# Why aren't 1Hz crystals used to measure seconds?

According to Wikipedia:

Many clocks use a 32.768KHz crystal. Is this because the crystal is smaller than a 1Hz crystal?

If 1.0 Hz == 1.0 second. Then, why the need for the division?

• Given the speed of sound in typical solids, a 1Hz crystal fabricated the same way as watch crystals would likely be about a thousand feet long... – Brian Drummond Apr 5 '13 at 21:07
• If that is the case, then how does division help? Wouldn't a 32.768khz be firing off 32+ thousand times a second? What is it that controls the wave? Do you have to pair them up with a resistor or a cap? – JohnnyStarr Apr 5 '13 at 21:23
• I don't think so. High-frequency crystals may operate in a fashion analogous to an organ pipe, but watch crystals operate in a fashion analogous to a tuning fork. One may reduce the frequency of a tuning fork without changing its length by shifting mass toward the ends of the tines, or by making it less rigid. The further one goes with that, however, the less external acceleration the tuning fork will be able to accept without damage. Making the tuning fork bigger will allow one to reduce its frequency without making it more fragile, but will of course mean that it's bigger. – supercat Apr 5 '13 at 21:26
• @JohnnyStarr 32768 is 2^15, that means every 2 seconds your clock overflows if it is a 16-bit timer. – Kortuk Apr 5 '13 at 21:32
• Only few things are simpler than dividing by two in electronics. – jippie Apr 5 '13 at 21:53

The main reason is that a 1 Hz crystal would have to be physically very big. A crystal is a piece of quartz that mechanically vibrates at the specific frequency. Since quarts exhibits a fairly strong piezo-electric effect, those vibrations also cause electrical signals and vice versa.

Getting a physically small crystal down to 33 kHz resonant frequency was quite a breakthru not that long ago. The trick is to shape the quartz like a tuning fork. That allows for much slower oscillations than a solid block of quartz of the same size. However, extending that another 3½ orders of magnitude is going to make the crystal a lot bigger.

It's hard to imagine what use a 1 Hz crystal would be, considering how cheap and easy it is to start with a faster frequency and then divide down with a counter. 33 kHz is already so slow that you won't get any significant power savings by running the logic any slower. In fact, filtering the harmonics from a 1 Hz square wave and still providing the drive for the size crystal that it would take to make that frequency would take significantly more power. It just doesn't make sense. Put another way, a 33 kHz crystal with its drive circuit and a digital counter is smaller, cheaper, and takes less power than a 1 Hz crystal with the drive circuitry it would require.

• Well, we could get a big mass and hang it on the end of a long rod. Then, let it swing back and forth. Yes, that's it...and we can build a cabinet for it and mount it right below the clock. – gbarry Apr 6 '13 at 0:19
• @gbarry I saw a clock built in 1877 which is in an 85 foot church bell tower. It has a pendulum that looks like a cucumber 2 feet long, weighs about 100 pounds. The clock is actually quite accurate, changing by about 1 minute a month. They add or remove pennies on top of the weight to adjust the going rate from summer to winter. I laughed so hard when I read your comment! – user56384 Jan 23 '16 at 2:49

Aside from the practical aspects of making a 1 Hz crystal, every crystal is going to have some degree of jitter. If you have a 1Hz crystal to generate 1 second ticks, every bit of that jitter manifests as error in your clock. If you start with a higher frequency and divide down, that error gets minimized.

For example, a 1Hz crystal with 1% jitter would give you 1 sec +/- 1% ticks. A 1kHz clock with 1% jitter going through three divide by 10 chips will give you 1 sec +/- 0.001 % ticks.

EDIT: http://www.silabs.com/Support%20Documents/TechnicalDocs/Clock-Division-WP.pdf shows a great discussion on this. Look particularly at the phase noise reduction as division increases in figure 6, and the following table, which shows the jitter expressed in time as staying constant.

• Actually, that's not correct, I believe: a 5 parts-per-million error would remain 5 PPM no matter how much you divided it. Similarly with percentages. – Anindo Ghosh Apr 5 '13 at 21:43
• @AnindoGhosh (and his upvoters). No, this is not how it works. Because the jitter gets averaged. If you convert a 1kHz clock to 1Hz, you're taking 1000 jittery cycles to make a single cycle. The 1% jitter in any one short cycle is averaged over a thousand cycles. – Kaz Apr 5 '13 at 21:49
• 5 ppm in FREQUENCY would carry right through. 5ppm JITTER would average – Scott Seidman Apr 5 '13 at 21:51
• So yes, if there was a systematic inaccuracy in the clock, like an overall drift 1%, then of course that translates to a 1% error in the divided clock also. But this is jitter, so it is different. – Kaz Apr 5 '13 at 21:52
• @AnindoGhosh, look at it this way. 1% jitter on a 1KHz clock will be 0.01ms. Now think of that triggering a count-to-1000 999 times, to average near zero mean jitter. Now, that 1000th tick can still be +/- the same 0.01ms, or 0.001% of a 1-sec cycle. The more you divide, the less your effective jitter will be-- QED. Is that enough to rub out the downvotes? – Scott Seidman Apr 5 '13 at 22:09

Most of life's "physicality" isn't going to affect a 32k xtal. We live physically in the low tens of Hz maximum (except hearing) and a 1Hz xtal is gonna come in for a few resonant bumps. Given also that it's nearly a qtr of a mile long (according to Brian Drummond) settles the argument for me.

OK maybe bats can disturb a 32k xtal?

• It seems unintuitive that something really large would be disturbed by environmental impacts, but something tiny is not. – user56384 Jan 23 '16 at 2:55
• Think of mechanical resonance. – Andy aka Jan 23 '16 at 10:29

There is also the problem with drift, due to environmental issues. From wiki:

A crystal's frequency characteristic depends on the shape or 'cut' of the crystal. A tuning fork crystal is usually cut such that its frequency over temperature is a parabolic curve centered around 25 °C. This means that a tuning fork crystal oscillator will resonate close to its target frequency at room temperature, but will slow down when the temperature either increases or decreases from room temperature. A common parabolic coefficient for a 32 kHz tuning fork crystal is −0.04 ppm/°C².

In a real application, this means that a clock built using a regular 32 kHz tuning fork crystal will keep good time at room temperature, lose 2 minutes per year at 10 degrees Celsius above (or below) room temperature and lose 8 minutes per year at 20 degrees Celsius above (or below) room temperature due to the quartz crystal.

In practical terms, a 1Hz crystal will mean that the slightest change in temperature, will cause the clock to be fast or slow by minutes per day, instead of nanoseconds. Over a year, that would make it one of the most inaccurate clocks ever, without daily adjustment.

And that is just temperature. Pressure (And Altitude), Humidity, and vibration also come into play. So unless the crystal is in a a completely controlled environment, it is simply impractical for common everyday time keeping use.

• Perhaps I am super dense, but can you explain why 1 cycle per 1 second with 0.04ppm drift differs from 1000 cycles per 1 second with 0.04ppm drift. Unlike jitter, drift adds up, right? – angelatlarge Apr 6 '13 at 1:07
• A 33 kHz tuning fork crystal scaled up to resonate a 1 Hz may be impractically large, but I don't see how its fractional error as a function of temperature should be any different. 1 PPM is still 32 seconds per year, whether derived from a 33 kHz oscillator, 1 Hz oscillator, or anything else. – Olin Lathrop Jan 23 '16 at 14:45

There are 1Hz oscillators, only they are made using MEMS tech (bye quartz).

http://www.sitime.com/products/32-khz-oscillators/sit1544

• The SiT544 is a programmable 32KiHz oscillator: Factory programmed between 1 and 32.768 kHz in powers of 2. There is just a bunch of toggle flip flops to divide by 2. – Paebbels Jan 8 '15 at 21:54