Quartz and Atomic Clocks March 2007 John R

Quartz and Atomic Clocks March 2007 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

Rev. 8. 5. 3. 6 Quartz Crystal Resonators and Oscillators For Frequency Control and Timing Applications - A Tutorial January 2007 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

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

Electronics Applications of Quartz Crystals Military & Aerospace Communications Navigation IFF Radar Sensors Guidance systems Fuzes Electronic warfare Sonobouys Industrial Communications Telecommunications Mobile/cellular/portable radio, telephone & pager Aviation Marine Navigation Instrumentation Computers Digital systems Research & Metrology CRT displays Disk drives Atomic clocks Modems Instruments Astronomy & geodesy Tagging/identification Utilities Space tracking Sensors Celestial navigation 1 -1 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

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

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

Clock for Very Fast Frequency Hopping Radio Example Jammer J t 1 Radio R 1 Let R 1 to R 2 = 1 km, R 1 to J =5 km, and J to R 2 = 5 km. Then, since propagation delay =3. 3 s/km, t 1 = t 2 = 16. 5 s, t. R = 3. 3 s, and tm < 30 s. Allowed clock error 0. 2 tm 6 s. t 2 t. R Radio R 2 To defeat a “perfect” follower jammer, one needs a hop-rate given by: For a 4 hour resynch interval, clock accuracy requirement is: 4 X 10 -10 tm < (t 1 + t 2) - t. R where tm message duration/hop 1/hop-rate 1 -13

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

Bistatic Radar Conventional (i. e. , "monostatic") radar, in which the Illuminator 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 (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 Target 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. 1 -17

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

Oscillation At the frequency of oscillation, the closed loop phase shift = 2 n. 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. 2 -2

Oscillator Acronyms 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 Rb. XO………. Rubidium-Crystal Oscillator 2 -5

Crystal Oscillator Categories +10 ppm Voltage Tune 250 C Output Crystal Oscillator (XO) Temperature Sensor Compensation Network or Computer +1000 C -450 C T -10 ppm -450 C +1 ppm +1000 C T XO -1 ppm Temperature Compensated (TCXO) Oven control XO Temperature Sensor -450 C +1 x 10 -8 +1000 C T -1 x 10 -8 Oven Controlled (OCXO) 2 -7

Hierarchy of Oscillators Oscillator Type* Crystal oscillator (XO) Temperature compensated Accuracy** Typical Applications 10 -5 to 10 -4 Computer timing 10 -6 Frequency control in tactical radios 10 -8 to 10 -7 Spread spectrum system clock 10 -8 (with 10 -10 per g option) Navigation system clock & frequency standard, MTI radar Small atomic frequency 10 -9 C 3 satellite terminals, bistatic, & multistatic radar High performance atomic 10 -12 to 10 -11 Strategic C 3, EW crystal oscillator (TCXO) Microcomputer compensated crystal oscillator (MCXO) Oven controlled crystal oscillator (OCXO) standard (Rb, Rb. XO) standard (Cs) * Sizes range from <5 cm 3 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. , -40 o. C to +75 o. C) and one year of aging. 2 -8

Silicon Resonator & Oscillator www. Si. Time. com Resonator (Si): 0. 2 x 0. 01 mm 3 5 MHz; f vs. T: -30 ppm/o. C Oscillator (CMOS): 2. 0 x 2. 5 x 0. 85 mm 3 • ± 50 ppm, ± 100 ppm; -45 to +85 o. C (± 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

Why Quartz? Quartz is the only material known that possesses the following combination of properties: • Piezoelectric ("pressure-electric"; piezein = to press, in Greek) • Zero temperature coefficient cuts exist • Stress compensated cut exists • Low loss (i. e. , high Q) • Easy to process; low solubility in everything, under "normal" conditions, except the fluoride and hot alkali etchants; hard but not brittle • Abundant in nature; easy to grow in large quantities, at low cost, and with relatively high purity and perfection. Of the man-grown single crystals, quartz, at ~3, 000 tons per year, is second only to silicon in quantity grown (3 to 4 times as much Si is grown annually, as of 1997). 3 -1

Hydrothermal Growth of Quartz Cover Closure area Growth zone, T 1 Nutrient dissolving zone, T 2 Autoclave The autoclave is filled to some predetermined factor with water plus mineralizer (Na. OH or Na 2 CO 3). The baffle localizes the temperature gradient so that each zone is nearly isothermal. The seeds are thin slices of (usually) Z-cut single crystals. Seeds Baffle Solutenutrient Nutrient T 2 > T 1 5 -1 The nutrient consists of small (~2½ to 4 cm) pieces of single-crystal quartz (“lascas”). The temperatures and pressures are typically about 3500 C and 800 to 2, 000 atmospheres; T 2 - T 1 is typically 40 C to 100 C. The nutrient dissolves slowly (30 to 260 days per run), diffuses to the growth zone, and deposits onto the seeds.

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

Resonator Vibration Amplitude Distribution Metallic electrodes Resonator plate substrate (the “blank”) u Conventional resonator geometry and amplitude distribution, u 3 -5

Quartz is Highly Anisotropic The properties of quartz vary greatly with crystallographic direction. For example, when a quartz sphere is etched deeply in HF, the sphere takes on a triangular shape when viewed along the Z-axis, and a lenticular shape when viewed along the Y-axis. The etching rate is more than 100 times faster along the fastest etching rate direction (the Z-direction) than along the slowest direction (the slow-X-direction). The thermal expansion coefficient is 7. 8 x 10 -6/ C along the Zdirection, and 14. 3 x 10 -6/ C perpendicular to the Z-direction; the temperature coefficient of density is, therefore, -36. 4 x 10 -6/ C. The temperature coefficients of the elastic constants range from -3300 x 10 -6/ C (for C 12) to +164 x 10 -6/ C (for C 66). For the proper angles of cut, the sum of the first two terms in Tf on the previous page is cancelled by the third term, i. e. , temperature compensated cuts exist in quartz. (See next page. ) 3 -12

Zero Temperature Coefficient Quartz Cuts 90 o 60 o AT 30 o FC SC LC 0 -30 o z IT SBTC BT -60 o -90 o gly d n i S tate Ro t Cu Do ub Ro ly tat Cu ed t 0 o y 10 o 30 o The AT, FC, IT, SC, BT, and SBTC-cuts are some of the cuts on the locus of zero temperature coefficient cuts. The LC is a “linear coefficient” cut that has been used in a quartz thermometer. x 20 o Y-cut: +90 ppm/0 C (thickness-shear mode) xl X-cut: -20 ppm/0 C (extensional mode) 3 -13

Equivalent Circuits Spring C Mass L Dashpot R 3 -21

Equivalent Circuit of a Resonator Symbol for crystal unit CL C 0 CL C 1 L 1 R 1 { 3 -22 1. Voltage control (VCXO) 2. Temperature compensation (TCXO)

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

What is Q and Why is it Important? 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/Q 4 for quartz oscillators). 3 -26

Precision Frequency Standards Quartz crystal resonator-based (f ~ 5 MHz, Q ~ 106) Atomic resonator-based Rubidium cell (f 0 = 6. 8 GHz, Q ~ 107) Cesium beam (f 0 = 9. 2 GHz, Q ~ 108) Hydrogen maser (f 0 = 1. 4 GHz, Q ~ 109) Trapped ions (f 0 > 10 GHz, Q > 1011) Cesium fountain (f 0 = 9. 2 GHz, Q ~ 5 x 1011) 6 -1

Atomic Frequency Standard Basic Concepts 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 E 2 and E 1 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. 6 -2

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

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

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

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

The Units of Stability in Perspective 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 d. BW, 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 d. B? (As in -170 d. Bc/Hz phase noise. ) -170 d. B = 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. 4 -1

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

Influences on Oscillator Frequency Time • Short term (noise) • Intermediate term (e. g. , due to oven fluctuations) • Long term (aging) Temperature • Static frequency vs. temperature • Dynamic frequency vs. temperature (warmup, thermal shock) • Thermal history ("hysteresis, " "retrace") Acceleration • Gravity (2 g tipover) • Vibration Ionizing radiation • Steady state • Pulsed • Acoustic noise • Shock • Photons (X-rays, -rays) • Particles (neutrons, protons, electrons) Other • Power supply voltage • Atmospheric pressure (altitude) • Humidity • Load impedance 4 -3 • Magnetic field

Idealized Frequency-Time-Influence Behavior 3 Temperature Step Vibration Shock Oscillator Turn Off 2 -g & Tipover Turn On Radiation Off 2 Aging 1 0 -1 On -2 Short-Term Instability -3 t 0 t 1 t 2 t 3 t 4 4 -4 t 5 t 6 t 7 t 8 Time

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

Aging Mechanisms Mass transfer due to contamination Since f 1/t, f/f = - t/t; e. g. , f 5 MHz 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 4 -6

Typical Aging Behaviors A(t) = 5 ln(0. 5 t+1) f/f Time A(t) +B(t) = -35 ln(0. 006 t+1) 4 -7

Short-Term Stability Measures Measure Symbol Two-sample deviation, also called “Allan deviation” Spectral density of phase deviations Spectral density of fractional frequency deviations Phase noise y( )* S (f) Sy(f) L(f)* * Most frequently found on oscillator specification sheets f 2 S (f) = 2 Sy(f); L(f) ½ [S (f)] (per IEEE Std. 1139), and Where = averaging time, = carrier frequency, and f = offset or Fourier frequency, or “frequency from the carrier”. 4 -21

Frequency Noise and y( ) 3 X 10 -11 0. 1 s averaging time 0 100 s -3 X 10 -11 1. 0 s averaging time 0 100 s -3 X 10 -11 y( ) 10 -10 10 -11 10 -12 0. 01 1 0. 1 4 -24 10 100 Averaging time, , s

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

Acceleration vs. Frequency Change Z’ A 5 A 2 A 4 A 1 O A 3 A 6 A 2 Y’ A 3 Crystal plate G A 5 X’ Supports A 4 A 6 A 1 Frequency shift is a function of the magnitude and direction of the acceleration, and is usually linear with magnitude up to at least 50 g’s. 4 -62

Acceleration Is Everywhere Environment Acceleration f/f typical levels*, in g’s x 10 -11, for 1 x 10 -9/g oscillator Buildings**, quiesent 0. 02 rms 2 Tractor-trailer (3 -80 Hz) 0. 2 peak 20 Armored personnel carrier 0. 5 to 3 rms 50 to 300 Ship - calm seas 0. 02 to 0. 1 peak 2 to 10 Ship - rough seas 0. 8 peak 80 Propeller aircraft 0. 3 to 5 rms 30 to 500 Helicopter 0. 1 to 7 rms 10 to 700 Jet aircraft 0. 02 to 2 rms 2 to 200 Missile - boost phase 15 peak 1, 500 Railroads 0. 1 to 1 peak 10 to 100 Spacecraft Up to 0. 2 peak 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 4 -63

Vibration-Induced Sidebands 0 NOTE: the “sidebands” are spectral lines at f. V from the carrier frequency (where f. V = vibration frequency). The -10 lines are broadened because of the finite bandwidth of the spectrum analyzer. -20 L(f) -30 10 g amplitude @ 100 Hz = 1. 4 x 10 -9 per g -40 -50 -60 -70 -80 -90 4 -70 f 250 200 150 100 50 0 -50 -100 -150 -200 -250 -100

Clock Accuracy vs. Power Requirement* (Goal of R&D is to move technologies toward the upper left) 10 -12 Cs Accuracy 10 -10 Rb 10 -8 0. 001 1 ms/day 1 s/year OCXO TCXO 10 -6 10 -4 1 s/day 1 ms/year 1 s/day XO 0. 01 0. 1 1 Power (W) 10 100 * Accuracy vs. , size, and accuracy vs. cost have similar relationships 7 -2

IEEE Frequency Control Website A huge amount of frequency control information can be found at www. ieee-uffc. org/fc Available at this website are >100 K 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 10 -6

IEEE Electronic Library 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 10 -7