Dominik Schneuwly of Oscilloquartz and Greg Armstrong of IDT delivered an ITSF 2016 tutorial on phase locked loops and oscillators.

1. Tutorial:
Quartz Crystal Oscillators and Phase-
Locked Loops
Dominik Schneuwly (Oscilloquartz)
Greg Armstrong (IDT)
October 14th, 2016

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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

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1. Quartz Crystal Oscillator (XO) Technology

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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

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Vibration Modes, Resonance Frequency, High Q,
Cutting Orientation
Fundamental Mode
Thickness Shear
Third Overtone
Thickness
Shear
Thickness Shear
Mode
Face Shear
Mode
Extensional ModeFlexure Mode

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Frequency Drift Due to Ageing
Time [day]
Fractionalfrequencydeviation[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. Temperature
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)

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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

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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
Heating
Oven
XO
Temp.
Sensor
Temp.
Control
Heating
Temp.
Sensor
Heating
Temp.
Control
Outer Oven
Inner Oven

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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

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2. Phase-Locked Loops (PLL)

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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
P
NOM
IN
OUT
u
K
x
x



 
 
( )
C
P
u
t
u
t
g
t


0
OUT
C
V
u
K





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Phase-Time Deviation x(t)
Note: Phase-time x = random component only
Time 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

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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
 
 

 

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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

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PLL With Direct Digital Synthesis
Sine
Look-up
Table
Counts from
0 to 2
N
-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
2
OUT OSCN
M
 DAC = Digital-to-Analog Converter
LPF = Low-pass Filter

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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

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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

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3. PLL with 2 Inputs

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Imagine the Following:
Sine
Look-up
Table
Counts from
0 to 2
N
-1 in
steps of M
DAC
&
LPF
Phase
Comparator
Loop
Filter
M
Input 1
Sine
Look-up
Table
Counts from
0 to 2
N
-1 in
steps of M
DAC
&
LPF
Free-running
oscillator
Phase
Comparator
Loop
Filter
M
Input 2
Output

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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

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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)

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Imagine Three Spectral Densities (Phase-Time):
OSC
IN 1
IN 2
OUT
(log-log scales)
│SIN1 (f)│
f [Hz]
│SIN2 (f)│
│SOSC (f)│

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… Combined by the 2 Input PLL:
(log-log scales)
f [Hz]
│SOUT (f)│
OSC
IN 1
IN 2
OUT

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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

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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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