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

Magnus Danielson magnus at rubidium.dyndns.org
Fri Nov 18 16:36:13 EST 2016

```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, 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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```