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Tutorial:Quartz Crystal Oscillators and Phase-Locked Loops
Dominik Schneuwly (Oscilloquartz)
Greg Armstrong (IDT)
October 14th, 2016
© 2015 ADVA Optical Networking. All rights reserved.2
Content
1. Quartz Crystal Oscillator (XO) Technology
• Quartz Crystal Overview
• Ageing and Temperature
• XO, TCXO, OCXO, DOCXO
2. Phase Locked Loops (PLL)
• PLL Overview
• Response To Injected Noise
3. PLL with 2 inputs
© 2015 ADVA Optical Networking. All rights reserved.3
1. Quartz Crystal Oscillator (XO) Technology
© 2015 ADVA Optical Networking. All rights reserved.4
Quartz = SiO2
Pink = silicon atoms
Blue = oxygen atoms
Quartz Crystal
Piezo-Electric Effect:Mechanical strain voltage
Inverse Piezo-Electric Effect:Voltage mechanical deformation
= Oxigen atom
= Silicon atom
Oxygen atom
© 2015 ADVA Optical Networking. All rights reserved.5
Vibration Modes, Resonance Frequency, High Q, Cutting Orientation
Fundamental Mode
Thickness ShearThird Overtone
Thickness
Shear
Thickness Shear
Mode
Face Shear
ModeExtensional ModeFlexure Mode
© 2015 ADVA Optical Networking. All rights reserved.6
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
Frequency vs. TemperatureSC-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)
© 2015 ADVA Optical Networking. All rights reserved.7
XO Categories rel. Temp. Control
• XO, Crystal Oscillator:• LTP centered in the operation
temperature range
• > 1E-7 / °C
• TCXO, Temperature Compensated XO:
• Resonance frequency is modified by a varactor diode so as to compensate for temperature sensitivity
• 5E-8 to 5E-7 over [-55°C to 85°C]
UCONTROL
Temp.
Control
Temp.
Sensor
© 2015 ADVA Optical Networking. All rights reserved.8
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]
• DOCXO, Double Oven Controlled XO:
• Two temperature controlled ovens, one inside the other.
• 5E-11 to 5E-9 over [-30°C to 60°C]
XO
Temp.Sensor
Temp.Control
Hea
tin
g
Oven
XO
Temp.Sensor
Temp.Control
He
atin
g
Temp.Sensor
He
atin
g
Temp.Control
Outer Oven
Inner Oven
© 2015 ADVA Optical Networking. All rights reserved.9
Summary
Oscillator Type Temperature Sensitivity(Fractional Frequency vs. Temperature)
XO 1E-7 / °C
TCXO 5E-8 to 5E-7[-55°C to 85°C]
SOCXO 5E-9 to 5E-8[-30°C to 60°C]
DOCXO 5E-11 to 5E-9[-30°C to 60°C
© 2015 ADVA Optical Networking. All rights reserved.10
2. Phase-Locked Loops (PLL)
© 2015 ADVA Optical Networking. All rights reserved.11
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
OUT
C
V
uK
© 2015 ADVA Optical Networking. All rights reserved.12
Phase-Time Deviation x(t)
Note: Phase-time x = random component onlyTime Error TE = random and deterministic components
t1 t1 + x(t1)
nominal signal
actual signal
sin 2
sin 2
NO
NOM
M
t x t
t
x(t1)
t
© 2015 ADVA Optical Networking. All rights reserved.13
Transfer Function «Input-to-Output»
20log 2 [dB]INH j f
where impulse response
transfer function Laplace
OUT IN IN
OUT IN IN
IN
IN IN
x t x t h t
X s X s H s
h t
H s h t
© 2015 ADVA Optical Networking. All rights reserved.14
Transfer Function «Oscillator-to-Output»
20log 2 [dB]OSCH j f
where impulse response
transfer function Laplace
OUT OSC OSC
OUT OSC OSC
OSC
OSC OSC
x t x t h t
X s X s H s
h t
H s h t
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Both Transfer Functions
20
20
lo
log 2 [dB]
g 2 [dB]
IN
OSC
H j
H j f
f
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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
© 2015 ADVA Optical Networking. All rights reserved.17
PLL With Direct Digital Synthesis
Sine
Look-up
Table
Counts from
0 to 2N
-1 in
steps of M
DAC
&
LPF
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 DAC = Digital-to-Analog Converter
LPF = Low-pass Filter
© 2015 ADVA Optical Networking. All rights reserved.18
PLL With Digitally Controlled Oscillator
PFD – Phase & Frequency Detector
TDC – Time-to-Digital Converter
PFD
&
TDC
Digital
Loop
Filter
Digitally
Controlled
Oscillator
(DCO)
Divider
ref(t)
out(t)
Free-running
Oscillator
18
© 2015 ADVA Optical Networking. All rights reserved.19
PLL With VCO, DDS, and DCO 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
PLL with DCO
•Fully programmable
•Configurable pull-in range
•Configurable low pass filter
range
•Requires only free-running
oscillator
•Requires APLL to clean up
jitter
•Precision of TDC affects
close-in phase noise
19
© 2015 ADVA Optical Networking. All rights reserved.20
3. PLL with 2 Inputs
© 2015 ADVA Optical Networking. All rights reserved.21
Imagine the Following:
Sine
Look-up
Table
Counts from
0 to 2N
-1 in
steps of M
DAC
&
LPF
Phase
Comparator
Loop
Filter
MInput 1
Sine
Look-up
Table
Counts from
0 to 2N
-1 in
steps of M
DAC
&
LPF
Free-running
oscillator
Phase
Comparator
Loop
Filter
MInput 2
Output
© 2015 ADVA Optical Networking. All rights reserved.22
Imagine the Following:
│H2 (f)│ │HOSC (f)│f [Hz]
(log-log scales)
│HINT (f)││H1 (f)│f [Hz]
IN 1 OUT
INT
IN 2 INT
OSC
© 2015 ADVA Optical Networking. All rights reserved.23
What Do the Transfer Functions Look Like?
f [Hz]
log - log scales
│H1 (f)│ │H2 (f)│ │HOSC (f)│OUTIN 1
IN 2
OSC
(Application: T-BC with support from SyncE physical layer according to G.8273.2)
© 2015 ADVA Optical Networking. All rights reserved.24
Imagine Three Spectral Densities (Phase-Time):
OSC
IN 1
IN 2
OUT
(log-log scales)
│SIN1 (f)│
f [Hz]
│SIN2 (f)│
│SOSC (f)│
© 2015 ADVA Optical Networking. All rights reserved.25
… Combined by the 2 Input PLL:
(log-log scales)
f [Hz]
│SOUT (f)│OSC
IN 1
IN 2
OUT
© 2015 ADVA Optical Networking. All rights reserved.26
Physical Layer Support for T-BC and T-TSC
G.8273.2 calls for Telecom boundary clock (T-BC) and Telecom time slave clock (T-TSC) to use the physical layer (SyncE) in combination with PTP.
G.8273.2
© 2015 ADVA Optical Networking. All rights reserved.27
SyncE PTP Filtering in Combination
Transfer for SyncE Noise to Output:
OutDCOPTP
PLL 2
Osc
PTP
stack
SyncE
ToD
Counter
Loop
Filter
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