Quartz watch 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 Women Dress 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.1 Since 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.

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 t/T and f/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.

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 watchthat 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.3 It 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 Geneva Quartz Watch under test.

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.