Tsim Sha Tsui, Hong Kong SAR, 12th May 2014
Just in case you thought our work was easy, here's an email I just sent Mike:
Thanks for your note. As you know, I've had a long love-hate relationship with quartz. It's a tough cookie, for better or worse, when it comes to the talent show of materials. First, and most important for watchmaking, it is heavily piezoelectric. You can pound it and squeeze it with electricity, and it will go BOING! Fold it into a tuning fork shape and it will sing like a wine glass. A single note of exceptional quality. Good enough, in theory, to resonate to within one second a year accuracy. That's one part in 30 million.
I think the variations you're seeing are either measurement error in our equipment or the effects of temperature - you'd be surprised how much it varies. The thermometer on the wall divider in the lab is only attached with velcro - take it to your desk if you like.
In the last five years, I've done a lot of research into crystal (xtal) accuracy. These are the only factors I can identify, and how I we should address them:
- Xtal mass transfer. Mass is added or lost from the quartz wafer. This might be manufacturing crud falling off or onto it. We don't have control over the manufacturing process, so we can't avoid it. We should address it by offering occasional servicing or a user-activated recharacterization function.
- Xtal stress ageing. The vibrations themselves age the crystal. Not just its own lattice imperfections, but basic things like the epoxy that attaches it to the case. We can't control the physics down to that level of detail. So again, we should address it by offering occasional servicing or a user-activated recharacterization function.
- Xtal shock ageing. Sudden g-forces, such as dropping it, can expose tiny surface cracks that catastrophically detune the xtal by as much as 5ppm. This is the last reason we need to offer a offering occasional servicing or a user-activated recharacterization function. None of the other watchmakers discuss this kind of degradation in accuracy over time. We have to be the first to properly address it for what it is.
- Characterization of xtal frequency variance with thermal expansion. The textbooks tell you the variation in frequency with temperature is inverse parabolic. They're talking a load of parabolics. Quartz is real, not in Second Life. It's a far more nuanced relationship, and specific to every crystal, according to how it's cleaved. And each crystal has individual imperfections. Hence the desire to absolutely characterize every Hoptroff watch individually. There's no getting round the need to measure the thermistor ADC reading / crystal frequency relationship for each movement individually, across the entire ISO10553 temperature range and, ideally, much further, because we can. (Let's call that XCITE = Xtal Calibrated Individually for Thermal Expansion.)
- Difference in temperature between xtal and thermistor. I reckon I've designed this out by positioning them very close together on the circuit board. I did some tests cycling the temperature well beyond the ISO10553 temperature range in excess of 5°C/min (basically straight from oven to freezer and back, with the specific heats of the acetal and FR4 providing themal inertia) and it was showing thermal equilibrium on the way up and down.
- Characterization of thermistor temperature variance. Thermistors don't live in Second Life, either, an have individual nonlinearities. Fixed by XCITE.
- Thermistor bias tolerance. The thermistor circuit is a potential divider, specifically designed to be most sensitive inside the ISO10553 temperature range. However, the bias resistor is just a speck of 0402 carbon, and could be off-spec by 1%, which would set the temperature measurement right off if not characterized. Fixed by XCITE.
- Frequency counter calibration. How accurate is our measuring equipment? This was a real concern when I was using the Hameg frequency counter and the Trimble Thunderbolt GPSDO. It was pushing their limits to be measuring seconds per annum. Fixed now with the CSAC atomic clock in the XCITE process.
- Capacitance of circuit. The watch case and the human body should be far enough away not to impact too much, but the acetal shell is within 0.2mm of the capacitors and may have a dielectric influence. We have to make sure all calibration is done with the acetal shell attached.
- Correct function of measurement electronics. My job to get this right.
- Correct function of measurement software. Your job to get this right.
We should be targeting 1 second per annum. I don't know if we can achieve it - the physics may just get the better of us in such a confined, harsh environment - but I see no reason why we shouldn't at least be the best in the world. If Harrison could do it, if Breguet could do it, we can.