Mechanism
In modern quartz clocks, the quartz crystal resonator or oscillator 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 cycles per second. 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 Lavet type stepping motor or a liquid crystal display (in an LCD digital watch). Light-emitting diode (LED) displays for watches have become rare due to their comparatively high battery consumption.
The basic formula for calculating the fundamental frequency (f) of vibration of a cantilever as a function of its dimensions (quadratic cross-section) is:
where
- 1.875 the smallest positive solution of cos(x)cosh(x) = -1
- l is the length of the cantilever
- a is its thickness along the direction of motion
- E is its Young's modulus
- and ρ is its density
A cantilever made of quartz (E = 1011 N·m−2 = 100 GPa and ρ = 2634 kg·m−3 ) with a length of 3 mm and a thickness of 0.3 mm has thus a fundamental frequency of around 33 kHz. The crystal is tuned to exactly 215 = 32,768 Hz or runs at a slightly higher frequency with inhibition compensation (see below).
Read more about this topic: Quartz Clock
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