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The Accuracy and Stability of Quartz Watches

Horological Journal February 2008 57
The Accuracy and Stability of Quartz Watches
Quartz wristwatches are neither as
intricate nor as intriguing to many
collectors as their mechanical
counterparts, but with very few
exceptions, they do a considerably better
job of keeping time. At least one
manufacturer of low-priced quartz
watches specifies their accuracy as ±15
seconds per month, suggesting an
accumulated error of just a few minutes
per year. This type of accuracy is
sufficient for most people, who are
generally happy if their watch remains
within a minute or two of the correct time.
In fact, many quartz watch owners set
their watches only a few times per year –
typically when they change the battery,
change time zones, or switch to and from
daylight saving time. Unless their watch
is broken or the battery is dead, its
timekeeping accuracy is never in
But for those among us who view even
the cheapest quartz watch as a precision
scientific instrument, rather than as a
piece of jewellery or as a disposable
consumer item, some questions remain.
For example, exactly how accurate is a
‘run-of-the-mill’ quartz wristwatch? Can
they really keep time to within ±15
seconds per month? Does their accuracy
vary over time? This article attempts to
answer those questions. It characterises
the performance of four low-cost quartz
wristwatches by applying some
measurement and data analysis
techniques that are normally reserved for
laboratory type frequency standards.
The Watches Under Test
The four quartz watches chosen for
the test, 1-4, are members of the
author’s pedestrian collection. While
none of them will make a watch
enthusiast’s heart beat faster, they do
have the virtue of being common; and
similar watches have found their way on
to many wrists. Watch A is an ‘official’
Mickey Mouse watch, purchased at
Disneyland in California several years
ago for about $35 USD. Watch B is a
Rolex ‘replica’, purchased from a street
vendor in South America for about $15
USD, and somewhat surprisingly, still
running some two years later. Watch C
is a 20-year old dress watch that
originally sold (mid-1980s) for about
$100 USD, and was worn everyday for
more than a decade. Watch D is a
typical discount store watch, a new
(2007) Timex that sells for approximately
$30 USD.
Like nearly all quartz watches, the
four devices under test use 32.768 kHz
(215 Hz) quartz crystals as their oscillator.
The quartz watch industry standardised
on 32 kHz crystals in the early 1970s due
to their reliability, their compatibility with
existing electronic circuits, their small
dimensions, and their low power
consumption.1Since their introduction,
watch manufacturers have continued to
improve the timekeeping performance of
quartz watches. Most of the advances
have been related to crystal and mount
miniaturisation, better electronics, better
manufacturing techniques, and most
importantly, making the crystal frequency
less dependent on temperature.2
Accuracy versus Stability
The performance of a timekeeping
device is usually stated in terms of its
accuracy and stability, and measuring
both characteristics was the goal of this
test. Accuracy is related to the difference
between a measured value and an ideal
value. For example, a ‘perfect’ watch
would agree exactly with Coordinated
Universal Time (UTC), the international
reference for time, time interval, and
frequency. If a watch was synchronised
to UTC and then found to be 1.3 seconds
fast one day later, its time is said to be
accurate to within 1.3 seconds per day.
Frequency accuracy refers to the
difference between the measured
frequency of an oscillator and its nominal
frequency, or an ideal frequency with
zero uncertainty. For example, if a crystal
with a nominal frequency of 32768 Hz is
measured at 32768.5 Hz, its frequency is
said to be accurate to within 0.5 Hz.
Both time accuracy and frequency
accuracy are normally expressed as
dimensionless values by using the
equations Δt/T and Δf/f, respectively.
The two equations produce equivalent
answers when applied to the same
device. Thus a time accuracy of 1.3 /
86400 (seconds per day) and a
frequency accuracy of 0.5 Hz / 32768 Hz
both result in a dimensionless accuracy
value of about 1.5 × 10-5.
Stability indicates how well a device
can produce time or frequency with the
same accuracy over a given time
interval. It doesn’t indicate whether the
time or frequency produced by a device
is accurate or inaccurate, but only
whether it stays the same. In contrast,
accuracy indicates how well a clock has
been set on time or an oscillator has
been set on frequency. To understand
this difference, consider that an
inaccurate device can be stable, and an
unstable device can be at least
temporarily accurate. For example, a
quartz watch that gains exactly 10.5
seconds every day is very inaccurate,
but very stable. It might be possible,
then, to adjust the frequency of the
crystal and make the watch both
accurate and stable. In contrast, a watch
by Michael Lombardi 1-A 2-B
3-C 4-D
58 February 2008 Horological Journal
that fluctuates within a range of ±5
seconds of the correct time is unstable,
but on occasion would have the correct
time and be considered accurate.
The Allan deviation (ADEV) is a
statistic used internationally to estimate
frequency stability.3It differs from the
conventional standard deviation
because it does not use the average
accuracy of a device as a point of
reference. Instead, it compares the
frequency accuracy of the device under
test during a given measurement period
to its frequency accuracy during the
previous measurement period. This
reveals how an oscillator’s frequency is
changing over time due to effects such
as frequency drift and aging. ADEV is
regularly used to estimate the stability of
devices ranging from high-performance
mechanical watches4,5 to the world’s
best atomic oscillators, and will be
applied here to estimate the stability of
the quartz watches under test. ADEV,
expressed mathematically as σy(τ) is
computed as
where the
series contains estimates
of the frequency accuracy of the device
under test, M is the number of values in
series, and the data are equally
spaced in segments τseconds long.
The Measurement Method
To estimate their accuracy and
stability, the watches were measured
with a commercial watch analyser, 5.
This versatile device can simultaneously
measure the frequency of both the
quartz oscillator and the stepping motor
pulses. The watch analyser sensor can
automatically detect the quartz
frequency through several available
methods. If the watches have metal
cases, as did all of the watches tested
here, the mechanical quartz oscillations
are acoustically recorded. The device
can also capacitively record the stray
electrical field from quartz oscillators
with open movements or with cases
made of synthetic material. It is also
possible to derive the quartz frequency
from the supply current if the analyser is
providing power to the watch.6
The Watch analyser (with watch D
resting on the sensor)
To get a true picture of the timekeeping
capability of an analog quartz watch,
simply measuring the quartz frequency
is not adequate. It is also necessary to
measure the stepping motor pulses,
because many watches correct the
frequency of the stepping motor to
compensate for the frequency offset of
the quartz oscillator. This correction
system, sometimes called inhibition
compensation, can be implemented in
several different ways. One common
way is to design the oscillating circuit so
that the quartz crystal runs at a
frequency slightly higher than nominal.
To compensate for this intentional
frequency offset, a programmable
number of quartz oscillation pulses are
suppressed before they are sent to the
frequency divider that drives the
stepping motor. This removes the
frequency offset, and makes time
derived from the stepping motor more
accurate than time derived from the free
running quartz. The duration of the
inhibition period, usually 10 or 60
seconds, is automatically detected by
the watch analyser. Quartz pulses might
also be added or suppressed to
compensate for the aging rate of the
quartz crystal, or for temperature
The watch analyser displays
measurements of both the quartz
frequency and the stepping motor with a
resolution of 0.01 seconds/day. The
measurements are referenced to the
time base oscillator inside the watch
analyser, and to support this resolution,
the time base oscillator must have a
frequency accuracy of better than about
1.2 × 10-7. The watch analyser was
calibrated before and after it was used to
measure the watches under test. The
calibration was done by locking a
synthesised signal generator to the
United States national frequency
standard, and then deriving a reference
32768 Hz signal from the signal
generator that was accurate to parts in
1013 or better. When this reference signal
was applied to the watch analyser
sensor, it was correctly found to be within
0.01 seconds/day. This indicated that
the watch analyser was accurate enough
to support its measurement resolution.
The watches under test were each
measured for a period of at least 30
days. During the test, the watch analyser
produced readings every minute for both
the frequency of the quartz oscillator and
the stepping motor. It also produced a
temperature reading with a resolution of
1 °C. The watch analyser was interfaced
to a computer through its RS-232 port,
and all of the readings were stored for
later analysis.
The readings returned by the watch
analyser were expressed as seconds
per day. This was converted to
dimensionless frequency offset
(accuracy) using the equation Δt/T.
Average frequency accuracy was
computed by simply averaging all of the
1 minute samples collected during the
entire test. Frequency stability was
estimated by use of the Allan deviation
as previously described. The
dimensionless frequency offset values
served as the
idata series. Because a
new value was obtained every minute,
the base averaging time, τ0was equal to
1 minute.
Measurement Results
Table 1 shows the measured accuracy
of the watches under test, both as
dimensionless frequency accuracy, and
as time accuracy (seconds per day).
Due to inhibition compensation, all of the
watches are accurate to much better
than 1 second per day. In response to
our initial question, only one of the
watches under test failed to meet the
±15 seconds per month specification
that was discussed earlier. That was
Watch C, the oldest watch in the test,
and it missed by only a few seconds per
month. The quartz oscillators in watches
A, B, and Care not particularly accurate,
with frequency offsets (perhaps
intentionally introduced) ranging from
5.9 to 10 parts in 105. In contrast, the
quartz oscillator in Watch D was a stellar
performer, with an average frequency
offset of just 8 × 10-7, or less than 1 part
per million. The accuracy of Watch D’s
stepping motor was nearly identical to
the accuracy of its quartz oscillator, so it
is not clear if inhibition compensation is
used in the design. However, the watch
analyser detected an inhibition period of
10 seconds, as reported in Table 1.
The stability estimates for the four
watches are summarised in Table 2 and
illustrated in 6. The eight lines on the
graph show the stability of both the
quartz oscillator and the stepping motor
for each of the four watches. The graph
is an ‘all-tau’ graph, meaning that it
shows stability estimates for all possible
values of τ, ranging from 1 minute to 1
Horological Journal February 2008 59
week (in 1-minute increments). It is
interesting to note that the watches were
most stable at τ= 1 hour, when all of the
devices were stable to within less than
2.5 × 10-8. At τ= 1 day, all of the devices
were stable to at or near 3×10-8,
suggesting that their accuracy will vary
by only a few milliseconds per day.
The Allan deviation graph for the
watches under test
While inhibition compensation
dramatically improved the timekeeping
accuracy of three of the four watches
(Table 1), it seemed to only significantly
improve the stability at short averaging
times. At longer averaging times, the
stability of the stepping motor was about
the same or worse as the stability of the
quartz crystal. The crossover point
where the stability of the quartz oscillator
began to meet or exceed the stability of
the stepping motor occurred at less than
25 minutes for watches Aand C, and
near 1 hour for watches B and D.
As might be expected, the variation in
frequency for watches A, B, and Cwas
larger at one week than it was at one
day, due to the effects of frequency drift
and aging. Frequency drift is generally
attributed to factors external to the
oscillator, including environmental
factors such as temperature, vibration,
and humidity. These factors were
reasonably well controlled in the
laboratory environment, and the watches
were certainly subjected to fewer
environmental changes than they would
have been during normal use. However,
it should be noted that the laboratory
temperature during the tests (Table 1)
was lower than optimal. Quartz watches
are optimised to work best at a
temperature that reflects the expected
temperature of the watch in normal
operation. If the watch is worn as
intended, this means about 16 hours on
the wrist, and about 8 hours off the wrist
each day. If the watch is left off the wrist
for extended periods, its accuracy can be
expected to degrade. The angle of cut of
the crystal resonator used in
wristwatches is such that the zero
temperature coefficient is usually in the
range of 25 °C to 28 °C (27 °C is typical),
which is warmer than the laboratory
temperature during the test.
Aging is the systematic change in
frequency with time due to internal
changes in an oscillator. All quartz
oscillators age, but the aging rate often
depends upon its surface area to volume
ratio of the crystal; and in theory, small,
low frequency crystals will age slowly.7
The results seem to support this, as the
crystal in the watches under test all were
stable to within about 5 × 10-8 or better at
τ= 1 week, and watch Dwas nearly as
stable at one week as it was at one day.
The frequency stability of watch D
suggests that its timekeeping accuracy
would change by less than 2
milliseconds per day over the course of a
week. Thus, in response to one of our
questions, quartz watches do change
their accuracy slightly over time, but the
change is small and will probably not be
noticeable to the owner of the watch.
Based on these tests, it seems likely
that even the humblest quartz wristwatch
can maintain time accurate to within less
than 1 second per day with the aid of
inhibition compensation. And due to the
surprisingly good stability of 32 kHz
quartz crystal oscillators, the accuracy of
quartz wristwatches can be expected to
change by only a small amount over
The author is an employee of a US
Institute making this article a
contribution of the United States
government, and not subject to
copyright. The illustrations and
descriptions of commercial products
are provided only as examples of the
technology discussed, and this
neither constitutes nor implies
endorsement by the NATIONAL
Frequency Accuracy
Time Accuracy
(seconds per day)
during test (° C)
5.3 × 10-6
7.9 × 10-5
22 to 25
2.1 × 10-6
5.9 × 10-5
21 to 25
6.7 × 10-6
1.0 × 10-4
22 to 26
7.8 × 10-7
8.0 × 10-7
22 to 26
Table 1: The accuracy of the watches under test.
Stability (Allan deviation)
1 minute
1 hour
1 day
1 week
2.9 × 10-8
4.6 × 10-8
1.5 × 10-8
1.3 × 10-8
2.2 × 10-8
1.8 × 10-8
2.6 × 10-8
2.2 × 10-8
4.1 × 10-8
8.4 × 10-8
1.3 × 10-8
1.3 × 10-8
2.9 × 10-8
3.2 × 10-8
4.0 × 10-8
4.0 × 10-8
3.4 × 10-8
6.7 × 10-8
2.3 × 10-8
2.0 × 10-8
2.9 × 10-8
3.1 × 10-8
4.8 × 10-8
5.4 × 10-8
2.5 × 10-8
6.6 × 10-8
1.2 × 10-8
1.1 × 10-8
2.9 × 10-8
1.7 × 10-8
2.2 × 10-8
1.6 × 10-8
Table 2: The stability of the watches under test.
1 J. Engdahl and H. Matthey, 32 kHz Quartz
Crystal Unit for High Precision Wrist Watch,
Proceedings of the 1975 Frequency Control
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in Quartz Tuning Fork Resonators,
Proceedings of the 1997 IEEE Frequency
Control Symposium, May 1997, pp. 552-
3 IEEE, IEEE Standard Definitions of
Physical Quantities for Fundamental
Frequency and Time Metrology - Random
Instabilities, IEEE Standard 1139-1999,
March 1999.
4 J. A. Frieman, Performance of a Railroad
Watch, HJ, 141(7), July 1999, pp. 243-246.
5 P. Woodward, Performance of the Daniels
Coaxial Escapement, HJ, 146(8), August
2004, pp. 283-285.
6 Witschi Electronics Ltd., analyser Q1:
Instruction Manual, Witschi Document
Number 26.6410D35e, Rel. 1.0, 2005.
7 J. R. Vig and T. R. Meeker, The Aging of
Bulk Acoustic Wave Resonators, Filters,
and Oscillators, Proceedings of the 1991
IEEE Frequency Control Symposium, May
1991, pp. 77-101.
... The sync traces for New York City and Los Angeles (for same satellite configuration used in Figure 4) is shown in Figure 5 for a hold over time of 600 seconds (standard Rubidium clocks can hold time at 1 ns precision for around 600 s, even smaller CSACs can do so for around 60-100 s. For reference an ordinary quartz crystal wrist watch can hold time at around 1 millisecond precision for 100 seconds [38]). Simply put, sync traces are chopped up versions of the connection traces indicating regions of simultaneous connection (or non-simultaneous but within time τ of each other). ...
We propose a satellite-based scheme to perform clock synchronization between ground stations spread across the globe using quantum resources. We refer to this as a quantum clock synchronization (QCS) network. Through detailed numerical simulations, we assess the feasibility and capabilities of a near-term implementation of this scheme. We consider a small constellation of nanosatellites equipped only with modest resources. These include quantum devices such as spontaneous parametric down conversion (SPDC) sources, avalanche photo-detectors (APDs), and moderately stable on-board clocks such as chip scale atomic clocks (CSACs). In our simulations, the various performance parameters describing the hardware have been chosen such that they are either already commercially available, or require only moderate advances. We conclude that with such a scheme establishing a global network of ground based clocks synchronized to sub-nanosecond level (up to a few picoseconds) of precision, would be feasible. Such QCS satellite constellations would form the infrastructure for a future quantum network, able to serve as a globally accessible entanglement resource. At the same time, our clock synchronization protocol, provides the sub-nanosecond level synchronization required for many quantum networking protocols, and thus, can be seen as adding an extra layer of utility to quantum technologies in the space domain designed for other purposes.
... -Frequency standards (quartz clocks and quartz watches), being at least one order of magnitude more accurate compared with mechanical clocks [220], employ a crystal oscillator made from a quartz crystal that uses a combination of both direct and inverse piezoelectricity to generate a regularly timed series of electrical pulses. The quartz crystal (like any elastic material) exhibits a precise natural frequency that can be used to stabilize the frequency of a periodic voltage applied to the crystal. ...
Full-text available
This lecture text condenses the characteristics of quartz and its rich palette of varieties. The mineralogy and crystallography of quartz and its forms, the origin of its colors, and their important physical and chemical characteristics are discussed. The geological occurrence of quartz and its varieties in the world is also presented, with special attention to North Macedonia. Their applications in various industries are also included. Knowledge of the specific properties of SiO2 minerals is indispensable for understanding and reconstruction of geological processes, as well as for specific technical applications.
... Although quartz oscillators have many desirable properties, some drawbacks include variability of the natural resonance frequency in response to changes in temperature, pressure, and age (Marrison, 1948). Therefore, left to run on their own, consumer-grade quartz clocks can drift by several seconds per month even in relatively temperature-stable environments (e.g., Lombardi, 2008). To overcome these issues, the atomic clock was developed in the 1950s using the hyperfine structure (or energy levels) of atoms as a reference frequency to form a feedback loop with the quartz oscillator (McCarthy and Seidelmann, 2009). ...
Full-text available
The accuracy of timing across a seismic network is important for locating earthquakes as well as studies that use phase‐arrival information (e.g., tomography). The Global Seismographic Network (GSN) was designed with the goal of having reported timing be better than 10 ms. In this work, we provide a brief overview of how timing is kept across the GSN and discuss how clock‐quality metrics are embedded in Standard for Exchange of Earthquake Data records. Specifically, blockette 1001 contains the timing‐quality field, which can be used to identify time periods when poor clock quality could compromise timing accuracy. To verify the timing across the GSN, we compare cross‐correlation lags between collocated sensors from 1 January 2000 to 1 January 2020. We find that the mean error is less than 10 ms, with much of the difference likely coming from the method or uncertainty in the phase response of the instruments. This indicates that timing across the GSN is potentially better than 10 ms. We conclude that unless clock quality is compromised (as indicated in blockette 1001), GSN data’s timing accuracy should be suitable for most current seismological applications that require 10 ms accuracy. To assist users, the GSN network operators have implemented a “gsn_timing” metric available via the Incorporated Research Institutions for Seismology Data Management Center that helps users identify data with substandard timing accuracy (the 10 ms design goal of the GSN).
... N t π = t π + t j 2 t π f π ≈ 2t j t π t π f π = 1.7 × 10 −6 Hz −1/2 . (9) Over the time scale of the measurements (100 -400 s), N t π exceeds the typical centerfrequency drift in a quartz oscillator (approximately 10 −8 ) [28]. The π-pulse area noise is thus dominated by the short-term phase noise of the FPGA clock. ...
We present a spin-exchange relaxation-free vector magnetometer with suppressed 1/f probe noise, achieved by applying a small dc bias field and a comb of magnetic dc π pulses along the pump direction. This results in a synchronous orthogonal ac response for each of its two sensitive axes. The magnetometer is particularly well suited to applications such as biomagnetism in which the signal to be measured carries a dominant component of its power at low frequencies. The magnetometer reaches a technical noise floor of 8.4 fT Hz−1/2 (x^) and 11 fT Hz−1/2 (y^) at 0.01 Hz. A single-axis dc spin-exchange relaxation-free (SERF) magnetometer sharing the same experimental apparatus attains 61 fT Hz−1/2 at the same frequency. A noise minimum of 1.1 fT Hz−1/2 (x^) and 2.0 fT Hz−1/2 (y^) is reached by the magnetometer at 10 Hz, compared to 0.7 fT Hz−1/2 at 25 Hz for a dc SERF magnetometer.
Estimation of the time of death (TOD) is a central task to forensic pathologists. The current gold standard method for TOD-estimation is only applicable in the first 24 hours post-mortem and it is advisable to employ multiple methods, if possible. A wristwatch found on the decedent can be a valuable additional tool for TOD-estimation. This technical report provides a brief overview of the two major watch types – mechanical and quartz-based timepieces – and a step-by-step guide to using these for TOD-estimation. The methods are demonstrated using case illustrations.
The time shift of mechanical watches is caused by individual differences (manufacturing error), environmental temperature, magnetism, posture, impact force and dynamic environment. The easiest and clearest method of measuring the accuracy of mechanical watches is to measure the time shift by comparing it with the reference time. The disadvantage of this method is that it can only measure accuracy at a certain time. Another method for measuring the accuracy of mechanical watches uses a watch timing machine that obtains the vibration sound of a watch using a microphone and calculates accuracy in the short term. This method can measure the change in watch accuracy over time. However, it cannot be used to measure accuracy in a dynamic environment because the watch timing machine is large and there is a sound noise. To clarify the accuracy of mechanical watches in dynamic environment, this study developed an accuracy measurement system which can be carried and measure in a dynamic environment. This study monitors the movement of a partly constituted mechanical watch using a photo interrupter and develops a method to calculate the rate and amplitude of a balance wheel from the output value of the photo interrupter. The validity of the developed system is verified by comparing the time shift of the system and radio clock time over the long term. The developed system, can be used in a dynamic environment because it consists of the photo interrupter in the watch case. Moreover, this study conducted measurements under forced vibration using vibration generator and during walking with the system.
Watch testers offer a fast and accurate way to calibrate stopwatches using the time base method. Watch testers usually include microphone sensors that pick up either the ultrasound from quartz oscillators or the acoustic vibration from balance wheels, and instrumentation that measures the accuracy of these frequencies. As a laboratory instrument, the watch tester itself requires calibration. Two simple circuits have been developed to generate the acoustic signals for the calibration of quartz and mechanical watch testers, respectively. The reference frequency is obtained from a signal generator phase locked to the laboratory frequency standard. It is assumed that the laboratory frequency standard has been calibrated, has a known measurement uncertainty, and that metrological traceability to the International System (SI) second has been established.
The development of optical clocks has made a great progress in the past years. Optical atomic clocks have demonstrated higher accuracies and stabilities than state of the art microwave oscillators and show their potential to target fractional frequency inaccuracies below 10a 17. This has led to a proposal to redefine the SI second using an optical transition of an atom clock. Possible candidates are evaluated and within the next year one should be elected. Not only for such fundamental definitions of the metric system, but also for tests of the fundamental theories have these clocks provided an astonishing tool. Reaching into the atto-scale of fractional frequency inaccuracy the gravitational redshift is readily measurable within the laboratory. Prospects for tests of the Einstein equivalence principle both earth and space bound will open new boundaries for alternative theories of gravitation. Even the recently observed gravitational waves can be a research target of satellite missions with optical atomic clocks on board. In this work, a highly stable optical local oscillator for the use in the drop tower Bremen was developed. The drop tower Bremen allows the experimentalist for the use of 4,7 s free fall in microgravity. It is a first step in the evolution of experiments outside the laboratory and in terms of technology readiness this presents a first demonstration of an operation of an optical cavity in a relevant environment. Stringent requirements for weight, space and power consumption make it difficult to achieve the worlda s best performance. In this work the measured frequency stability was found to be I y(3,5 s) 7,2 A 10a 15 in the Allan deviation. The optical cavity used in the apparatus is a spherical ULE spacer with fused-silica mirrors. It shows a finesse of F a 480.000 for the reference cavity and F a 330.000 for the dropped cavity. We can report successful drops in the drop tower Bremen with no degeneracy in the performance. A detailed description of both apparatus is given and the special steps taken for the capsule integration are explained. Another part of this work is the detailed discussion of the mathematical framework for the electric signals of a photo detector, if two laser fields are detected simultaneously. The heterodyne measurement is explained and applied to the case, where the linewidth is to be measure by a self-referencing scheme. This includes both the long known delayed self-heterodyne interferometers as well as the discussion of the possibility for short-delayed self-heterodyne interferometers. A published work is disproved and discussed.
Time synchronization is crucial for wireless sensor networks (WSNs), where operations often rely on time ordering of events. WSNs are deployed in different scenarios, and therefore their timing requirements are often related to the peculiar characteristics of the specific environment they have to act in. Synchronization is anyway always an issue: transactional applications need monotonicity of the nodes' clocks to avoid time reversal, ultralow power applications call for minimal overhead to allow for low-duty-cycle operation, applications facing extreme environments have to maintain the needed precision in the presence of unforeseen thermal drift, and so on. Specially, control applications on battery-powered devices, where timing is an issue and low-power operation is highly desired, benefit from synchronization. However, to date, the problem of synchronization has been differently faced depending on the application domain. This paper proposes a general solution to the problem of synchronization in WSNs, which seamlessly integrates with the radio stack. In addition, it guarantees monotonic and continuous node clocks with low overhead for the infrastructure. The solution is based on a decentralized control scheme that is stable and robust to thermal stress, without the need for temperature measurements. The control scheme is simulated and implemented on real WSN nodes. The efficiency of the scheme is evaluated with simulations and experiments, providing insights on the maximum synchronization error between nodes, on the communication overhead, and on the limited nodes' power consumption. The solution is also compared with state-of-the-art alternatives.
Conference Paper
Full-text available
The aging of quartz crystal resonators, filters, and oscillators is reviewed, including such topics as the impacts of aging, typical aging characteristics, aging specifications, aging mechanisms, temperature dependence of aging, frequency and overtone dependence of aging, drive level dependence of aging, the effects of aging interruptions, the dependence of aging on material and mode type, state-of-the-art in low-aging oscillators, and aging acceleration effects. The aging mechanisms discussed include contamination transfer effects, stress effects, electrode effects, diffusion effects, changes in the quartz material, and circuit and other electrical changes. Isothermal and thermal step stress aging acceleration methods are reviewed. The full text of this paper may be downloaded for free (open access) from IEEE Xplore, DOI: 10.1109/FREQ.1991.145888
Conference Paper
The progress in quartz tuning fork resonators brought dramatically an epoch not only to the wristwatch technology but also to the fields of portable equipment and communication equipment in the sense of stable frequency sources with very low power consumption and very small size. This paper gives the historical review of the progress in quartz tuning fork resonators from the view points of both technology and business
  • Performance Woodward
  • Of The Daniels Coaxial
  • Escapement
Woodward, Performance of the Daniels Coaxial Escapement, HJ, 146(8), August 2004, pp. 283-285.
Instruction Manual, Witschi Document Number 26
  • Witschi Electronics Ltd
Witschi Electronics Ltd., analyser Q1: Instruction Manual, Witschi Document Number 26.6410D35e, Rel. 1.0, 2005.
Review of Progress in Quartz Tuning Fork Resonators
  • A Momosaki
  • Brief
Momosaki, A Brief Review of Progress in Quartz Tuning Fork Resonators, Proceedings of the 1997 IEEE Frequency Control Symposium, May 1997, pp. 552- 565. 3 IEEE, IEEE Standard Definitions of Physical Quantities for Fundamental Frequency and Time Metrology -Random Instabilities, IEEE Standard 1139-1999, March 1999.
Performance of a Railroad Watch
  • J A Frieman
J. A. Frieman, Performance of a Railroad Watch, HJ, 141(7), July 1999, pp. 243-246.
IEEE Standard Definitions of Physical Quantities for Fundamental Frequency and Time Metrology -Random Instabilities, IEEE Standard 1139-1999
IEEE, IEEE Standard Definitions of Physical Quantities for Fundamental Frequency and Time Metrology -Random Instabilities, IEEE Standard 1139-1999, March 1999.
Performance of the Daniels Coaxial Escapement
  • P Woodward
P. Woodward, Performance of the Daniels Coaxial Escapement, HJ, 146(8), August 2004, pp. 283-285.