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

Lars Walenius lars.walenius at hotmail.com
Wed Nov 23 15:57:07 EST 2016

```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<mailto: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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