: Method for the measurement of the load resonance frequency fL, load resonance RL and the calculation of other derived values of quartz crystal units up 30 MHz   483 (1976) Guide to dynamic measurements of piezoelectric ceramics with high electromechanical coupling   642 (1979) Piezoelectric ceramic resonators and resonator units for frequency control and selection. Chapter I: Standard Values and Conditions Chapter II: Measuring and test conditions   642-2 (1994) Part 2: Guide to the use of piezoelectric ceramic resonator units   642-3 (1992) Part 3: Standard outlines   679: Quartz Crystal Controlled Oscillators   679-1 (1980) Part 1: General information, test conditions and methods (Amendment 1 - 1985)   679-2 (1981) Part 2: Guide to the use of quartz crystal controlled oscillators   679-3 (1989) Part 3: Standard outlines and lead connections (First supplement - 1991) (Amendment 1 - 1994) 689 (1980) Measurements and test methods for 32 kHz quartz crystal units for wrist watches and standard values   758 (1993) Synthetic quartz crystal; specifications and guide for use   Specifications And Standards Relating To Frequency Control - 3

Specifications And Standards Relating To Frequency Control - 4: 

10-5 862: Surface Acoustic Wave (SAW) Filters:   862-1 (1989) Part 1: General Information, standard values and test conditions, Chapter I: General information and standard values, Chapter II: Test conditions   862-2 (1991) Part 2: Guide to the use of surface acoustic wave filters (Chapter III)   862-3 (1986) Part 3: Standard outlines (Chapter IV)   1019: Surface Acoustic Wave (SAW) Resonators   1019-1-1 (1990) Part 1: General information, standard values and test conditions, Section 1 - General information and standard values   1019-1-2 (1993) Section 2: Test conditions   1019-1-3 (1991) Part 3: Standout outlines and lead connections 1080 (1991) Guide to the measurement of equivalent electrical parameters of quartz crystal units   1178-1 (1993) Quartz crystal units - a specification in the IEC Quality Assessment System for Electronic Components (IECQ) Part 1: General Specification   1178-2 (1993) Part 2: Sectional specification - Capability approval   1178-2-1 (1993) Part 2: Sectional specification - Capability approval, Section 1: Blank detail specification   1178-3 (1993) Part 3: Sectional specification - Qualification approval   1178-3-1 (1993) Part 3: Sectional specification - Qualification approval, Section 1: Blank detail specification   1240 (1994) Piezoelectric devices - preparation of outline drawings of surface-mounted devices (MSD) for frequency control and selection, general rules   1253: Piezoelectric ceramic resonators - a specification in the IEC quality assessment system for electronic components (IECQ)   1253-1 (1993) Part 1: Generic specification - qualification approval   1253-2 (1993) Part 2: Sectional specification - qualification approval   1253-2-1 (1993) Section 1 - Blank detail specification - Assessment Level E   1261: Piezoelectric Ceramic Filters for use in Electronic Equipment, a specification in the IEC quality assessment system for electronic components (IECQ)   1261-1 (1994) Part 1: General specifications, qualification approval   1261-2 (1994) Part 2: Sectional specifications, qualification approval   1261-2-1 (1994) Part 2: Section 1, Blank detail specification, Assessment Level E International Telecommunication Union   Time signals and frequency standards emissions, List of ITU-R Recommendations http://www.itu.int/rec/recommendation.asp?type=products&parent=R-REC-tf   Specifications And Standards Relating To Frequency Control - 4

IEEE Frequency Control Website: 

10-6 A huge amount of frequency control information can be found at www.ieee-uffc.org/fc Available at this website are >100K pages of information, including the full text of all the papers ever published in the Proceedings of the Frequency Control Symposium, i.e., since 1956, reference and tutorial information, ten complete books, historical information, and links to other web sites, including a directory of company web sites. Some of the information is openly available, and some is available to IEEE UFFC Society members only. To join, see www.ieee.org/join IEEE Frequency Control Website

IEEE Electronic Library: 

10-7 The IEEE/IEE Electronic Library (IEL) contains more than 1.2 million documents; almost a third of the world's electrical engineering and computer science literature. It features high-quality content from the Institute of Electrical and Electronics Engineers (IEEE) and the Institution of Electrical Engineers (IEE). Full-text access is provided to journals, magazines, transactions and conference proceedings as well as active IEEE standards. IEL includes robust search tools powered by the intuitive IEEE Xplore interface. www.ieee.org/ieeexplore IEEE Electronic Library