[MarianaM (OP)]

Nev is wondering...

Why does the time on my digital wrist watch always end up being 5 minutes ahead within 3 months? I always turn it back but it still jumps ahead. Every digital wrist watch I've ever had did this.

Let's not waste time... can you help?

[alancalverd]

Cheap electronic watches rely on being worn for about 16 hours per day in a normal ambient. The driving crystal oscillator is temperature-sensitive with a minimum drift at around 25 - 35 deg C, the temperature on your wrist. If you work in particularly hot or cold conditions, the watch will drift.

I can recommend Citizen (other brands are available, but this is what I use) Eco-drive pilot watches. Slightly less temperature sensitive (optimum crystal cut, but the crystal is bigger), and no battery. I paid less than £100 for mine, about 10 years ago, and it has gained exactly 21 seconds since then. Or you can spend a lot more and get one that resynchronises to a national radio time standard. The problem with those is that in the absence of a radio signal, they may not keep particularly good time over a few days as they expect to be resynchronised every hour or so!

[evan_au]

The standard 32,768Hz "tuning fork"  crystal has a parabolic temperature coefficient.
- This frequency is chosen so a simple, low-power 15-stage binary divider brings it down to 1Hz to drive a clock mechanism (or display).
- But it seems that if the temperature is higher or lower than the center frequency, it actually runs slower than the nominal 32,768Hz.
- So that means that a watch should run slow?

Some other crystal cuts have a cubic temperature coefficient.
- This allows them to stay close to the nominal frequency over a wider temperature range
- But these typically oscillate at a higher frequency (MHz), and need a larger divider ratio (consuming slightly more power).

There are many crystal vendors, but this one illustrates the difference between parabolic and cubic temperature coefficients:
https://abracon.com/Support/Tuning-Fork-Crystals-and-Oscillator.pdf

With a temperature sensor, it is possible to compensate for the crystal temperature drift in software - but this produces even more complex behaviors.
- If the software is internet-connected, it can keep aligned with a local time server.
- Smartphones typically are connected to the mobile network and GPS, which provide additional time references.

[alancalverd]

Just another possibility. I have a bedside clock/radio with battery backup for the clock. After an extended power cut the clock always seems to have gained a few seconds or even minutes. I dimly recall using 32768 Hz crystals in a number of projects in the past, and IIRC a simple double-inverter oscillator would run fast during power-down transients, almost as though the crystal wasn't being sufficiently stressed either direction. And again IIRC there are actually two resonant frequencies for a simple crystal oscillator - we used a bit of capacitive damping to suppress one of them - presumably the higher.