On Mon, Nov 7, 2016 at 10:34 AM, Scott Stobbe <[email protected]> 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. _______________________________________________ time-nuts mailing list -- [email protected] To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
