RTC crystal thermal response and calibration

[sebmadgwick]

I just posted some information in another forum as part of a discussion but I thought it might also be of interest or use to people here.  I collected some data to investigate the accuracy of a RTC crystal over a temperature range and test potential thermal calibration models.

The plot below (Fig1 - Thermal response) shows the RTC crystal error of 8 devices over a temperature range.  The parts were a dsPIC33 and a 20 ppm crystal.



From this data, I was able to calculate the crystal characteristics shown in the table below (Fig2 - Crystal parameters).  These values are close to the typical values defined in the datasheet (e0 = 20 ppm; c = 0.035; T0 = 25).



I then wanted to determine the accuracy of temperature calibration models of various complexities.  A calibration model would use the temperature measurement to estimate the crystal error which would then be compensated for in software.  The following plots demonstrate the error of the above 8 crystals when compensated for each calibration solution.

The simplest calibration model would assume the typical values define in the datasheet (i.e. assume every crystal is identical).  This calibration model yields the crystal error shown the in the plot below (Fig3 - Calibration using typical values).



A slightly more complicated calibration solution would be to use the same second-order model indicated by the datasheet characteristics but to use the actual characteristic values for each crystal as listed in the above table.  This results in the crystal error show in the plot below (Fig4 - Calibration using actual values).



The final calibration solution (most complex) would be to use the actual characteristic values for each crystal in a third-order calibration model.  This results in the crystal error show in the plot below (Fig5 - Calibration using 3rd order).  The large errors from below -15 degrees Celsius are due to unstable temperatures in the thermal chamber at the start of the experiment.



I hope this is of interest or use to others.