[time-nuts] Thermal impact on OCXO
kb8tq at n1k.org
Mon Nov 14 07:15:43 EST 2016
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.
> 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>
>> 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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