Quartz Resonator

1
Quartz Crystal Resonators and Oscillators
John R. Vig US Army Communications-Electronics
Research, Development Engineering Center Fort
Monmouth, NJ, USA J.Vig_at_IEEE.org
2
Electronics Applications of Quartz Crystals
3
Frequency Control Device Market
(as of 2001)
1-2
4
Impacts of Oscillator Technology Improvements

• 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)

1-11
5
Crystal Oscillator
Tuning Voltage
Crystal resonator
Output Frequency
Amplifier
2-1
6
Oscillation

• 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.

2-2
7
Oscillator Acronyms

• Most Commonly Used
• XO..Crystal Oscillator
• VCXOVoltage Controlled Crystal Oscillator
• OCXOOven Controlled Crystal Oscillator
• TCXOTemperature Compensated Crystal
  Oscillator
• Others
• TCVCXO..Temperature Compensated/Voltage
  Controlled Crystal Oscillator
• OCVCXO..Oven Controlled/Voltage Controlled
  Crystal Oscillator
• MCXOMicrocomputer Compensated Crystal
  Oscillator
• RbXO.Rubidium-Crystal Oscillator

2-5
8
Crystal Oscillator Categories
10 ppm
Voltage Tune
250C
-450C
1000C
Output
T
? Crystal Oscillator (XO)
-10 ppm
Temperature Sensor
Compensation Network or Computer
1 ppm
-450C
XO
-1 ppm
? Temperature Compensated (TCXO)
Oven
XO
Oven control
Temperature Sensor
? Oven Controlled (OCXO)
2-7
9
Hierarchy of Oscillators

• 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 Spre
ad 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 lt5cm3 for clock oscillators
to gt 30 liters for Cs standards Costs range
from lt5 for clock oscillators to gt 50,000 for
Cs standards. Including environmental
effects (e.g., -40oC to 75oC) and one year of
aging.
2-8
10
Why Quartz?
11
Hydrothermal Growth of Quartz

• 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
Growth zone, T1
Seeds
Baffle
Nutrient dissolving zone, T2
Solute- nutrient
Nutrient
T2 gt T1
5-1
12
Quartz is Highly Anisotropic
13
Deeply Dissolved Quartz Sphere
Anisotropic Etching
Z
X
Looking along Y-axis
Looking along Z-axis
5-2
14
The Piezoelectric Effect in Quartz
Z
X
Y
15
Modes of Motion(Click on the mode names to see
animation.)
Flexure Mode
Extensional Mode
Face Shear Mode
Fundamental Mode Thickness Shear
Third Overtone Thickness Shear
Thickness Shear Mode
3-4
16
Resonator Vibration Amplitude Distribution
Metallic electrodes
Resonator plate substrate (the blank)
u
Conventional resonator geometry and amplitude
distribution, u
17
Motion Of A Thickness Shear Crystal
CLICK ON FIGURE TO START MOTION
18
Resonant Vibrations of a Quartz Plate
X-ray topographs (210 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.
3-6
19
Overtone Response of a Quartz Crystal
jX
Spurious responses
Spurious responses
Spurious responses
Reactance
0
Frequency
5th overtone
3rd overtone
-jX
Fundamental mode
3-7
20
Zero Temperature Coefficient Quartz Cuts
90o
60o
FC
IT
AT
30o
SC
LC
?
0
SBTC
-30o
BT
-60o
-90o
0o
10o
20o
30o
?
Singly Rotated Cut
Doubly Rotated Cut
21
Comparison of SC and AT-cuts

• 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)

3-14
22
Resonator Packaging
Two-point Mount Package
Three- and Four-point Mount Package
Quartz blank
Electrodes
Quartz blank
Bonding area
Bonding area
Cover
Mounting clips
Cover
Mounting clips
Seal
Base
Pins
Seal
Pins
Base
Top view of cover
3-20
23
Equivalent Circuits
Spring
C
L
Mass
R
Dashpot
24
Equivalent Circuit of a Resonator
CL
Symbol for crystal unit
C0
CL
L1
R1
C1

1. Voltage control (VCXO) 2. Temperature
compensation (TCXO)
3-22
25
Crystal Oscillator f vs. T Compensation
Uncompensated frequency
Frequency / Voltage
T
Compensated frequency of TCXO
Compensating voltage on varactor CL
3-23
26
Resonator Reactance vs. Frequency
Area of usual operation in an oscillator

Resonance, fr
Antiresonance, fa
Reactance
0
Frequency
-
3-24
27
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/Q4 for quartz
  oscillators).

3-26
28
Decay Time, Linewidth, and Q
Decaying oscillation of a resonator
Oscillation
TIME
Exciting pulse ends
Max. intensity
td
Resonance behavior of a resonator
Maximum intensity
BW
½ Maximum intensity
FREQUENCY
3-27
29
Factors that Determine Resonator Q
30
Why 32,768 Hz?
31
Quartz Tuning Fork
Z
Y
X
a) natural faces and crystallographic axes of
quartz
Z
Y
050
Y
arm
base
X
b) crystallographic orientation of tuning fork
c) vibration mode of tuning fork
3-37
32
Watch Crystal
3-38
33
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 dBW, is as bright as a flashlight in Los
  Angeles would look in New York City, 5000 km
  away (neglecting earths 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.

4-1
34
Accuracy, Precision, and Stability
Accurate but not precise
Not accurate and not precise
Accurate and precise
Precise but not accurate
f
f
f
f
0
Time
Time
Time
Time
Accurate (on the average) but not stable
Stable but not accurate
Not stable and not accurate
Stable and accurate
4-2
35
Influences on Oscillator Frequency
36
Idealized Frequency-Time-Influence Behavior
Oscillator Turn Off Turn On
2-g Tipover
Temperature Step
Radiation
Vibration
Shock
3
Off
2
Aging
1
0
-1
On
-2
Short-Term Instability
-3
t5
t6
t7
t8
t0
t1
t2
t3
t4
Time
4-4
37
Aging and Short-Term Stability
Short-term instability (Noise)
30
25
20
?f/f (ppm)
15
10
Time (days)
10
15
20
25
5
4-5
38
Aging Mechanisms
? Mass transfer due to contamination
Since f ? 1/t, ?f/f -?t/t e.g., f5MHz ? 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
39
Typical Aging Behaviors
A(t) 5 ln(0.5t1)
Time
?f/f
A(t) B(t)
B(t) -35 ln(0.006t1)
4-7
40
Force-Frequency Coefficient
30
10-15 m ? s / N
AT-cut quartz
25
20
15
Z
F
10
?
X
Kf (?)
5
F
0
-5
-10
-15
?
00
100
200
300
400
500
600
700
800
900
41
Bonding Strains Induced Frequency Changes
6
Blank No. 7
Z
5
Blank No. 8
4
?
X
3
Apparent angle shift (minutes)
2
?
1
0
-1
-2
300
600
900
Bonding orientation, ?
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.
4-14
42
Bending Force vs. Frequency Change
AT-cut resonator
SC-cut resonator
fo 10Mz
fo 10Mz
30
5gf
5gf





10










20





























Frequency Change (Hz)



Frequency Change (Hz)



360



240
120
180
60
300












10
Azimuth angle ? (degrees)




-10
0
240
120
180
60
300
360
Azimuth angle ? (degrees)
Frequency change for symmetrical bending, SC-cut
crystal.
Frequency change for symmetrical bending, AT-cut
crystal.
4-15
43
Frequency Noise and ?y(?)
0.1 s averaging time
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
0.1
1
10
100
Averaging time, ?, s
4-24
44
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
45
Causes of Short Term Instabilities
46
Noise in Crystal Oscillators
? 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. ? 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
lt 1 kHz, SAW is lower noise at f gt 1
kHz can phase lock the two to get the best of
both.
4-36
47
TCXO Noise
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 crystals
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 Ts, so the stability can be
good there, but millidegree fluctuations will
cause 10-9 f fluctuations at the T extremes.
The TCXOs 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 Ts 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.
4-40
48
Quartz Wristwatch Accuracy vs. Temperature
Temperature coefficient of frequency -0.035
ppm/0C2
0
Time Error per Day (seconds)
10
20
-100C Winter
490C Desert
-550C Military Cold
280C Wrist Temp.
850C Military Hot
49
Frequency vs. Temperature Characteristics
f (LTP)
Inflection Point
Frequency
f (UTP)
Temperature
Upper Turnover Point (UTP)
Lower Turnover Point (LTP)
50
Resonator f vs. T Determining Factors
51
Frequency-Temperature vs. Angle-of-Cut, AT-cut
Z
AT-cut
BT-cut
25
49o
??
35¼o
R
20
r
R
8
m
Y
m
R
-1
r
R
15
7
0
6
Z
10
Y-bar quartz
1
5
5
(ppm)
2
4
0
3
?f f
3
-5
2
4
1
-10
5
0
? 35o 20 ??, ? 0 for 5th overtone AT-cut ?
35o 12.5 ??, ? 0 for fundamental mode
plano-plano AT-cut
-15
6
-1
-20
7
8
-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
Temperature (oC)
4-44
52
OCXO Ovens Effect on Stability
TURNOVER POINT
OVEN SET POINT
Frequency
TURNOVER POINT
OVEN OFFSET
2? To
Typical f vs. T characteristic for AT and SC-cut
resonators
OVEN CYCLING RANGE
Temperature
Oven Parameters vs. Stability for SC-cut
Oscillator Assuming Ti - TLTP 100C
100 10 1 0.1 0
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.
4-46
53
Warmup of AT- and SC-cut Resonators
10-3
10-4
10-5

Deviation from static f vs. t , where,
for example, ?-2 x 10-7 s/K2 for a typical
AT-cut resonator
10-6
10-7
Fractional Frequency Deviation From Turnover
Frequency
10-8
0
3
6
9
12
15
Time (min)
-10-8
Oven Warmup Time
-10-7
-10-6
4-48
54
TCXO Thermal Hysteresis
1.0
0.5
Fractional Frequency Error (ppm)
0.0
-25
-5
15
35
55
75
Temperature (0C)
-0.5
TCXO Temperature Compensated Crystal Oscillator
-1.0
55
OCXO Retrace
15
14 days
10
OVEN OFF
5
(a)
OVEN ON
0
X 10-9
15
14 days
10
OSCILLATOR OFF
5
(b)
OSCILLATOR ON
0
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.
4-51
56
TCXO Trim Effect
2
-6 ppm aging adjustment
1
0
15
-5
T (0C)
35
55
75
-25
-1
6 ppm aging adjustment
In TCXOs, 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.)
4-52
57
Why the Trim Effect?
Compensated f vs. T
CL
Compensating CL vs. T
58
Effects of Harmonics on f vs. T
50
40
30
20
?
10
5
0
3
(ppm)
-10
1
-20
M
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)
-30
-40
-50
?T, 0C
-100
-80
-40
-20
-0
20
40
60
80
-60
4-55
59
Activity Dips
fL2
fL1
10 X10-6
Frequency
fR
RL2
RL1
Resistance
R1
-40
-20
0
20
40
60
80
100
Temperature (0C)
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.
4-59
60
Activity Dips
fL2
fL1
10 X10-6
Frequency
fR
RL2
RL1
Resistance
R1
-40
-20
0
20
40
60
80
100
Temperature (0C)
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.
4-60
61
Frequency Jumps
2.0 x 10-11
30 min.
No. 2
Frequency deviation (ppb)
No. 3
No. 4
8
10
0
2
4
6
Elapsed time (hours)
4-61
62
Acceleration Is Everywhere
Acceleration typical levels, in gs 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
Environment Buildings, quiesent Tractor-trail
er (3-80 Hz) Armored personnel carrier Ship -
calm seas Ship - rough seas Propeller
aircraft Helicopter Jet aircraft Missile - boost
phase Railroads Spacecraft
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
63
Acceleration Affects Everything

• 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)

4-634
64
2-g Tipover Test(?f vs. attitude about three
axes)
Axis 3
10.000 MHz oscillators tipover test
(f(max) - f(min))/2 1.889x10-09 (ccw)
(f(max) - f(min))/2 1.863x10-09 (cw)
delta ? 106.0 deg.
4
2
0
45
90
135
180
225
270
315
360
Axis 1
Axis 2
(f(max) - f(min))/2 6.841x10-10
(ccw) (f(max) - f(min))/2
6.896x10-10 (cw) delta ? 150.0
deg.
4
2
0
45
90
135
180
225
270
315
360
Axis 2
(f(max) - f(min))/2 1.882x10-09
(ccw) (f(max) - f(min))/2
1.859x10-09 (cw) delta ? 16.0
deg.
4
2
Axis 1
0
45
90
135
180
225
270
315
360
g
4-65
65
Vibration-Induced Sidebands
0
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.
L(f)
-10
-20
-30
-40
-50
-60
-70
-80
-90
-100
0
f
50
-50
100
150
200
250
-250
-200
-150
-100
4-70
66
Vibration-Induced SidebandsAfter Frequency
Multiplication
Each frequency multiplication by 10 increases the
sidebands by 20 dB.
L(f)
0
-10
-20
-30
-40
10X
-50
-60
-70
1X
-80
-90
-100
0
f
50
-50
100
150
200
250
-250
-200
-150
-100
4-71
67
Sine Vibration-Induced Phase Noise
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
L(fv), in dBc
-46 -66
-86 -106 -126
Vibr. freq., fv, in Hz 1
10 100 1,000
10,000
4-72
68
Random Vibration-Induced Phase Noise
Random vibrations 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
L(f), in dBc/Hz -53 -73
-93 -113 -133
Offset freq., f, in Hz 1
10 100 1,000
10,000
4-73
69
Random-Vibration-Induced Phase Noise
-70
.07
-80
.04
PSD (g2/Hz)
-90
L(f) under the random vibration shown
-100
5
300
1K
2K
-110
Frequency (Hz)
L (f) (dBc)
-120
Typical aircraft random vibration envelope
45 dB
-130
L(f) without vibration
-140
-150
-160
4-74
70
Acceleration Sensitivity vs. Vibration Frequency
10-8
10-9
Vibration Sensitivity (/g)
Spectrum analyzer dynamic range limit
10-10
100
200
300
400
500
1000
Vibration Frequency (Hz)
71
Low-Noise SAW and BAW Multiplied to 10 GHz(in a
nonvibrating environment)
0
BAW bulk-acoustic wave oscillator SAW
surface acoustic wave oscillator
-20
-40
-60
-80
L(f) in dBc/Hz
BAW 5 MHz x 2000
-100
-120
BAW 100 MHz x 100
-140
SAW 500 MHz x 20
BAW is lower noise
SAW is lower noise
-160
5500
200
10-1
100
101
102
103
104
105
106
Offset frequency in Hz
4-37
72
Low-Noise SAW and BAW Multiplied to 10 GHz(in a
vibrating environment)
73
Shock
The frequency excursion during a shock is due
to the resonators 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).
3
2
Shock
1
0
-1
-2
-3
tO
t1
4-82
74
Radiation-Induced Frequency Shifts
fO
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
?fSS
Frequency
fSS
ft
t0
t
Time

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)

Idealized frequency vs. time behavior for a
quartz resonator following a pulse of ionizing
radiation.
4-83
75
Frequency Change due to Neutrons
1000
5 MHz AT-cut
900
800
700
600
Slope 0.7 x 10-21/n/cm2
500
400
300
200
100
0
0 1 2 3 4 5 6 7 8 9
10 11 12
Fast Neutron Exposure (nvt)
x1017
4-89
76
Neutron Damage
(1)
(2)
(3)
(4)
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.
4-90
77
Other Effects on Stability
? 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 ltlt10-10 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).
4-94
78
Interactions Among Influences
79
Ions in Quartz - Simplified Model
A)
B)
a
Oxygen
Axis of channel
H
H
Si4
Al
Al
E)
D)
C)
Na
Li
K
Al
Al
Al
0.143 eV
0.2 eV
0.089 eV
0.055 eV
5-7
80
Sweeping
Oven T 500OC
Thermometer
Ammeter
Cr-Au
Z
E 1000 V/cm
High voltage power supply
I
0.5 ?a/cm2
Time
5-9
81
Internal Friction (i.e., the Q) of Quartz
100
60
40
Most probable internal friction curve for
quartz excluding mounting losses
20
10
Value of Q, in millions
8
6
4
90 mm
30 mm
2
Diameter of shaped quartz plates, in vacuum
1
15 mm
0.8
0.6
0.4
Flat quartz plates, in air
0.2
0.1
0.1
0.2
0.4
0.6
1.0
2
4
6
8
10
20
40
60
100
Frequency in MHz
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.
5-18
82
Langasite and Its Isomorphs

• 
  
• 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
• Thicker than quartz at the same frequency
• Temperature-compensated

5-19
83
Internal Friction of Quartz
100
60
40
Most probable internal friction curve for
quartz excluding mounting losses
20
10
Value of Q, in millions
8
6
4
90 mm
30 mm
2
Diameter of shaped quartz plates, in vacuum
1
15 mm
0.8
0.6
0.4
Flat quartz plates, in air
0.2
0.1
0.1
0.2
0.4
0.6
1.0
2
4
6
8
10
20
40
60
100
Frequency in MHz
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.
5-18
84
Langasite and Its Isomorphs

• 
  
• 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
• Thicker than quartz at the same frequency
• Temperature-compensated

5-19
85
Oscillator Comparison
Quartz Oscillators
Atomic Oscillators
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 lt1,000
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 lt10,000
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
Accuracy (per year) Aging/Year Temp.
Stab. (range, 0C) Stability,?y(?) (?
1s) Size (cm3) Warmup Time (min) Power (W) (at
lowest temp.) Price ()
Including environmental effects (note that the
temperature ranges for Rb and Cs are narrower
than for quartz).
7-1
86
Weaknesses and Wearout Mechanisms
7-6
87
Why Do Crystal Oscillators Fail?

• 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

7-8
88
Oscillator Selection Considerations
? 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
7-9
89
Clock Accuracy vs. Power Requirement
10-12
Cs
1?s/day
1ms/year
10-10
Rb
10-8
1ms/day
Accuracy
OCXO
1s/year
TCXO
10-6
1s/day
XO
10-4
0.01
0.1
1
10
100
0.001
Power (W)
Accuracy vs, size, and accuracy vs. cost have
similar relationships
90
Battery Life vs. Oscillator Power
1000
Operation at 30oC. The oscillators are assumed
to consume ½ of the battery capacity. Batteries
(except alkaline) are derated for temperature.
1 Year
6 Months
100
1 Month
Days of Battery Life
10
BA 5567, 9.2 cm3
BA 5093, 621 cm3
BA 5800, 127 cm3
BA 5590, 883 cm3
1 Week
AA Alkaline, 8 cm3, 25C
Li Ion (Cell Phone), 135 cm3
1 Day
1
0.1
10
0.001
0.01
0.1
1
XO
Mini Rb/Cs
Small RB Std
Small OCXO
TCXO
MCXO
Oscillator Power (Watts)
7-4
91
Crystal Oscillator Specification MIL-PRF-55310
MIL-PRF-55310D 15 March
1998 ----------------------- SUPERSEDI
NG 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 lthttp\\www.ieee.org/uffc/fcgt
7-10
92
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 gt100K 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.
10-6
93
IEEE Electronic Library
The IEEE/IEE Electronic Library (IEL) contains
more than one 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/iee
explore
10-7