Jeffrey Pawlan wrote:
Indeed, the observed crystal aging is a sum of a larger number of physical processes.It was Rick who wrote about crystal aging. It is not predictable whether the crystal will go higher or go lower in frequency and there is no guarantee that it will age at a linear rate. The worst-case is when a crystal erratically jumps.
- Some of them are stronger than others - some of them decay faster or slower than other others - many of them show a logarithmic frequency change over time - a few of them have the shape of an exponential decay.The usual approximation used to predict frequency aging - as used in MIL-PRF55310 - is
df/f = f0 + a1*log(a2*t+1),where a1 can be understood as a measure of the strenght of aging, and 1/a2 is a kind of time constant, i.e. small a2 values stand for slowly aging processes and large ones for fast agers. A better approach to describe frequency aging would thus be a mathematical sum of several logarithmic terms as in the above equation. As nicely shown in John Vig's tutorial, you can easily get a reversal of the aging rate (i.e. a change from positive to negative aging or vice versa), if you simply superimpose a fast and weaker (positive) aging process with a slower but stronger negative aging process - see attached copy.
O.K. you now can say: why not make aging prediction by mathematical fitting of a sum of logarithmic terms through the observed frequency data over time? Basically this would/could improve the degree of fitting, correct. BUT: There is a big leveraging effect, if you make a mathematical prediction over a long period of time from data taken over a relatively small time period. In other words: If you just vary one or a few data points by a very small amount (i.e. to eliminate jumps), the effect on the extrapolated curve is enormous. Just try it using EXCEL's solver ... I had published an example for that 10 years ago - see a copy of my paper " Correlation of predicted and real aging behaviour" on our website www.axtal.com. In that paper I used data from about 9 months of aging, and compared the predictions made from different time periods with the real aging.
From my standpoint the MIL-PRF55310 method of prediction is just a standardized method to define how the aging numbers in a spec are "verified" in a reasonable time of 4 weeks, It does not say: "This is how the crystal will age over decades"
There is much more to say, but I will stop here, hoping that this contribution gave some time nuts a better understanding - and may kill their firm believe into aging predictions ;-)
Best regards Bernd Neubig DK1AG
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