Atomic Clocks
for
Amateur Radio Astronomy
Presented by
Shad Nygren
at
Society of Amateur Radio Astronomers regional meeting
Owens Valley CA
Feb 28 & 29, 2004
Presentation revised Sept 26, 2007
Radio Astronomy Applications of
Accurate Time and Frequency
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VLBI
Pulsar timing
Doppler shift measurements
Zeeman effect
Relativity
Time scales for VLBI
• Two time scales are important:
• Over periods of a few minutes, frequency stability must be adequate to
provide sufficient integration time for extracting the VLBI
observables.
• Over periods from several hours to a day, the frequency standard must
work as a stable clock for recording signal arrival times.
• All VLBI observations must be phase-coherent, so a frequency
reference standard which is significantly better than 1/(highest
observing frequency) is required. The stability should be maximized
over a period of 1 to 1000 seconds, the latter being the approximate
length of a source scan. (Source:
http://newton.jb.man.ac.uk/tmfrq.htm)
Coherence Time
• The coherence time is the temporal interval
over which we can reasonably predict the
phase of the light wave at a given point in
space. Temporal coherence relates to the
finite bandwidth of the source
What types of Atomic Clocks are
available to amateurs
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Quartz
Rubidium
Cesium
GPS
Loran
Factors affecting clocks
especially Quartz
• Aging is "the systematic change in frequency with time
due to internal changes in the oscillator"
• Drift is "the systematic change in frequency with time of
an oscillator." Drift is due to aging plus changes in the
environment and other factors external to the oscillator.
• Environment, Temperature, Vibration, Atmospheric
Pressure?, Voltage, Magnetic Fields
• Vibration / Acceleration / Gravity (The acceleration can be
a steady-state acceleration, vibration, shock, attitude
change (2-g tipover), or acoustic noise.)
• Clock Noise
Clock Noise
Power-law noise processes are models of precision oscillator noise
that produce a particular slope on a spectral density plot. We often
classify these noise processes into one of five categories. For plots
of Sf (f), they are:
• 1.Random walk FM (random walk of frequency), Sf plot
goes down as 1/f4.
• 2.Flicker FM (flicker of frequency), Sf plot goes down as
1/f3.
• 3.White FM (white of frequency), Sf plot goes down as
1/f2.
• 4.Flicker PM (flicker of phase), Sf plot goes down as 1/f.
• 5.White PM (white of phase), Sf plot is flat.
Phase Noise
• Phase Noise is the noise level relative to the maximum signal. Note
that the “distance” from the carrier is actually specified in frequency...
• Phase Noise is given at any frequency “away” from the carrier in units
relative to the maximum signal gain at the carrier. These units have the
mysterious name “dBc/Hz” (ratio at a given freq of noise to signal at a
1 Hz bandwidth)
• dBc is decibels relative to the carrier. dBc/Hz is decibels relative to the
carrier per Hertz. These units are used to describe in decibels how far
down signals and noise are relative to a known signal. (Source:
http://www.radarproblems.com/chapters/ch06.dir/ch06pr.dir/c06p7.dir/
c06p7.htm)
• Phase noise is a small fraction of undesirable frequency near the output
frequency. Phase noise is dependent mostly on the crystal with the
circuitry making up the unit playing a small role. The measurement is
commonly in the 1 Hz bandwidth. The description of phase noise is "at
x Hz offset it is y dBc/Hz
• SSB (Single Side Band)
Phase Modulation
Phase Noise Components
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White Phase: Crystal Q
Flicker Phase: Thermal noise
White Frequency: Oscillator components
Flicker Frequency: Oscillator Q
Each segment of phase noise has been
identified as being caused by unique
characteristics….
Random Walk Noise
• A type of oscillator noise caused by
environmental factors such as mechanical
shock, vibration and temperature
fluctuations which cause random shifts in
frequency. As a general rule, random walk
noise cannot be removed by averaging.
Flicker Noise
• A type of low frequency noise where the power spectral
density is inversely proportional to the frequency. For this
reason, it is sometimes referred to as 1/f noise.
• Flicker noise is one of the least understood. It is usually
attributed to manufacturing noise mechanisms or device
surface states. Experimental data shows that this type of
noise has a dependence on dc current and is similar to shot
noise
• Reminded someone of candle flickering
• Also called “pink noise”
White Noise
• Also known as Shot Noise
• Is independent of frequency
• Shot noise is generated by the random
fluctuations in the normal current flow.
Because each electron carries a discrete
amount of charge and the flow of electrons
is subject to small random fluctuations, a
noise current is generated.
Random White Noise
How is clock performance
characterized?
• Allan Variance
• Drift
• Phase Noise
Allan Variance
• The advantage of this variance over the classical variance is that it
converges for most of the commonly encountered kinds of noise. In
contrast the classical variance does not always converge to a finite
value. For example, Flicker noise and random walk noise are two types
which commonly occur in clocks and in nature where the classical
variance does not converge.
• If the fluctuations are characterized by flicker noise or any other nonwhite-noise frequency deviations, what happens to the standard
deviation for that data set? One can show that the standard deviation is
a function of the number of data points in the set; it is also a function
of the dead time and of the measurement system bandwidth. For
example, using flicker noise frequency modulation as a model, as the
number of data points increases, the standard deviation monotonically
increases without limit. REFERENCE:
http://www.boulder.nist.gov/timefreq/phase/Properties/four.htm
Allan Variance Concept
Source: http://www.ieee-uffc.org/freqcontrol/tutorials/Parker_2002_files/frame.htm
Allan Deviation Noise
Source: http://www.boulder.nist.gov/timefreq/general/glossary.htm
Modified Allan Variance
• The Allan variance filter cannot distinguish between
white Phase Noise and flicker Phase Noise.
• Synchronization networks require frequency
standards which have good time and phase stability.
• White PM and flicker PM levels are an important
indicator of time/ phase stability.
• Therefore, another algorithm is necessary to
distinguish between the various noise components.
• Modified Allan variance (MVAR) will discern white PM
and flicker PM.
Modified Allan Noise
Quartz Crystal
• AT cut or SC (Stress Compensated) cut
• XO gives 5 ppm to 10 ppm per year.
• TCXO (Temperature Compensated) gives 0.5 ppm
to 2 ppm per year.
• OCXO (Oven Controlled) 0.05 ppm to 0.1 ppm
per year.
• The highest precision OCXOs can age a few parts
in 1012 per day, i.e., less than 0.01 ppm per year.
Quartz Crystal Cont
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The frequency accuracy of resonators is affected by many variables, some of
which are temperature, aging, drive level, retrace and vibration. The SC-cut,
Silicon Dioxide Crystal, is the only known resonator which has the inherent
compensation required to minimize frequency shift versus all of the above
factors.
Prior to the SC discovery, the most versatile design was the single rotation ATCut, which was discovered by groups from America, Germany and Japan in
1929, and still remains the most widely used design today.
Although the doubly rotated SC-cut (Stress Compensated) crystal was
developed in the 1970's(4,&5) it has only been in recent years that Piezo
Crystal and a few other companies have refined the manufacturing processes
to the point where the crystal is being produced in substantial quantities with
respectable yields over a wide range of frequencies.
Source: http://www.corningfrequency.com/library/dasc.html
Rubidium
• Resonance 6,834,682,608 Hz
• Optical pumping relies on the natural
coincidence of optical resonant frequencies
between 85Rb and 87Rb, both at 795nm.
• Good short term stability
• Poor long term stability
• Used in VLBI until superseded by
Hydrogen Maser
Cesium
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Resonance at 9,192,631,770 Hz by definition of the second
C-Field
Tube life approx 3 years
Cost of used HP 5061A on eBay approx $1500
Cost of new tube is about $10K
While cesium clocks have excellent long-term stability, the
greatest weakness is the short-term stability caused by shot
noise in the cesium beam.
• Not used for VLBI because of poor short term stability
Hydrogen Maser
• Resonance at 1420MHz
• Active and Passive designs.
• Currently the most stable frequency standard for averaging times
between 103 and 104 seconds where stabilities as good as 7x10-16 are
reached.
• Hydrogen masers are used as VLBI standards because of their
excellent short term stability.
• Their long-term accuracy, however, is subject to drift.
• H-Maser Oscillators have a wear out mechanism, mainly from
Hydrogen depletion and Ion Pump failures, which begin to show up in
3 to 5 years for active masers and 5 to 7 years for passive masers.
• Cost >$60K to >$200K
Cesium Fountain NIST-F1
• Laser Cooled
• The nation's primary time and frequency standard
• Uncertainty about 5 x 10-16
Time Scales
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TAI
UTC
UT1
GPS
Loran
TDB – Barycentric Dynamical Time
TAI timescale
• The reference used is International Atomic Time
(TAI), a time scale calculated at the BIPM using
data from some two hundred atomic clocks in over
fifty national laboratories.
• TAI is a uniform and stable scale which does not,
therefore, keep in step with the slightly irregular
rotation of the Earth.
Leap Seconds
• Currently 13 leap seconds (+1 in 2007)
• As of 2007 these leaps have always been positive
UT1 timescale
• is the principal form of Universal Time.
• It is computed from the raw observed UT0 by
correcting UT0 for the effect of polar motion on
the longitude of the observing site.
• UT1 is the same everywhere on Earth, and is
proportional to the true rotation angle of the Earth
with respect to a fixed frame of reference.
• Since the rotational speed of the earth is not
uniform, UT1 has an uncertainty of plus or minus
3 milliseconds per day.
• The ratio of UT1 to mean sidereal time is defined
−11
UTC
• Such a scale is Coordinated Universal Time (UTC), which
is identical with TAI except that from time to time a leap
second is added to ensure that, when averaged over a year,
the Sun crosses the Greenwich meridian at noon UTC to
within 0.9 s
• (Coordinated Universal Time) is an atomic timescale that
approximates UT1.
• It is the international standard on which civil time is based.
• It ticks SI seconds, in step with TAI. It usually has 86400
SI seconds per day, but is kept within 0.9 seconds of UT1
by the introduction of occasional intercalary leap seconds.
• When an accuracy better than one second is not required,
UTC can be used as an approximation of UT1.
UTC
• Official international time is Coordinated Universal Time,
UTC
• UTC is a paper clock generated once a month by the
Bureau International des Poids et Mesures, BIPM with
data collected from about 230 atomic clocks in 50 labs
around the world and distributed in BIPM Circular T.
• The method of time transfer is primarily common-view
GPS and some Two-Way Satellite Time and Freq Transfer.
• Local representations of UTC are hardware clocks with
ticks generated in real time, UTC(NIST) for example.
Local UTC’s are estimations of UTC.
BIPM
USNO
• Source of GPS time
• 61 Atomic Clocks, 11 Hydrogen Masers and
50 HP-5071 Cesium
NIST
• http://www.boulder.nist.gov/timefreq/
• Traceability
Time and Frequency Transfer
• One-Way
• Common-View
• Two-Way
Common View Satellite
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GPS
GOES (obsolete)
GLONASS (partial)
GALILEO (future)
Fixed plus variable
delay components
Two-Way Satellite Time and
Frequency Transfer
• This technique provides stable
and accurate time transfer since
nearly all of the propagation
delay cancels out due to
symmetry.
• Recently the BIPM has started
using two-way transfer via a
commercial Ku-band
communication satellite as the
primary time transfer technique
for some European and
transatlantic links, since it
performs significantly better
than GPS common view.
Time Sources
• GPS
• Loran
• WWV / WWVB
GPS
• The Block IIF satellite, the latest generation of GPS vehicles that
began replacing older satellites in 2001, feature four advanced atomic
clocks composed of both cesium and rubidium technologies. These
extremely accurate GPS atomic clocks keep time to within 8
nanoseconds a day.
• The atomic clocks aboard the satellites maintain their time to a very
high degree of accuracy. However, there will always be a slight
variation in clock rates from satellite to satellite. Close monitoring of
the clock of each satellite from the ground permits the control station
to insert a message in the signal of each satellite which precisely
describes the drift rate of that satellite's clock. The insertion of the drift
rate effectively synchronizes all of the GPS satellite clocks.
GPS Cont
• Excellent Long Term Stability
• Poor Short Term Stability
• Short term stability is degraded by satellite
orbital variations, ionosphere delay,
troposphere delay, signal multipath from
nearby terrain and buildings, receiver
electronics, installation (antenna cable) and
selective availability (presently turned off)
GPS Cont 2
• Receiver electronics have more or less
delay
• Best units < 30ns rms ref to UTC
• Worst units > 1us rms ref to UTC
Loran
• Long Range Navigation time, is an atomic time
scale implemented by the atomic clocks in LoranC chain transmitter sites.
• Loran time was zero at 0h 1-Jan-1958 and since it
is not perturbed by leap seconds it is now ahead of
UTC by 23 seconds.
• Making a comeback after almost being cancelled
as GPS backup
• System being upgraded to enhanced version
known as eLoran
Loran Cont
• US Public Law 100-223, Section 310 requires the
control the transmission of LORAN signals to
within +/- 100 nanoseconds of UTC at times of
coincidence (TOC).
• The Coast Guard has worked with USNO to steer
LORAN transmissions to UTC
• USNO monitors & measures LORAN time
differences (TD) in far field to determine
difference between LORAN Chain & UTC
PRS10 Rubidium + GPS
Source: http://www.thinksrs.com/products/PRS10.htm
HP Z3801A Stability
Source: http://www.leapsecond.com/pages/z3801a-osc/
Comparison of Frequency Standards
Source: http://www.ieee-uffc.org/freqcontrol/quartz/vig/vigcomp.htm
Allan Deviation Comparison
Source: http://www.leapsecond.com/museum/manyadev.gif
Equipment Sources
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eBay
Stanford Research PRS10
Garmin
Rubidium Efratom FRS-C
GPS / Motorola Oncore
Information Sources
• http://www.leapsecond.com
• http://www.boulder.nist.gov/timefreq/
Conclusion
• Atomic Clocks are practical and affordable
for Amateur Radio Astronomy.
• The combination using a Rubidium
disciplined to GPS gives good short and
long term performance.
• Opens up the possibility of amateur VLBI
and other scientifically meaningful
measurements.
Recommendations
• Use equipment with external 10MHz
reference inputs
• Mfg / Vendors should design equipment to
accept external 10MHz reference
Questions?
Clock History
• Christian Huygens’ (Galileo’s?) pendulum
clock (1582) was stable to 1 min/day, but
useless for moving platforms
• John Harrison’s “Marine Chronometer”
(1761) kept time on a rolling ship to 0.2
s/day; determined longitude to 0.5 deg
• Quartz clocks have evolved from 1930’s to
be stable to better than 1 part in 1013
HP 58540A
Brooks Shera's GPS Controller