© Copyright 2012

Timekeeping

From clocks to a time scale for

reliable and highly accurate national, global, or

regional timing reference

October 7, 2013

Sam Stein

Chief Scientist

2© Copyright 2012

Clocks

Definition of Terms and Performance

3© Copyright 2012

For Frequency Generation

You need…

The Earth rotating

A pendulum (mechanical oscillator)

Electronic Oscillator

… a method of generating a repeatable event

Atomic resonance

4© Copyright 2012

Frequency

Frequency = the number of cycles per second

Ideal frequency source generates a pure, repeatable sine wave

Frequency = the number of cycles per second

Ideal frequency source generates a pure, repeatable sine wave

5© Copyright 2012

Frequency Definitions

• Offset – the frequency error from the ideal (fast or slow)

• Accuracy – refers to the frequency offset of a device without direct

calibration

• Stability – the constancy of frequency over a given time interval

–Short Term Stability – the change of frequency over 1-100 seconds

from noise and vibration. Sometimes called jitter

–Long Term Stability – the change of frequency over hours, days, or

months. Likely due to aging and temperature

• Aging – change of frequency over time (also called drift)

• Temperature Stability – the change of frequency over temperature

• Accumulated Time Error – total of all the above characteristics

6© Copyright 2012

What is Frequency Stability & Accuracy

Courtesy John Vig

7© Copyright 2012

Oscillator Stability Over Time

Frequency stability typically improves in the short

term, stabilizes, then becomes worse in the long

term

Frequency stability typically improves in the short

term, stabilizes, then becomes worse in the long

term

8© Copyright 2012

What are the Influences on Oscillator

Frequency?

• Time

– Short term (noise)

– Long term (aging)

• Temperature

– Static frequency versus temperature

– Dynamic frequency versus temperature (warm-up)

– Thermal history (retrace)

• Acceleration

– Gravity, vibration, shock

• Other

– Power supply variation

– Humidity

9© Copyright 2012

Taking Frequency Measurements

Frequency measurements are performed over a time interval:

t1 to t2: Signal 1 = Signal 2

t1 to t3: Signal 2 is more stable than Signal 1

10© Copyright 2012

Short and Long Term Oscillator

Stability

1.00E-15

1.00E-14

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

1.00E-08

1.00E-07

1.00E-06

1 Sec 10 Sec 100 Sec 1K Sec 10K Sec 100K Sec Week Month

Stab

ilit

y

Time

Frequency Stability

OCXO

Hi-Stab OCXO

Rb

Cs-High Perf

H-Maser

GPS

Some oscillators perform better short term… others

long term

11© Copyright 2012

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 when viewed in New York

City, ~5000 km away

Putting the Fundamentals into

Perspective…

The second is the most precise SI unit of measure!

12© Copyright 2012

Frequency Sources for Precision Timekeeping

Quartz Crystal Oscillators

Gas Cell Passive Atomic Frequency Standards

Gas Cell Active Atomic Frequency Standards

Atomic Beam Frequency Standards

Cold Atom Frequency Standards

13© Copyright 2012

* Sizes range from <5cm3 for clock oscillators to > 30 liters for Cs standards

Costs range from <$5 for clock oscillators to > $50,000 for Cs standards

** Including environmental effects (e.g., -40oC to +75oC) and one year of aging

Hierarchy of Oscillator Types

Oscillator Type* Accuracy** Typical Applications

• Crystal oscillator (XO)

• Temperature compensatedcrystal oscillator (TCXO)

• Microcomputer compensated crystal oscillator (MCXO)

• Oven controlled crystal oscillator (OCXO)

• Small atomic frequencystandard (Rb, RbXO)

• Active Hydrogen Maser

• High performance atomic standard (Cs)

10-5 to 10-4

10-6

10-8 to 10-7

10-8 (with 10-10

per g option)

10-9

10-10

10-12 to 10-11

Computer timing

Frequency control in tacticalradios

Spread spectrum system clock

Navigation system clock &

frequency standard, MTI radar

C3 satellite terminals, bistatic,& multistatic radar

Timekeeping, radio astronomy

Strategic C3, EW

14© Copyright 2012

Temperature

SensorCompensation

Network or

Computer

XO

Temperature Compensated (TCXO)

-450Cff∆

+1 ppm

-1 ppm

+1000CT

Oven

control

XO

Temperature

Sensor

Oven

Oven Controlled (OCXO)

-450C ff∆

+1 x 10-8

-1 x 10-8

+1000CT

Voltage

Tune

Output

Crystal Oscillator (XO)

-450C

-10 ppm

+10 ppm

250C

T+1000C

ff∆

Crystal Oscillator Types

15© Copyright 2012

Crystal Oscillator Portfolio:

Price vs. Performance overview

Low Portable/Battery High Flight/Mission Critical Space Ref Standards

9250

Low-g

OCXO

9638

OCXO

Ta

ctic

al

Mil

ita

ry

U

AV

/Av

ion

ics

S

atc

om

s

M

ast

er

Osc

9700

OCXO

8200LN

Rb

9940

VCXO

Performance

Ap

pli

cati

on

s

Pri

ce

9600QT

OCXO

9500B

USO

9960

TCXO

16© Copyright 2012

Gas Cell Atomic Clocks

• Rb: 6.8 GHz Passive Buffer gas

• H Maser: 1.4 GHz Active Wall coated cell

The resonant frequency of atoms does not age… the apparatus to

interrogate or confine atoms is affected by the environment and ages in

time

17© Copyright 2012

Rubidium Frequency Standard Basics

O/P

DiscriminatorSignal

Servo Modulation

Frequency Lock Loop

µWInterrogation

ControlVoltage

RF ChainPhysicsPackage

ServoAmplifier

CrystalOscillator

O/PAmp

Lamp Oven Filter Oven Cavity Oven

Filter

Cell

Absorption

Cell

Lamp

Coil

C-Field Coil

LampExciter

Magnetic Shield

SignalOut

C-FieldCurrent

RFExcitation

Photo-Detector

(3) Oven Temperature Sensors and Heaters

LampRb-87

Rb-87Rb-85

18© Copyright 2012

Rubidium Gas Cell Frequency Standards

• Most widely used type of atomic clock

–Smallest, lightest, lowest power

–Least complex, least expensive, longest life

–Excellent performance, stability & reliability

• Device of choice when better stability is needed compared to

crystal oscillator

–Lower aging, lower temperature sensitivity

–Faster warm-up, excellent retrace

–Used as an inexpensive holdover technology

19© Copyright 2012

SA.31M Laser Pumped Rb &

Chip Scale Atomic Clock (CSAC)

• Rb Miniature Atomic Clock (MAC)

– Small form factor: 51mm x 51mm x 18mm (H)

– Lower power: 5W @ 25o C

– Stability

• 1s <3E-11; 100s <8E-12

– Aging: <3E-10/month

– Temp Stability: <1E-10 (–10o C to +75oC)

• CSAC (Chip Scale Atomic Clock)

– Volume: <17 cc

– Weight : 35g

– Very Low power: <120 mW

– Stability

• 1s <2E-10; 100s <2E-11

– Aging: <3E-10/month

– Temp Stability: <5E-10 (0 to +75o C)

20© Copyright 2012

Active Hydrogen Maser Block Diagram

Microwaveoutput

Teflon coatedstorage bulb

Microwavecavity

State selector

Hydrogenatoms

21© Copyright 2012

Active Hydrogen Masers

• Excellent frequency stability up to 1

month

– 40X superior to high performance cesium

• Mature technology with good operating

lifetime and reliability

• Design of choice when the ultimate

frequency stability is required

• Applications: National time scale and

Radio Astronomy applicationsMHM 2010

MASER: Microwave Amplification by Stimulated

Emission of Radiation

22© Copyright 2012

H Maser Applications

• Metrology

– Where?

• International timekeeping laboratories

– Why a Maser?

• Provides superior frequency stability out to one month

• Stability is the key attribute in a timescale application and today’s primary standards

research

• Time scale reference clock steered to the cesium ensemble or primary standards

• Radio Astronomy

– Where?

• VLBI – Very long baseline interferometry

• VLBA – Very large baseline arrays

– Why a Maser?

• Offers frequency stability for multiple VLBA stations to operate coherently

“Perfect Clock”: Maser (short term) + Cesium (long term)

23© Copyright 2012

Cesium Beam Tube Fundamentals

F=3F=3+

F=4

N

S

N

S

Detector

"B" Magnet"A" Magnet

F=3

F=4

Magnetically-Selected CBT

9192 MHz

F=3+

F=4F=4

• Advantages: Unperturbed flow of atoms

• Disadvantage: Finite life, relatively short interrogation time

24© Copyright 2012

• Cesium Technology is considered the most

comprehensive holdover option against GNSS

vulnerabilities

– Exhibit no frequency drift

– Maintains 5x10-13 accuracy over the life of the

instrument

• Critical for long-term autonomous operation

• No on-going calibration required

• More expensive than Rubidium and OCXO

– Consumes more power and space

• Typical applications

– Fixed wireline communications infrastructure

– Under sea (Submarine)

– Satellite ground stations

– Metrology and Time Keeping

Cesium Technology Applications

25© Copyright 2012

Frequency and Time Relationship

26© Copyright 2012

Time is Derived from Frequency

• Every clock ever made is an oscillator + a counter

• The 1 pulse-per-second (PPS) is the epoch or definition of the on-time marker of

a clock

• Further counting of the 1PPS is used to keep track of seconds, minutes, hours,

days, and years

OSC Counter 1PPS

FAST / EARLY SLOW / LATE

1PPS

Clock 1PPS rising edge is typically on-time: HH:MM:SS.000000000

27© Copyright 2012

OCXO Accumulated Time Error

Clock operating from an OCXO with an offset & aging of 5×10-10 and a

temperature error of 1 degree C

Accumulated Time Error

050

100150200250300350400

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57

Hours

Mic

rose

con

ds

Aging Error(uS) Offset Err.(uS)

Temp Err.(uS) Total Err.(uS)

Oscillator errors accumulate impacting clock performance

28© Copyright 2012

Cesium Time Error Due to Offset

Cesium Time Error (Offset 2E-12)

0

1

2

3

4

5

6

1 4 7 10 13 16 19 22 25 28 31

Days

Mic

rose

cond

s

Offset Err.(uS)

Time error = Freq offset * seconds/day

or

2×10-12 x 86400s = ~0.2µs / day

Cesium atomic oscillators do not age

29© Copyright 2012

Time Scale Basics

30© Copyright 2012

Concept of Time

Identification when:

• An event occurs

• Duration of an event

• Interval between events

Three concepts that relate to time are:

• Date: A reference point represented by the exact time-of-day and, often day and year, that indicates when an event occurred

• Interval: The duration or elapsed time between two instants or subsequent events

• Synchronization: Refers to two clocks set to the same time or two events happening at the same instant of time

31© Copyright 2012

What is Time Scale and Types

• Time scale is an agreed upon measuring system for counting time

• Time Scales Types

Astronomical: UT1 Universal Time (polar corrections)

Earth rotation angle

Atomic: TAI International Atomic Time

Commercial & Primary clocks

Atomic - with periodic adjustments:

UTC Coordinated Universal Time

UTC(Lab) UTC per contributing laboratory

Time scales are based on agreements between humans

32© Copyright 2012

International Atomic Time

(TAI)

Atomic

Clock

Atomic

Clock

Atomic

Clock

Atomic

Clock

Atomic

Clock

International Earth

Rotation Service (IERS)

ENSEMBLE AVERAGE

Coordinated Universal Time

UTCAdd leap seconds to

correct for Earth’s rotation

National Metrology Institute

(NMI)

UTC(k)

Radio, Telephone, Network,

Satellite Dissemination of UTC(k)

What is UTC Time Scale

USNO (US) NIST (US) NPL (UK) PTB (Germany) CRL (Japan)

BIPM*

BIPM*

BIPM Circular T

Report

*BIPM – Bureau of Weights and Measures

33© Copyright 2012

Timing Keeping by Clock Types

87%

12% 1%

BIPM International Atomic Time Component Clocks by Weight

5071A

Maser

Others

99% of world time keeping powered by Cesium and Masers

CesiumCesium

H-Maser(s)H-Maser(s)

Cesium

Based on BIPM Annual Report 2011

34© Copyright 2012

What is Precise Time-Scale System

Cesium (5071A)Cesium (5071A)

H-Maser(s)H-Maser(s)

5MHz

5MHz

Correction

BIPM

UTC(k)

Precise Time-Scale System

The frequency stability of Symmetricom’s ensures the uniformity of

the world’s time

35© Copyright 2012

How Does a Time Scale Work?

• Step 1

Measure the time differences between all the clocks and the reference

clock

• Step 2

Estimate the time, frequency, and aging differences between all the

clocks and the reference clock

• Step 3

Apply the time scale algorithm to calculate the corrections to the

reference clock’s time, frequency, and aging needed to render it equal

the time scale

• Step 4

Connect a synthesizer to the reference clock and steer the output of

the synthesizer to approximate the time scale using corrections from

step 3

36© Copyright 2012

Symmetricom Time Scale Hardware

Non-redundant Time Scale with 5 Cesium Clocks

Real-time Clock

Measurement

System

Time Servers

Cesium

Clocks

UPSCharger

Batteries

Database

Computer

37© Copyright 2012

Baseline Precise Time-Scale System

Consists of:

• Equipment rack

• One 5071A high performance cesium standard

• 8 channel measurement hardware with database

server

• Real-time clock with chassis mainframe and modules

• UTC recovery, steering, common view, monitor and

control software

• LCD monitor

• Keyboard

• Battery backup unit

• System integration and packaging

• On-site installation and training

38© Copyright 2012

Precise Time-Scale System Key Functions

• Generates timing outputs synced to UTC using a GNSS receiver

• Option to incorporate multiple clocks to optimize availability

• Measurement system to provide clock time differences

• Distributes the real-time clock: 5MHz, 1PPS and IRIG-B

• Uses a time-scale algorithm to combine the clocks into one

output

• Archives data for review

• Performs GNSS common view time transfer using BIPM procedure

• Automatically prepares BIPM reports

39© Copyright 2012

Precise Time-Scale Key System Specifications

• Frequency Accuracy:

+1x10-14 for 10 day

average after 60 days of

continuous operation

• Frequency Holdover:

+1x10-13 for 30 days over

the full temp range

Offset Freq (Hz) 5 MHz (dBc/Hz) 10 MHz (dBc/Hz)

1 -106 -100

10 -136 -136

100 -151 -145

1KHz -156 -151

10 KHz, 100 KHz -160 -154

Ƭ (s) σY(Ƭ)

1 5x10-12

10 3.5x10-12

100 8.5x10-13

1k 2.7x10-13

10k 8.5x10-14

100k 2.7x10-14

Short-Term Stability (ADEV)

Phase Noise

40© Copyright 2012

Precise Time-Scale System

Features and Benefits

• Features

– State-of-the-art UTC generation

– Support for participaton with BIPM

– User friendly GUI and Database for archiving

• Performance

– Frequency accuracy + 1x10-14

– Time accuracy of + 10 ns RMS to UTC

• Customer Benefits

– Less than 1 year to full UTC participation

– Performance on par with the best national laboratories due to time

scale algorithm from Symmetricom

– Reduced complexity and ease of integration

41© Copyright 2012

Precise Time-Scale User Interface & Database

Web-Based User Interface

• Configure MMS

• Manage Clocks

• Retrieve and manipulate data

• Add user accounts

Database (includes Manager)

• 10 years of data storage capacity

• TCP/IP interface to MMS w/listener process

• Every second data from MMS is sent

to listener for data processing and storing

RAID 5 Disk Array• 4 on-line diskes striped for 360 GB actual

storage

• 1 auto-failover hot spareFront Panel of Database w/RAID 5 disk array

Web Interface for database and measurement systems

Clock Steering GUI with estimated offset from UTC

42© Copyright 2012

Precise Time-Scale System

Sample Performance

• Performance vs. UTC

-10

-5

0

5

10

15

54300 54400 54500 54600 54700

ns

MJD

UTC - UTC(lab)

RMS = 5 ns

Mean = 2.5 ns

2 August 2007

through

11 June 2008

43© Copyright 2012

Performance of KAS-2 Time Scale

• Analyzed using the method of the N-cornered hat

5 High Performance and1 Standard PerformanceCesium Clocks

3 High Performance Cesium ClocksAnd 3 Hydrogen Masers

44© Copyright 2012

Effect of Additional Cesium Clocks

• Precise Time-Scale can achieve

better performance with additional

clocks:

– Availability

– Stability

• Cesium maintains specified accuracy

for life of instrument

– Long term autonomous operation

5071A Cesium clock

Quartz or Rubidium not suitable since they exhibit frequency drift

45© Copyright 2012

Effect of Maser Clock to the System

• Adding an active Hydrogen Maser to the system improves the stability of the time scale

• Symmetricom’s Maser has a reputation for its excellent short and long term stability, reliability and long life

MHM-2010 active

hydrogen Maser

46© Copyright 2012

Precise Time-Scale System Service Offering

Standard Services

• System design, integration and testing

• System packaging and documentation

• On-site installation and training

• Rack, monitor, keyboard and cables

Optional Services

• Site survey and verification

• Customer-witnessed factory acceptance testing

• Extended warranty and in-country support

• System spares program

• Software and systems support 24x7

• BIPM contribution and timekeeping consulting

47© Copyright 2012

Overview

Time Scale Technical Details

• What is a time scale?

• Why is this an interesting

problem?

• Types of time scales

• Historical perspective

• Symmetricom turn-key

time scale

• Performance

48© Copyright 2012

What is a Time Scale?

Why do We Need Them?

• A time scale is a method of computing corrections for each

member of an ensemble (group) of clocks so that any of them

may be steered to produce the time and frequency of a more

nearly perfect clock

• Why are they needed?

– Extend beyond the life of one clock

– More uniform than any single clock

– More robust than any single clock

– Improved availability

• An example of a time scale is International Atomic Time (TAI)

• Applications for time scales

– Metrology – can benefit from post processing

– Synchronization – requires real time output

– Science – highest performance in real time and non-real time

49© Copyright 2012

Why is This an Interesting Problem?

• Computing a time scale is more than just an estimation problem

• The inputs to the calculation are the time differences between

the clocks

• There are an infinite number of solutions for the times of the

clocks that are consistent with the measurements

• There are two components to the problem

– How much of a measured time difference between two clocks is

attributable to each clock?

• We can estimate this

– How much of the time change of a clock is unobserved because the

clocks move together?

• We have no way to address this question

50© Copyright 2012

Types of Time Scales

• Batch processing vs. Bayesian (recursive)

– Batch algorithms save measurements over time and compute the

next set of time scale values using all measurements at once

– The Bayesian approach is to save the state at the time of the last

computation and update it using measurements at the next time

• Real-time vs. after the fact (filter vs. smoother)

– Smoothers compute the time scale at a point in time based on prior

and subsequent data

– Smoothing produces better estimates than filtering

• Model dependent vs. model independent

• Clocks are weighted based on their performance at one

averaging time vs. multiple averaging times (single vs. multi-

resolution)

• Cookbook recipes vs. designed approaches

51© Copyright 2012

Historical View of Time Scales

• Earliest time scales (circa 1968) used the ‘basic’ time scale equation

– Sum of the random shocks for the clock phases is zero

– Detailed performance of the algorithm depended on the method of

frequency estimation

• In 1990, Stein developed an algorithm where the sum of the

random shocks for every clock state is zero (KAS-2)

– Time scale performance can be optimized over each averaging time for

which a different noise process is dominant

– For the first time the state estimation problem was separated from the

time scale computation problem

• In 2004, Davis, Stacey, and Greenhall used Markov noise processes

to model flicker noise in clocks in a time scale

• In 2011, Senior and Percival developed a model independent multi-

scale time scale algorithm using the discrete wavelet transform

52© Copyright 2012

0)(ˆ1

=∑=

N

iii ta ε

Clock Model

• Traditional model

– Noise in a clock can most generally be describe as Sy(f) = hαfα

• Addition of Markov noise per Stacey et. al.

( ) ( ) ( )1 i k i k i kx t x t s t+ = Φ +r r r

2

2

0 1 / 2

0 1 / 2

0 0 1

0 0 0 1

δ δδ δ

δ

Φ =

White phase noise

White frequency noise

Random walk frequency noise

Random run frequency noise

4 Markov processes

For each noise process

So there are 4 weights that determinePerformance over 4 averaging times

53© Copyright 2012

Time Scale Computation

• Kalman filter operates on the clock time differences to estimate

the noise differences between each clock and the reference

– Observed time differences are used to estimate the random shocks

of the time, frequency, and frequency aging

• KAS-2 Time scale algorithm separates the noise difference

estimates into individual clock noise estimates

– Uses the assumption that the sum of the random shocks over all the

clocks is zero (true in the limit of an infinite number of clocks)

• References

– U. S. Patents 5,155,695 and 5,315,566

– S. R. Stein “Advances in Time Scale Algorithms”, 23rd Annual PTTI

Meeting, 1992.

– S. R. Stein, “Time Scales Demystified,” Proceedings of the 57th

Annual Frequency Control Symposium, 2003.

54© Copyright 2012

Why Add Markov Noise?

• Markov noise processes can be used to model the transition

between white or random walk phase noise and random walk

frequency noise (flicker region)

Maser Allan Deviation

White phasenoise Random walk frequency

noise plus aging

55© Copyright 2012

Sum of 4 Markov Processes Models Flicker FM

Over 3 Decades of Averaging Time

• From Davis, Greenhall, and Stacey (PTTI 2004)

56© Copyright 2012

Comparison of Model Dependent Time Scale

with a Wavelet Multi-Resolution Time Scale

• Issue – the multi-resolution analysis does not have a built in

forecasting method, which is desirable for real-time applications

and steering

57© Copyright 2012

Technical Take Aways

• Use of Kalman filter provides minimum squared error estimates

that have optimum transient response

• Bayesian approach is just as effective as those that require large

memory of past data and extensive recomputation

– Allows compact highly automated time-scale system with low power

computer and small memory

• All noise types of atomic clocks are well modeled making future

time prediction highly optimal

• Weighting by noise type provides equal advantage (multi-

resolution analysis) as the wavelet approach but provide the

added capability to forecast clock times

58© Copyright 2012

Precise Time-Scale System Key Take Away’s

• Affordable time scale system for international markets

– Base system includes RTC/Measurement HW, SW and one Cesium clock

– System integration, Installation and Training included

– Optional support services available

– Option to add additional clocks

– Can use existing 5071A and Symmetricom Maser in the lab

• Key customer benefits

– Lower total cost of ownership

– High availability

– Affordable price point with options to grow

– Proven support services

– Reduced complexity and ease of operation

– Ability to participate in the BIPM time scale quickly

59© Copyright 2012

Samuel R Stein

sstein@symmetricom.com

4775 Walnut St

Boulder, CO 80301

Tel: +1 303-539-4904

Fax: +1 303-443-5152

www.symmetricom.com