[time-nuts] Thermal impact on OCXO

[Bob Camp]

Hi

If you already *have* data over a year (or multiple years) the fit is fairly easy.
If you try to do this with data from a few days or less, the whole fit process is
a bit crazy. You also have *multiple* time constants involved on most OCXO’s. 
The result is that an earlier fit will have a shorter time constant (and will ultimately
die out). You may not be able to separate the 25 year curve from the 3 month
curve with only 3 months of data.

Bob

> On Nov 13, 2016, at 10:59 PM, Scott Stobbe <scott.j.stobbe at gmail.com> wrote:
> 
> On Mon, Nov 7, 2016 at 10:34 AM, Scott Stobbe <scott.j.stobbe at gmail.com>
> wrote:
> 
>> Here is a sample data point taken from http://tycho.usno.navy.mil/ptt
>> i/1987papers/Vol%2019_16.pdf; the first that showed up on a google search.
>> 
>>         Year   Aging [PPB]  dF/dt [PPT/Day]
>>            1       180.51       63.884
>>            2       196.65        31.93
>>            5          218       12.769
>>            9       231.69       7.0934
>>           10       234.15        6.384
>>           25        255.5       2.5535
>> 
>> If you have a set of coefficients you believe to be representative of your
>> OCXO, we can give those a go.
>> 
>> 
> I thought I would come back to this sample data point and see what the
> impact of using a 1st order estimate for the log function would entail.
> 
> The coefficients supplied in the paper are the following:
>     A1 = 0.0233;
>     A2 = 4.4583;
>     A3 = 0.0082;
> 
> F =  A1*ln( A2*x +1 ) + A3;  where x is time in days
> 
>     Fdot = (A1*A2)/(A2*x +1)
> 
>     Fdotdot = -(A1*A2^2)/(A2*x +1)^2
> 
> When x is large, the derivatives are approximately:
> 
>     Fdot ~= A1/x
> 
>     Fdotdot ~= -A1/x^2
> 
> It's worth noting that, just as it is visually apparent from the graph, the
> aging becomes more linear as time progresses, the second, third, ...,
> derivatives drop off faster than the first.
> 
> A first order taylor series of the aging would be,
> 
>     T1(x, xo) = A3 + A1*ln(A2*xo + 1) +  (A1*A2)(x - xo)/(A2*xo +1) + O(
> (x-xo)^2 )
> 
> The remainder (error) term for a 1st order taylor series of F would be:
>      R(x) = Fdotdot(c) * ((x-xo)^2)/(2!);  where c is some value between x
> and xo.
> 
> So, take for example, forward projecting the drift one day after the 365th
> day using a first order model,
>     xo = 365
> 
>     Fdot(365) =  63.796 PPT/day, alternatively the approximate derivative
> is: 63.836 PPT/day
> 
>     |R(366)| =  0.087339 PPT (more than likely, this is no where near 1
> DAC LSB on the EFC line)
> 
> More than likely you wouldn't try to project 7 days out, but considering
> only the generalized effects of aging, the error would be:
> 
>     |R(372)| = 4.282 PPT (So on the 7th day, a 1st order model starts to
> degrade into a few DAC LSB)
> 
> In the case of forward projecting aging for one day, using a 1st order
> model versus the full logarithmic model, would likely be a discrepancy of
> less than one dac LSB.
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