How does a quartz watch count to 32,768?
Sometimes I find myself with a question that is sufficiently interesting to lodge itself into my brain but not so urgent that I actually try to find an answer. It ends up lingering in the background and occasionally rears its head.
One such question is how a quartz watch "knows" when 32,768 vibrations have passed. Most folks here probably know that a quartz watch is considerably more accurate than a mechanical watch because it is designed around a high frequency crystal: Apply a small electric current to this crystal, and it begins to vibrate at a precisely known frequency. If the watch manages to tick the seconds hand every 32,768 vibrations, that's once per second (with a very small deviation, which add to around 10 seconds per month in basic quartz models). But how does the watch actually do this?
I had never bothered to check, but I just stumbled across a video that has the answer:
32,768 is 2 to the power of 15. (It's also above 20,000 hertz, which is the upper limit of what the human ear can hear. That's why your quartz watch doesn't audibly hum.) If you feed a current with frequency 32,768 through a flip-flop circuit, it gets cut in half. If you then feed it through a second flip-flop, it is halved again. And if you feed it through a chain of 14 flip-flops, it is reduced to a frequency of 1. That 1-hertz current can then power a stepper motor to move the seconds hand. (If you remove the final two flip-flops, you end up with a 4-hertz current, which would equal the beat frequency of many mechanical watches and smooth the sweeping action of the hand, but it would drain the battery too quickly.)
Voila. That puts my question to rest. Have a great week, everyone!
