How a Quartz Watch Keeps Time With a Vibrating Crystal

A quartz watch keeps time by counting the vibrations of a tiny piece of quartz crystal. In most watches the crystal vibrates 32,768 times a second. Electronics divide that number down until there is one pulse per second, and that pulse moves the hands or the digits. The method is steady because the crystal's rate barely changes, and because dividing a fast, stable vibration into slow ticks makes any small error tiny.

Why quartz can vibrate on command

Quartz is piezoelectric. According to Wikipedia, Jacques and Pierre Curie discovered this property in 1880. Squeezing or bending the crystal produces an electric charge, and applying an electric charge makes it flex. That two-way link lets a circuit drive the crystal and listen to it at the same time.

In a crystal oscillator, an amplifier sends its output through the quartz, which lets one frequency pass and filters out the rest. That frequency is fed back into the amplifier, so the circuit locks onto the crystal's natural rate. Wikipedia explains that in modern standard-quality quartz clocks the crystal is cut in the shape of a small tuning fork and trimmed so that it vibrates at 32,768 Hz. One hertz (Hz) is one vibration per second.

Why 32,768?

The number is not random. It is 2 to the power of 15, which means 15 simple divide-by-two circuits in a row turn it into exactly one pulse per second. Wikipedia adds that the figure is above the range of human hearing, yet low enough to keep power use, cost and size down. NIST, the United States national measurement institute, confirms in its timekeeping FAQ that a quartz crystal in a wristwatch circuit usually vibrates at 32,768 Hz and that the circuit divides by 32,768 to produce one-second ticks.

Why dividing improves accuracy

NIST gives a worked example. Suppose the crystal is off by 0.1 Hz. Because the watch has to count 32,768 vibrations for each second, it takes 327,680 seconds for that error to add up to one full second. That is about 0.26 seconds lost or gained per day. The higher the frequency being counted, the smaller each tick-sized error becomes.

• The crystal vibrates at a steady rate, usually 32,768 Hz
• A chain of dividers cuts that to 1 Hz
• The 1 Hz pulse drives a small motor for the hands or updates a digital display

How accurate is it?

Wikipedia says standard 32,768 Hz resonators are warranted to about six parts per million over the long term at 31 degrees Celsius. That is roughly 15 seconds per 30 days. Higher-grade movements can do much better: Wikipedia lists ±1 to ±25 seconds per year for high-accuracy movements, and notes that watches certified by the Swiss COSC chronometer test are allowed ±25.55 seconds per year at 23 degrees Celsius.

For comparison, NIST says a 1 GHz atomic clock off by 1 Hz would lose one second in about 31.7 years. Atomic clocks operate at far higher precision and are a different class of device from a wristwatch crystal.

What makes a quartz watch drift

Temperature is the main cause. The crystal's rate changes slightly as it warms or cools. Wikipedia gives the figures: a deviation of 1 degree Celsius from the ideal costs about 0.035 parts per million, which is around 1.1 seconds a year, while a deviation of 10 degrees costs about 3.5 parts per million, around 110 seconds a year. Consumer crystals work best at roughly 25 to 28 degrees Celsius. Wikipedia points out that a watch worn on the wrist stays close to body temperature, so the case acts as a small "crystal oven" that lessens big swings.

Ageing of the crystal and the tuning of the individual watch also play a part. Many quartz watches have a small adjustment inside, and some more expensive ones measure temperature and correct for it. The sources used here do not say how common that feature is.

A short history

According to Wikipedia, the first quartz clock was built at Bell Telephone Laboratories in October 1927 by Joseph W. Horton and Warren A. Marrison, and was accurate to about 0.01 second per day. It filled a room's worth of equipment rather than a wrist. In December 1969 Seiko produced the first commercial quartz wristwatch, the Quartz-Astron 35SQ, which Wikipedia says used an 8,192 Hz oscillator and was accurate to 0.2 seconds a day, about one minute a year. Later watches settled on 32,768 Hz.

Today the same idea sits in many devices. Computers, microcontrollers and household appliances often contain a small 32,768 Hz crystal to keep a clock running, though the sources here are about watches and do not list specific devices.

Sources

• Timekeeping and clocks FAQs, NIST
• Quartz clock, Wikipedia