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The Accuracy and Stability of Quartz Watches

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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
question.
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
y
i
series contains estimates
of the frequency accuracy of the device
under test, M is the number of values in
the
y
i
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
changes.
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
y
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
=
+
=
1
1
2
1
)(
)1(2
1
)(
M
i
iiy
yy
M
τσ
5
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.
Summary
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
time.
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
INSTITUTE OF STANDARDS AND
TECHNOLOGY (NIST).
Dimensionless
Frequency Accuracy
Time Accuracy
(seconds per day)
Temperature
during test (° C)
Watch
Stepping
Motor
Quartz
Oscillator
Stepping
Motor
Quartz
Oscillator
Range
Average
A
5.3 × 10-6
7.9 × 10-5
0.46
6.79
22 to 25
23.3
B
2.1 × 10-6
5.9 × 10-5
0.18
5.09
21 to 25
23.8
C
6.7 × 10-6
1.0 × 10-4
0.58
8.76
22 to 26
23.9
D
7.8 × 10-7
8.0 × 10-7
0.07
0.07
22 to 26
23.3
Table 1: The accuracy of the watches under test.
Stability (Allan deviation)
1 minute
1 hour
1 day
1 week
Watch
Motor
Quartz
Motor
Quartz
Motor
Quartz
Motor
Quartz
A
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
B
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
C
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
D
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.
References
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6
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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
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