quartz crystal oscillators and phase-locked loops

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


1. Quartz Crystal Oscillator (XO) Technology


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


Vibration Modes, Resonance Frequency, High Q, Cutting Orientation

Fundamental Mode

Thickness ShearThird Overtone

Thickness

Shear

Thickness Shear

Mode

Face Shear

ModeExtensional ModeFlexure Mode


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)


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


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


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


2. Phase-Locked Loops (PLL)


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


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


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


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


Both Transfer Functions

20

20

lo

log 2 [dB]

g 2 [dB]

IN

OSC

H j

H j f

f


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


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


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


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


3. PLL with 2 Inputs


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


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


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)


Imagine Three Spectral Densities (Phase-Time):

OSC

IN 1

IN 2

OUT

(log-log scales)

│SIN1 (f)│

f [Hz]

│SIN2 (f)│

│SOSC (f)│


… Combined by the 2 Input PLL:

(log-log scales)

f [Hz]

│SOUT (f)│OSC

IN 1

IN 2

OUT


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


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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