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

Lars Walenius lars.walenius at hotmail.com
Wed Nov 23 15:58:34 EST 2016

Bob,
I have to ask about the B-term. In the paper that Scott started this with I see that B was 4.45. But if I understand you correct Bt<1 even at 30days is normal? That would mean a B of <0.033?

Lars

>Bob wrote:
>In a conventional fit situation, you have < 30 days worth of data and the “time constant”
is > 30 days. Put another way bt <= 1 in the normal case. It is only when you go out to years
that bt gets large.

Bob

>> On Nov 18, 2016, at 9:58 PM, Scott Stobbe <scott.j.stobbe at gmail.com> wrote:
>
> 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
> <Lars_1Year.png><Lars_FitAfterDay10.png><Lars_FitToMil55310.png><Lars_ForceAcoef.png>_______________________________________________
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