The Accuracy and Stability of Quartz by Michael Lombardi Quartz wristwatches are neither as 1-A 2-B intricate nor as intriguing to many collectors as their mechanical counterparts, but with very few exceptions, they do a considerably better job of keeping . At least one manufacturer of low-priced quartz watches specifies their accuracy as ±15 per , suggesting an accumulated error of just a few per . This type of accuracy is sufficient for most people, who are generally happy if their remains within a or two of the correct time. 3-C 4-D In fact, many quartz watch owners set their watches only a few per year – typically when they change the battery, change time zones, or switch to and from . 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 or as a disposable consumer item, some questions remain. Like nearly all quartz watches, the frequency, or an ideal frequency with For example, exactly how accurate is a four devices under test use 32.768 kHz zero uncertainty. For example, if a ‘run-of-the-mill’ quartz wristwatch? Can (215 Hz) quartz as their oscillator. with a nominal frequency of 32768 Hz is they really keep time to within ±15 The quartz watch industry standardised measured at 32768.5 Hz, its frequency is seconds per month? Does their accuracy on 32 kHz crystals in the early due said to be accurate to within 0.5 Hz. vary over time? This article attempts to to their reliability, their compatibility with Both time accuracy and frequency answer those questions. It characterises existing electronic circuits, their small accuracy are normally expressed as the performance of four low-cost quartz dimensions, and their low power dimensionless values by using the wristwatches by applying some consumption.1 Since their introduction, equations Δt/T and Δf/f, respectively. measurement and data analysis watch manufacturers have continued to The two equations produce equivalent techniques that are normally reserved for improve the timekeeping performance of answers when applied to the same laboratory type frequency standards. quartz watches. Most of the advances device. Thus a time accuracy of 1.3 / have been related to crystal and mount 86400 (seconds per ) and a The Watches Under Test miniaturisation, better electronics, better frequency accuracy of 0.5 Hz / 32768 Hz The four quartz watches chosen for manufacturing techniques, and most both result in a dimensionless accuracy the test, 1-4, are members of the importantly, making the crystal frequency value of about 1.5 × 10-5. author’s pedestrian collection. While less dependent on temperature.2 Stability indicates how well a device none of them will make a watch can produce time or frequency with the enthusiast’s heart beat faster, they do Accuracy versus Stability same accuracy over a given time have the virtue of being common; and The performance of a timekeeping interval. It doesn’t indicate whether the similar watches have found their way on device is usually stated in terms of its time or frequency produced by a device to many wrists. Watch A is an ‘official’ accuracy and stability, and measuring is accurate or inaccurate, but only Mickey Mouse watch, purchased at both characteristics was the goal of this whether it stays the same. In contrast, Disneyland in California several test. Accuracy is related to the difference accuracy indicates how well a has ago for about $35 USD. Watch B is a between a measured value and an ideal been set on time or an oscillator has Rolex ‘replica’, purchased from a street value. For example, a ‘perfect’ watch been set on frequency. To understand vendor in South America for about $15 would agree exactly with Coordinated this difference, consider that an USD, and somewhat surprisingly, still (UTC), the international inaccurate device can be stable, and an running some two years later. Watch C reference for time, time interval, and unstable device can be at least is a 20-year old dress watch that frequency. If a watch was synchronised temporarily accurate. For example, a originally sold (mid-) for about to UTC and then found to be 1.3 seconds quartz watch that gains exactly 10.5 $100 USD, and was worn everyday for fast one day later, its time is said to be seconds every day is very inaccurate, more than a decade. Watch D is a accurate to within 1.3 seconds per day. but very stable. It might be possible, typical discount store watch, a new Frequency accuracy refers to the then, to adjust the frequency of the (2007) Timex that sells for approximately difference between the measured crystal and make the watch both $30 USD. frequency of an oscillator and its nominal accurate and stable. In contrast, a watch

Horological Journal February 2008 57 that fluctuates within a range of ±5 here, the mechanical quartz oscillations to support its measurement resolution. seconds of the correct time is unstable, are acoustically recorded. The device The watches under test were each but on occasion would have the correct can also capacitively record the stray measured for a period of at least 30 time and be considered accurate. electrical field from quartz oscillators days. During the test, the watch analyser The Allan deviation (ADEV) is a with open movements or with cases produced readings every minute for both statistic used internationally to estimate made of synthetic material. It is also the frequency of the quartz oscillator and frequency stability.3 It differs from the possible to derive the quartz frequency the stepping motor. It also produced a conventional standard deviation from the supply current if the analyser is temperature reading with a resolution of because it does not use the average providing power to the watch.6 1 °C. The watch analyser was interfaced accuracy of a device as a point of to a computer through its RS-232 port, reference. Instead, it compares the The Watch analyser (with watch D and all of the readings were stored for frequency accuracy of the device under resting on the sensor) later analysis. test during a given measurement period To get a true picture of the timekeeping The readings returned by the watch to its frequency accuracy during the capability of an analog quartz watch, analyser were expressed as seconds previous measurement period. This simply measuring the quartz frequency per day. This was converted to reveals how an oscillator’s frequency is is not adequate. It is also necessary to dimensionless frequency offset changing over time due to effects such measure the stepping motor pulses, (accuracy) using the equation Δt/T. as frequency drift and aging. ADEV is because many watches correct the Average frequency accuracy was regularly used to estimate the stability of frequency of the stepping motor to computed by simply averaging all of the devices ranging from high-performance compensate for the frequency offset of 1 minute samples collected during the mechanical watches4,5 to the world’s the quartz oscillator. This correction entire test. Frequency stability was best atomic oscillators, and will be system, sometimes called inhibition estimated by use of the Allan deviation applied here to estimate the stability of compensation, can be implemented in as previously described. The the quartz watches under test. ADEV, several different ways. One common dimensionless frequency offset values σ τ expressed mathematically as y( ) is way is to design the oscillating circuit so served as the yi data series. Because a computed as that the quartz crystal runs at a new value was obtained every minute, τ frequency slightly higher than nominal. the base averaging time, 0 was equal to 1 M −1 To compensate for this intentional 1 minute. σ (τ ) = ∑( y − y )2 frequency offset, a programmable y − i+1 i 2(M 1) i=1 number of quartz oscillation pulses are Measurement Results suppressed before they are sent to the Table 1 shows the measured accuracy frequency divider that drives the of the watches under test, both as

where the yi series contains estimates stepping motor. This removes the dimensionless frequency accuracy, and of the frequency accuracy of the device frequency offset, and makes time as time accuracy (seconds per day). under test, M is the number of values in derived from the stepping motor more Due to inhibition compensation, all of the the yi series, and the data are equally accurate than time derived from the free watches are accurate to much better spaced in segments τ seconds long. running quartz. The duration of the than 1 per day. In response to inhibition period, usually 10 or 60 our initial question, only one of the The Measurement Method seconds, is automatically detected by watches under test failed to meet the To estimate their accuracy and the watch analyser. Quartz pulses might ±15 seconds per month specification stability, the watches were measured also be added or suppressed to that was discussed earlier. That was with a commercial watch analyser, 5. compensate for the aging rate of the Watch C, the oldest watch in the test, This versatile device can simultaneously quartz crystal, or for temperature and it missed by only a few seconds per measure the frequency of both the changes. month. The quartz oscillators in watches quartz oscillator and the stepping motor The watch analyser displays A, B, and C are not particularly accurate, pulses. The watch analyser sensor can measurements of both the quartz with frequency offsets (perhaps automatically detect the quartz frequency and the stepping motor with a intentionally introduced) ranging from frequency through several available resolution of 0.01 seconds/day. The 5.9 to 10 parts in 105. In contrast, the methods. If the watches have metal measurements are referenced to the quartz oscillator in Watch D was a stellar cases, as did all of the watches tested time base oscillator inside the watch performer, with an average frequency analyser, and to support this resolution, offset of just 8 × 10-7, or less than 1 part 5 the time base oscillator must have a per million. The accuracy of Watch D’s frequency accuracy of better than about stepping motor was nearly identical to 1.2 × 10-7. The watch analyser was the accuracy of its quartz oscillator, so it calibrated before and after it was used to is not clear if inhibition compensation is measure the watches under test. The used in the design. However, the watch calibration was done by locking a analyser detected an inhibition period of synthesised signal generator to the 10 seconds, as reported in Table 1. national frequency The stability estimates for the four standard, and then deriving a reference watches are summarised in Table 2 and 32768 Hz signal from the signal illustrated in 6. The eight lines on the generator that was accurate to parts in graph show the stability of both the 1013 or better. When this reference signal quartz oscillator and the stepping motor was applied to the watch analyser for each of the four watches. The graph sensor, it was correctly found to be within is an ‘all-tau’ graph, meaning that it 0.01 seconds/day. This indicated that shows stability estimates for all possible the watch analyser was accurate enough values of τ, ranging from 1 minute to 1

58 February 2008 Horological Journal Watch Inhibition Dimensionless Time Accuracy Temperature Period Frequency Accuracy (seconds per day) during test (° C) (seconds) Stepping Quartz Stepping Quartz Range Average Motor Oscillator Motor Oscillator (in 1-minute increments). It is A 10 5.3 × 10-6 7.9 × 10-5 0.46 6.79 22 to 25 23.3 interesting to note that the watches were B 60 2.1 × 10-6 5.9 × 10-5 0.18 5.09 21 to 25 23.8 τ most stable at = 1 , when all of the C 60 6.7 × 10-6 1.0 × 10-4 0.58 8.76 22 to 26 23.9 devices were stable to within less than D 10 7.8 × 10-7 8.0 × 10-7 0.07 0.07 22 to 26 23.3 2.5 × 10-8. At τ = 1 day, all of the devices Table 1: The accuracy of the watches under test. were stable to at or near 3×10-8, Watch Stability (Allan deviation) suggesting that their accuracy will vary 1 minute 1 hour 1 day 1 week by only a few milliseconds per day. 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 -8 -8 -8 -8 -8 -8 -8 -8 The Allan deviation graph for the B 4.1 × 10 8.4 × 10 1.3 × 10 1.3 × 10 2.9 × 10 3.2 × 10 4.0 × 10 4.0 × 10 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 watches under test 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 While inhibition compensation Table 2: The stability of the watches under test. dramatically improved the timekeeping the wrist, and about 8 off the wrist can maintain time accurate to within less accuracy of three of the four watches each day. If the watch is left off the wrist than 1 second per day with the aid of (Table 1), it seemed to only significantly for extended periods, its accuracy can be inhibition compensation. And due to the improve the stability at short averaging expected to degrade. The angle of cut of surprisingly good stability of 32 kHz times. At longer averaging times, the the crystal used in quartz crystal oscillators, the accuracy of stability of the stepping motor was about wristwatches is such that the zero quartz wristwatches can be expected to the same or worse as the stability of the temperature coefficient is usually in the change by only a small amount over quartz crystal. The crossover point range of 25 °C to 28 °C (27 °C is typical), time. where the stability of the quartz oscillator which is warmer than the laboratory began to meet or exceed the stability of temperature during the test. The author is an employee of a US the stepping motor occurred at less than Aging is the systematic change in Institute making this article a 25 minutes for watches A and C, and frequency with time due to internal contribution of the United States near 1 hour for watches B and D. changes in an oscillator. All quartz government, and not subject to As might be expected, the variation in oscillators age, but the aging rate often copyright. The illustrations and frequency for watches A, B, and C was depends upon its surface area to volume descriptions of commercial products larger at one week than it was at one ratio of the crystal; and in theory, small, are provided only as examples of the day, due to the effects of frequency drift crystals will age slowly.7 technology discussed, and this and aging. Frequency drift is generally The results seem to support this, as the neither constitutes nor implies attributed to factors external to the crystal in the watches under test all were endorsement by the NATIONAL oscillator, including environmental stable to within about 5 × 10-8 or better at INSTITUTE OF STANDARDS AND factors such as temperature, vibration, τ = 1 week, and watch D was nearly as TECHNOLOGY (NIST). and humidity. These factors were stable at one week as it was at one day. reasonably well controlled in the The frequency stability of watch D laboratory environment, and the watches suggests that its timekeeping accuracy were certainly subjected to fewer would change by less than 2 environmental changes than they would milliseconds per day over the course of a have been during normal use. However, week. Thus, in response to one of our References it should be noted that the laboratory questions, quartz watches do change 1 J. Engdahl and H. Matthey, 32 kHz Quartz temperature during the tests (Table 1) their accuracy slightly over time, but the Crystal Unit for High Precision Wrist Watch, was lower than optimal. Quartz watches change is small and will probably not be Proceedings of the 1975 Frequency Control are optimised to work best at a noticeable to the owner of the watch. Symposium, May 1975, pp. 187-194. temperature that reflects the expected Summary 2 E. Momosaki, A Brief Review of Progress temperature of the watch in normal Based on these tests, it seems likely in Quartz Tuning Fork , operation. If the watch is worn as that even the humblest quartz wristwatch Proceedings of the 1997 IEEE Frequency intended, this means about 16 hours on Control Symposium, May 1997, pp. 552- 565. 3 IEEE, IEEE Standard Definitions of 6 Physical Quantities for Fundamental Frequency and - 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.

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