MadSci Network: Engineering
Query:

Re: How does a digital watch or timer keep time correctly?

Date: Fri May 15 17:09:00 1998
Posted By: Steve Czarnecki, senior technical staff member, Lockheed Martin
Area of science: Engineering
ID: 894376678.Eg
Message:

At the heart of a digital watch or timer is a quartz crystal that vibrates 
at a specific frequency, much like a tuning fork.  As you know, the 
frequency, (rate of vibration) of a tuning fork depends on the material 
it's made of and the size and shape of the legs of the fork.

In the case of digital watches or timers, the quartz crystal is cut to very 
accurate size (often by laser) to make sure it vibrates at a very 
particular frequency.  This frequency is typically, 32,768 vibrations per 
second or hertz (abbreviated Hz), with an accuracy of plus or minus
1 Hz for cheap watches to perhaps 0.001 Hz for precision timers.  These 
accuracies correspond to accuracies of 3 seconds per day to 1 second per 
month.

The quartz is not actually cut to the shape of a tuning fork but into a 
slab.  Nonetheless, this slab of quartz has a particular frequency at which 
it naturally resonates (much as a solid block of metal suspended by a thin 
wire will ring at a particular pitch when struck). 

As the crystal vibrates, it shrinks and expands slightly. The quartz 
crystal has an interesting property in that mechanical forces create 
a voltage called piezoelectricity. This means that if you compress the 
crystal slightly, a small voltage is created.  Conversely, if you try to 
pull the crystal apart, the opposite voltage is created.  The vibrations 
act to compress and expand the crystal, causing an oscillating voltage to 
be created across the face of the crystal.  Conversely, if you apply a 
voltage to the crystal, it will shrink or expand slightly. 

An aside: piezoelectricity is also what makes the "needle" work on crystal 
pickups for phonographs, or how the "crystal headphones" used in the early 
days of radio work.

This piezoelectric voltage is picked up by electrodes affixed to the 
crystal, and amplified by electronic circuitry and converted into 32768 
pulses per second.  A digital circuit known as a divider has the neat 
property that it will produce one output pulse for every TWO input pulses. 
 A chain of dividers is used to count the pulses:  the first gets 32768 
pulses per second, and produces 16384 per second.  The second divider takes 
this signal and produces 8192 pulses per second, feeding the third, which 
produces 4096, and so, and so on, until the 15th divider takes the two 
pulses per second it's given and produces one pulse per second at its 
output.  Note that 32768 = 2**15 = 2*2*...*2 (fifteen times)

This one pulse per second is used to trigger the display electronics to 
change the state of the display to the next higher count.  (When you "set" 
the time, you are initializing a count in the display).

Quartz watches with analog hands either use the 1 pulse per second (or some 
higher multiple) to trigger a tiny electric stepping motor that drives the 
hands, or to supply a tiny synchronous AC motor whose motion is locked to 
the input frequency.  

One further refinement in understanding: left to its own devices, the 
vibrations of the quartz crystal would quickly die out.  In practice, 
the electrodes on the crystal serve to make it part of an electronic 
circuit known as an oscillator. The highly resonant nature of the crystal 
serves to lock the electronic oscillator's frequency at the crystal's 
resonant frequency.  The oscillator circuit in turn gives the crystal a bit 
of energy every cycle to keep the vibration going (it gets just enough of a 
energy kick every cycle to offset energy losses due to internal friction 
within the crystal and vibrations transmitted to surrounding air and 
packaging).    

If you want to find out more about how these circuits work, you might try 
your school library to find books on simple electronics projects.  You 
might also try looking at "cookbooks" of simple electronics circuits.  
Radio Shack used to sell these, as well as the necessary parts (or part 
kits) to experiment with building your own digital timers.  Another great 
reference that will discuss quarz crystal oscillators is the "Radio 
Amateur's Handbook".  Your school library should have a copy.

Try experimenting with electronics or even amateur radio yourself! More 
than one grown-up electrical engineer cut their teeth this way. 

It's fun, and there's a lot more to electronics than the simple cogs and 
gears of a computer that lets you see Web pages :-)  

Steve Czarnecki 

 


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