Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 1
Quartz Crystal Oscillators
and
Phase Locked Loops
Dominik Schneuwly
Yves Schwab
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 2
Content
1. Quartz Crystal Resonator Technology
Quartz, crystal lattice and piezo-electric effect
Vibration modes and equivalent circuit
Cuts
Ageing mechanisms
2. Quartz Crystal Oscillator (XO) Technology
TCXO
MCXO
OCXO
DOCXO
3. XO Performance vs. Telecom Requirements
Frequency holdover
Phase holdover
4. Phase Locked Loops (PLL)
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 3
1. Quartz Crystal Resonator Technology
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 4
Quartz Crystal
Quartz = SiO2
Pink = silicon atoms
Blue = oxygen atoms
Quartz lattice
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 5
Cuts
Small disks are cut out of the crystal at given angles.
z
y
x
z
y
x
Single rotated cut
(e.g. AT-cut)
Double rotated cut
(e.g. SC-cut)
X
Y
Z
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 6
Cuts
Angle accuracy: + 10’’ (for SC-cut)
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 7
Vibration Modes
Fundamental Mode
Thickness Shear
Third Overtone
Thickness Shear
Thickness Shear
Mode
Face Shear Mode Extensional Mode Flexure Mode
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 8
Piezo-electric Effect
Piezo-electric effect:
Mechanical strain voltage
Voltage mechanical deformation
= Oxigen atom
= Silicon atom
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 9
Piezo-electric Effect
x x x
y x y
z y
Field Axis & Mode Strain Axis
(A) (B) (C)
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 10
Equivalent Circuit
C0
C3
C2
C1
R3
R2
L3
L2
L1
R1
Vibration mode 1
Vibration mode 2
Vibration mode 3
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 11
Admittance Y(f)
Y(f) Arg ( Y(f) )
Frequency [MHz]
Arg
(Ad
mitta
nce
) [r
ad
]
1 102 5
2
1
0
- 1
- 2
/ 2
/ 2
Frequency [MHz]
1 102 5
1E-2
1E-3
1E-4
1E-5
1E-6
1E-7
Ad
mitta
nce
[
mh
o]
Note: Exaggerated resistance values R1, R2 and R3 for better readability
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 12
Quartz Crystal Oscillator (XO)
CL R
UIN
= 0
IIN
G
UOUT
= G IIN
0 0
00
Open Loop Gain: 1
1 1If and then 1
resonance frequency2
GH G Y
j L Rj C
G HR L C
f
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 13
Frequency Drift Due to Ageing
Time [day]
Fra
cti
on
al fr
eq
uen
cy d
evia
tio
n [1
]
41 3
3E-10
2E-10
1E-10
- 1E-10
- 2E-10
- 3E-10
2 50
0
Positive ageing
Negative ageing
Ageing reversal
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 14
Ageing Mechanisms
Mass transfer due to contamination (e.g. electrode
metal atoms into the crystal
Stress relief in the resonator's mounting and bonding structure,
electrodes, and in the quartz
Other mechanisms:
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
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 15
BVA Resonator
Electrodes not in direct contact with the resonator body
contamination of the resonator body is stopped
Ageing improves by a factor of 10 or more
Other performance parameters improve also (Q, temperature
sensitivity, phase noise, etc.)
Courtesy Jean-Pierre Aubry
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 16
AT-cut Resonator
AT-cut:
Θ = 35°
Φ = 0
Δf/f as a function of temperature
(parameter: ΔΘ = deviation from
reference angle)
Lower Turnover Point (LTP)
Inflection Point (IP)
Upper Turnover Point (UTP)
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 17
SC-cut Resonator
SC-cut:
Θ = 34°
Φ = 22°
Δf/f as a function of temperature
(parameter: ΔΘ = deviation from
reference angle)
Lower Turnover Point (LTP)
Inflection Point (IP)
Upper Turnover Point (UTP)
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 18
Advantages of the SC-cut Thermal transient compensated (allows faster warm-up OCXO)
Static and dynamic f(T) allow higher stability OCXO
Planar stress compensated; lower f due to edge forces and bending
Better f(T) repeatability allows higher stability OCXO (less f for oscillator reactance changes)
Lower drive level sensitivity
Higher Q for fundamental mode resonators of similar geometry
Higher capacitance ratio (less f for oscillator reactance changes)
Less sensitive to plate geometry - can use wide range of contours
Far fewer activity dips
Lower sensitivity to radiation
Disadvantages of the SC-cut More difficult to manufacture
SC- versus AT-cut
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 19
2. Quartz Crystal Oscillator (XO) Technology
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 20
XO Categories rel. Temp. Control
XO, Crystal Oscillator:
LTP centered in the operation temperature range
> 1E-7 / °C
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 21
XO Categories rel. Temp. Control
TCXO, Temperature Compensated XO:
Resonance frequency is modified by a varactor diode so as to compensate temperature sensitivity
5E-8 to 5E-7 over [-55°C to 85°C]
UCONTROL
Temp.
Control
Temp.
Sensor
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 22
XO Categories rel. Temp. Control
MCXO, Microcomputer Compensated XO:
Dual mode oscillator generating fundamental (f1) and third overtone (f3).
Difference between f3 and 3 x f1 is used to measure temperature and compensate temperature sensitivity of f3.
f1
x 3
MixerTemp.
Control
Synthesizer
3 x f1
fOUT
fC = 3 x f
1 - f
3 ~ Temp. -1
f3
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 23
XO Categories rel. Temp. Control
OCXO, Oven Controlled XO:
A control loop maintains the oven containing the XO at (nearly) constant temperature.
5E-9 to 5E-8 over [-30°C to 60°C]
XO
Temp.
Sensor
Temp.
Control
Hea
ting
Oven
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 24
XO Categories rel. Temp. Control
DOCXO, Double Oven Controlled XO:
Two temperature controlled ovens, one inside the other.
2E-10 to 5E-9 over [-30°C to 60°C]
BVA resonator: 1E-10 over [-30°C to 60°C], 5E-11 over [-15°C to 60°C]
XO
Temp.
Sensor
Temp.
Control
Heating
Temp.
Sensor
Heating
Temp.
Control
Outer Oven
Inner Oven
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 25
Typical XOs
SOCXO:
DOCXO:
BVA-DOCXO: …mm
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 26
3. XO Performance vs. Telecom
Requirements
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 27
Frequency Holdover Autonomy
How long can the SSU stay in holdover mode until the MTIE hits
the Network Limit for PRC-traceable SSU outputs (G.823)?
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 28
Frequency Holdover Autonomy
Notes: 1) OSA 8741 2) OSA 8663 3) OSA 8600 4) TNT RMO
Holdover autonomy for different oscillator types and for different temperature conditions (temp. change during holdover):
OCXO1 DOCXO2 BVA-
DOCXO3
Rb4
Const.
Temp.
9 h 21 h 51 h 9 days
2°C 1.4 h 17 h 46 h 5.5 days
5°C 30 min 13 h 39 h 67 h
10°C 15 min 8.3 h 31 h 33 h
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 29
Holdover Autonomy T of cdma2000 Base Stations
Temperature variation: + 10°C
Criterion: phase-time accumulation < 7 microseconds
1.0E-11
1.0E-10
1.0E-09
1.0E-12 1.0E-11 1.0E-10 1.0E-09 1.0E-08
Frequency Drift Due to Ageing [1/day]
Fra
ctio
na
l F
req
ue
ncy D
evia
tio
n D
ue
to T
em
pe
ratu
re V
aria
tio
ns [1
]
T = 6 h T = 12 h T = 24 h T = 48 h T = 72 h
Phase Holdover Autonomy (e.g. 1PPS)
DOCXO
BVA-DOCXO
Rb
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 30
4. Phase Locked Loops (PLL)
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 31
PLL: Working principle
Phase
Comparator
Loop
Filter
Voltage
Controlled
Oscillator
( )INu t( )OUTu t
0,
0,
( ) sin 2 sin 2
( ) sin 2 sin 2
IN NOM IN
OUT NOM
IN
OOU
IN
OT UT TU
u t A t A
u t A t A
t
t t
x
x
t
P
PNO
M
IN
OU
T
u
K
x
x
( )C
P
ut
ut
gt
0
OU
T
C
V
uK
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 32
Phase-time deviation x(t)
t1 t1 + x(t1)
nominal signal
actual signal
sin 2
sin 2
NO
NOM
M
t x t
t
x(t1)
t
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 33
PLL: Transfert function
10- 5
0
- 20
- 40
- 60
- 80
20
10- 4
10- 3
10- 2
10- 1
10 0
10 1
20log 2 [dB]H j f
f [Hz]
where impulse response
transfer function Laplace
OUT IN
IN OUT
u t u t h t
U s U s H s
h t
H s h t
Red curve = PLL transfer
function
Blue curve = transfer function
for oscillator noise
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 34
PLL: Jitter filtering
0
100 200
t [s]
xIN(t) [s]
xOUT(t) [s]
1 x 10 - 6
5 x 10 - 7
- 5 x 10 - 7
- 1 x 10 - 6
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 35
PLL with Direct Digital Synthesis
Sine
Look-up
Table
Counts from
0 to 2N
-1 in
steps of M
Digital-to-
Analog
Converter
Free-running
Oscillator
Phase
Comparator
Loop
Filter
Replaces
the VCO!
M
νOSC
νOUT
where output of the digital loop filter (integer)
size of the counter in bits (integer)
frequency of output signal
free-run frequency of the oscilla
OUT OUT
OSC
M
N
u t
tor
2OUT OSCN
M
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 36
PLL with VCO and with DDS compared
Pros Cons
PLL with VCO
•Very low phase
noise
•PLL’s pull-in
range depends on
VCO’s pulling
range
•Requires VCO
PLL with DDS
•Configurable pull-in
range
•Requires only free-
running oscillator
•Some
quantization phase
noise
Ed. 2006-02 D. Schneuwly Oscilloquartz © 2006 Slide № 37
Thank you