I recently finished running an ETA calibre 252.611 (Longines VHP Perpetual) movement through my temperature tests to determine how well it compensated for temperature changes. After finishing the test, I realized that I had amassed a large amount of data and I should see if I could decipher how this movement actually went about providing an accurate time reading.
The equipment that I use gives me one data point each 10 seconds. The data is an offset of the seconds hand solenoid discharge from a GPS signal and the time of day. The offset is recorded to an accuracy of 0.000001 seconds. A plot of the data looks something like this:
The figure shows 3 cycles of the data at a constant movement temperature of 98 ºF. Each cycle corresponds to an adjustment of the movement to the original error in the crystal (I call this the primary adjustment). The primary adjustment is factory set but can be tuned using the digital calibration method explained by our resident ETA guru - ppaulusz. The factory set primary adjustment is made once per cycle. I (and others on this forum) have referred to one cycle as an inhibition period.
For a non-thermocompensated movement, nothing else happens during the inhibition period. One factory correction and that's it. However, things are not so simple for a thermocompensated movement. During each inhibition period, other adjustments are made. These adjustments help the movement compensate for changes in crystal frequency with temperature. The figure below shows the effect of temperature on a non-thermocompensated movement.
For the ETA 252.611 movement, two adjustments are made to account for temperature changes during each inhibition cycle. These adjustment are similar in size. The following figure shows two cycles of the ETA movement with the various adjustments labeled.
The adjustments compensate for the "raw rate" of the movement, i.e., the rate that the movement would show if no adjustments were made at all. This raw rate can be determined from any one of the 3 straight line segments during each inhibition period. I made this calculation for several cycles and plotted the results as rate versus temperature.
This looks a lot like the graph of rate versus temperature previously displayed for a non-thermocompensated movement. Of course, this is how it should look if a typical 32kHz crystal is used in the movement.
So, what happens to the primary and secondary adjustment as the temperature changes? We might expect that the primary adjustment would not change significantly with temperature. We would hope that the secondary adjustments would change as they are the expected mechanism for temperature compensation. First, let's look at the primary adjustment.
There is a small change in the primary adjustment with temperature. Expanding the vertical axis shows this effect better.
The primary adjustment varies only 5.6 sec/yr over the 50 to 98 ºF temperature range. Notice that the value of the primary adjustment is similar in size, but with an opposite sign to the raw rate.
We expect the secondary adjustments to be stronger functions of temperature. This is clearly shown in a graph of the secondary adjustment versus temperature.
The secondary adjustment is clearly a strong function of temperature (varying by 111 sec/yr over the shown temperature range). Both secondary adjustments are similar in size, varying from each other by less than 0.6 sec/yr at any temperature.
Note that the secondary adjustment curve is an inverse of the raw rate curve.
So, how is the actual rate of the ETA 252.611 movement found? At the temperature of interest, take the raw rate then add the primary and both secondary adjustments. For example, at 90 ºF the raw rate is 1077 sec/yr, the primary adjustment is -1153 sec/yr and the secondary adjustments are both 33 sec/yr. Thus, the movement rate is:
rate = 1077 - 1153 + 33 + 33 = -10 sec/yr
The rate I actually measured over many inhibition cycles was -10 sec/yr. In general, the rates computed via the graphs are in good agreement with the actual measured rates.
This ETA calibre is pretty simple to analyze. When I am feeling really well rested, I will get into the Seiko twin quartz movements. These movements vary both the adjustment size and inhibition period length.