Hi Lars, There are a few other pieces I have yet to fully appreciate. One of which is that Aln(Bt+1) isn't a time-invariant model. In the most common case (for the mfg) the time scale aligns with infancy of the OCXO, when it's hot off the line. However after pre-aging, perhaps some service life, what time reference is best? Sometime I will try adding an additional parameter for infancy time and see how that goes.
A fit of the full ten year data-set, attached in the two plots "Lars_10Year.png", "Lars_10Year_45Day.png". I would agree to your description of 1/sqrt(t) aging for the first 1000 days, but sometime after, it follows 1/t. Attached is plot of age rate "Lars_AgeRate.png". You can see during the first 1000 days the age rate declines at 1 decade for 2 decades time indicating t^(-1/2), but eventually it follows 1/t. On Wed, Nov 23, 2016 at 3:57 PM, Lars Walenius <[email protected]> wrote: > Hi Scott. > > > > Here is a textfile with data for the 10 years (As in the graph 2001-2011). > > > > Also the ln(bt+1) fit, as Magnus said, has the derivate b/(b*t+1) that > with b*t >>1 is 1/t. But my data has the aging between 1 and 10 years more > like 1/sqrt(t) If I just have a brief look on the aging graph. > > > > Lars > > > > *Från: *Scott Stobbe <[email protected]> > *Skickat: *den 19 november 2016 04:11 > > Hi Lars, > > > > I agree with you, that if there is data out there, it isn't easy to find, > > many thanks for sharing! > > > > Fitting to the full model had limited improvements, the b coefficient was > > quite large making it essentially equal to the ln(x) function you fitted in > > excel. It is attached as "Lars_FitToMil55310.png". > > > > So on further thought, the B term can't model a device aging even faster > > than it should shortly after infancy. In the two extreme cases either B is > > large and (Bt)>>1 so the be B term ends up just being an additive bias, or > > B is small, and ln(x) is linearized (or slowed down) during the first bit > > of time. > > > > You can approximated the MIL 55310 between two points in time as > > > > f(t2) - f(t1) = Aln(t2/t1) > > > > A = ( f(t2) - f(t1) )/ln(t2/t1) > > > > Looking at some of your plots it looks like between the end of year 1 and > > year 10 you age from 20 ppb to 65 ppb, > > > > A ~ 20 > > > > The next plot "Lars_ForceAcoef", is a fit with the A coefficient forced to > > be 2 and 20. The 20 doesn't end-up fitting well on this time scale. > > > > Looking at the data a little more, I wondered if the first 10 day are going > > through some behavior that isn't representative of long-term aging, like > > warm-up, retrace (I'm sure bob could name half a dozen more examples). So > > the next two plots are fits of the 4 data points after day10, and seem to > > fit well, "Lars_FitAfterDay10.png", "Lars_1Year.png". > > > > If you are willing to share the next month, we can add that to the fit. > > > > Cheers, > > > > On Fri, Nov 18, 2016 at 1:26 PM, Lars Walenius <[email protected]> > > wrote: > > > > > > Hopefully someone can find the correct a and b for a*ln(bt+1) with > > stable32 or matlab for this data set: > > > Days ppb > > > 2 2 > > > 4 3.5 > > > 7 4.65 > > > 8 5.05 > > > 9 5.22 > > > 12 6.11 > > > 13 6.19 > > > 25 7.26 > > > 32 7.92 > > >
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