Hi > On Nov 17, 2016, at 10:34 AM, Scott Stobbe <[email protected]> wrote: > > I couldn't agree more, that, once you add a correlated disturbance or > 1/f^a power law noise, things get even messier. Gaussian is just the > easiest to toss in. > > I once herd a story from once upon a time that, if you bought a 10% > resistor, what you ended up with is something like this in the figure > attached. > > Of course 1% percent resistors (EIA96) are manufactured in high yield > today, but I would guess some of this still applies to OCXOs, you > aren't likely to find a gem in the D grade parts. After pre-aging for > a couple of weeks they are either binned, labeled D, or the ones that > show promise are left to age some more before being tested to C grade, > etc, etc.
Most (> 99%) OCXO’s are made to custom specs for large OEM’s. The sort consists of “ship these” and “send these to the crusher”. Needless to say, the emphasis is on a process that throws out as few as possible. Bob > > On Wed, Nov 16, 2016 at 8:06 PM, Bob Camp <[email protected]> wrote: >> Hi >> >> The issue in fitting over short time periods is that the noise is very much >> *not* gaussian. You have effects from things like temperature and warmup >> that *do* have trends to them. They will lead you off into all sorts of dark >> holes fit wise. >> >> Bob >> >>> On Nov 16, 2016, at 6:48 PM, Scott Stobbe <[email protected]> wrote: >>> >>> A few different plots. I didn't have an intuitive feel for what the B >>> coefficient in log term looks like on a plot, so that is the first >>> plot. The same aging curve is plotted three times, with the exception >>> of the B coefficient being scaled by 1/10, 1, 10 respectively. In hand >>> waving terms, it does have an enormous impact during the first 30 days >>> (or until Bt >>1), but from then on, it is just an additive offset. >>> >>> The next 4 plots are just sample fits with noise added. >>> >>> Finally the 6th plot is of just the first 30 days, the data would seem >>> to be cleaner than what was shown as a sample in the paper, but the >>> stability of the B coefficient in 10 monte-carlo runs is not great. >>> But when plotted over a year the results are minimal. >>> >>> A1 A2 A3 >>> 0.022914 6.8459 0.00016743 >>> 0.022932 6.6702 0.00058768 >>> 0.023206 5.7969 0.0026103 >>> 0.023219 4.3127 0.0093793 >>> 0.02374 2.8309 0.016838 >>> 0.023119 5.0214 0.0061557 >>> 0.023054 5.8399 0.0031886 >>> 0.022782 9.8582 -0.0074089 >>> 0.023279 3.7392 0.012161 >>> 0.02345 4.1062 0.0095448 >>> >>> The only other thing to point out from this, is that the A2 and A3 >>> coefficients are highly non-orthogonal, as A2 increases, A3 drops to >>> make up the difference. >>> >>> On Wed, Nov 16, 2016 at 7:38 AM, Bob Camp <[email protected]> wrote: >>>> Hi >>>> >>>> The original introduction of 55310 written by a couple of *very* good guys: >>>> >>>> http://tycho.usno.navy.mil/ptti/1987papers/Vol%2019_16.pdf >>>> >>>> A fairly current copy of 55310: >>>> >>>> https://nepp.nasa.gov/DocUploads/1F3275A6-9140-4C0C-864542DBF16EB1CC/MIL-PRF-55310.pdf >>>> >>>> The “right” equation is on page 47. It’s the “Bt+1” in the log that messes >>>> up the fit. If you fit it without >>>> the +1, the fit is *much* easier to do. The result isn’t quite right. >>>> >>>> Bob >>>> >>>> >>>>> On Nov 15, 2016, at 11:58 PM, Scott Stobbe <[email protected]> >>>>> wrote: >>>>> >>>>> Hi Bob, >>>>> >>>>> Do you recall if you fitted with true ordinary least squares, or fit with >>>>> a >>>>> recursive/iterative approach in a least squares sense. If the aging curve >>>>> is linearizable, it isn't jumping out at me. >>>>> >>>>> If the model was hypothetically: >>>>> F = A ln( B*t ) >>>>> >>>>> F = A ln(t) + Aln(B) >>>>> >>>>> which could easily be fit as >>>>> F = A' X + B', where X = ln(t) >>>>> >>>>> It would appear stable32 uses an iterative approach for the non-linear >>>>> problem >>>>> >>>>> "y(t) = a·ln(bt+1), where slope = y'(t) = ab/(bt+1) Determining the >>>>> nonlinear log fit coefficients requires an iterative procedure. This >>>>> involves setting b to an in initial value, linearizing the equation, >>>>> solving for the other coefficients and the sum of the squared error, >>>>> comparing that with an error criterion, and iterating until a satisfactory >>>>> result is found. The key aspects to this numerical analysis process are >>>>> establishing a satisfactory iteration factor and error criterion to assure >>>>> both convergence and small residuals." >>>>> >>>>> http://www.stable32.com/Curve%20Fitting%20Features%20in%20Stable32.pdf >>>>> >>>>> Not sure what others do. >>>>> >>>>> >>>>> On Mon, Nov 14, 2016 at 7:15 AM, Bob Camp <[email protected]> wrote: >>>>> >>>>>> 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 <[email protected]> >>>>>> wrote: >>>>>>> >>>>>>> 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. >>>>>> >>>>>> _______________________________________________ >>>>>> 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. >>>>>> >>>>> _______________________________________________ >>>>> 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. >>>> >>>> _______________________________________________ >>>> 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. >>> <AGING_30DAYS_0p5ppb.png><AGING_30DAYS_0p5ppb_simple.png><AGING_30DAYS_0p5ppb_zoomin.png><AGING_30DAYS_5ppb.png><AGING_30DAYS_5ppb_simple.png><AGING_SCALE_A2.png>_______________________________________________ >>> 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. >> >> _______________________________________________ >> 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. > <10percentResistor.png>_______________________________________________ > 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. _______________________________________________ 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.
