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

Magnus Danielson magnus at rubidium.dyndns.org
Wed Nov 23 17:49:07 EST 2016

```It really means that B will be harder to get a qualitative value for.

Also, you need to have "clean" data or else you will be far off.
Plot the estimated variant and also plot the difference.
As Jim Barnes used to teach, always check the whiteness of matching
residues!

Cheers,
Magnus

On 11/23/2016 09:58 PM, Lars Walenius wrote:
> 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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```