# [time-nuts] Excel logarithmic function (was Thermal impact on OCXO)

Scott Stobbe scott.j.stobbe at gmail.com
Wed Nov 23 23:21:42 EST 2016

```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 <lars.walenius at hotmail.com>
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 <scott.j.stobbe at gmail.com>
> *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 <lars.walenius at hotmail.com>
>
> 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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