Quartz Clocks

A quartz clock is a clock that uses an electronic oscillator that is regulated by a quartz crystal to keep time. This crystal oscillator creates a signal with very precise frequency, so that quartz clocks are at least an order of magnitude more accurate than good mechanical clocks. Generally, some form of digital logic counts the cycles of this signal and provides a numeric time display, usually in units of hours, minutes, and seconds. Since the 1970s, they have become the most widely used timekeeping technology.
Chemically, quartz is a compound called silicon dioxide. When a crystal of quartz is properly cut and mounted, it can be made to bend in an electric field. When the field is removed, the quartz will generate an electric field as it returns to its previous shape. This property is known as piezoelectricity. Many materials can be formed into plates that will resonate. However, since quartz can be directly driven by an electric signal, no additional speaker or microphone is required.

Quartz has the further advantage that its size does not change much as temperature fluctuates. Fused quartz is often used for laboratory equipment that must not change shape along with the temperature, because a quartz plate's resonance frequency, based on its size, will not significantly rise or fall. Similarly, a quartz clock will remain relatively accurate as the temperature changes.

In modern quartz clocks the quartz crystal resonator is in the shape of a small tuning fork, laser-trimmed or precision lapped to vibrate at 32,768 Hz. This frequency is equal to 215 Hz. A power of 2 is chosen so a simple chain of digital divide-by-2 stages can derive the 1 Hz signal needed to drive the watch's second hand. In most clocks, the resonator is in a small can or flat package, about 4 mm long. The reason the 32,768 Hz resonator has become so common is due to a compromise between the large physical size of low frequency crystals for watches and the large current drain of high frequency crystals, which reduces the life of the watch battery. During the 1970s, the introduction of Metal Oxide Semiconductor (MOS) integrated circuits allowed a 12-month battery life from a single coin cell when driving either a mechanical stepper motor, indexing the second hand (Quartz Analog), or a liquid crystal display (LCD Digital). Light-emitting diode (LED) displays for watches have become rare due to their very high battery consumption.

The basic formula for calculating the frequency of a quartz tuning fork as a function of its dimensions (quadratic cross-section) are as follows:

l = length = 3 mm (or 4 mm)
a = thickness = 0.3 mm
E = Young's modulus of quartz = 1x1011 N·m?2 = 100 GPa
? = density of quartz = 2500 kg·m-3 (actually, 2650 kg·m-3)
fo = fundamental frequency = 3.52
f = frequency (Hz)

If we use the above numbers in the formula for a vibrating cantilever:
The above returns f ~ 34 kHz, which is approximately 215, or 32,768 Hz.

The relative stability of the resonator and its driving circuit is much better than its absolute accuracy. Standard-quality resonators of this type are warranted to have a long-term accuracy of about 6 parts per million at 31 °C: that is, a typical quartz wristwatch will gain or lose less than a half second per day at body temperature.

If a quartz wristwatch is "rated" by measuring it against an atomic clock's time broadcast, and the wristwatch is worn on one's body to keep its temperature constant, then the corrected time will easily be accurate within 10 seconds per year. This is more than adequate to perform celestial navigation.
Some premium clock designs self-rate. That is, rather than just counting vibrations, their computer program takes the simple count, and scales it using a ratio calculated between an epoch set at the factory, and the most recent time the clock was set. These clocks usually have special instructions for changing the battery (the counter must not be permitted to stop), and become more accurate as they grow older.
It is possible for a computerized clock to measure its temperature, and adjust for that as well. Both analog and digital temperature compensation have been used in high-end quartz watches.

Quartz chronometers designed as time standards often include a crystal oven, to keep the crystal at a constant temperature. Some self-rate and include "crystal farms," so that the clock can take the average of a set of time measurements.