The Accuracy and Stability of Quartz Watches 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 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. 3-C 4-D 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. 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 crystal ‘run-of-the-mill’ quartz wristwatch? Can (215 Hz) quartz crystals 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 1970s 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 day) 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 years test. Accuracy is related to the difference accuracy indicates how well a clock 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 Universal Time (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-1980s) 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 second 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.