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

Bob Camp kb8tq at n1k.org
Fri Nov 18 17:51:55 EST 2016

```Hi

> On Nov 18, 2016, at 4:36 PM, Magnus Danielson <magnus at rubidium.dyndns.org> wrote:
>
> Hi Lars,
>
> Now, consider f(t) = a*log(b*t+1), then the derivate is a*b/(b*t+1) and second derivate - a * b^2 / (b*t + 1)^2.
>
> Forming first f'(t) and second f"(t) derivate estimates from data is trivial. Given that we can estimate a and b using
>
> a = - f('t)^2 / f"(t)
>
> b = - f'(t) / (f'(t) * t - a)
>
>  = - f"(t) / (f("t) * t - f'(t))
>
> A bit of paper and pen work or you get Maxima to do some work for you.
> I haven't seen how any real estimator of this drift function is implemented,

By far the most common implementation of the equation as an estimator is in factory test of OCXO’s that
are built to the 55310 spec. It also is fairly common to use it on commercial OCXO’s as well. Put another way:
It’s how you answer “Does it meet the 20 year aging spec?” in less than 20 years.

Bob

> but I wanted to provide some notes from note-book of stuff being unfinished.
>
> Cheers,
> Magnus
>
> On 11/18/2016 07:26 PM, Lars Walenius wrote:
>> Bob wrote:
>>> As mentioned earlier in this thread. The function that has been used in several posts
>>> isn’t the right log function. The proper fit is to ln(bt+1)
>>
>> You are absolutely right. It was my mistake to use the ln(t) in the graph. As that was what I know in Excel and I don´t have Stable32 or MatLab. In Excel I actually double checked that (a*ln(bt+1)) with b 5 to 1000 gave about the same as (a*ln(t)) for my data set (only the offset was largely different).
>>
>> 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
>>
>> It would also be interesting if I could get the drift after 10 years to see if it is about 6E-13/day as with the ln(t).
>>
>>
>> Peter wrote:
>>>> I'm not very good with Excel, but this curve-fitting function sounds very
>>>> useful.  Could you please tell me how it's done?
>>
>> In the graph I only right-clicked the curve and selected ”add trendline” here I checked the logarithmic and show equation.
>>
>> Lars
>>
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```