Hi Scott.

Here is a textfile with data for the 10 years (As in the graph 2001-2011).

Also the ln(bt+1) fit, as Magnus said, has the derivate b/(bt+1) that with bt >>1 is 1/t. But my data has the aging between 1 and 10 years more like 1/sqrt(t) If I just have a brief look on the aging graph.

Lars

Från: Scott Stobbemailto:scott.j.stobbe@gmail.com
Skickat: den 19 november 2016 04:11

Hi Lars,

I agree with you, that if there is data out there, it isn't easy to find,
many thanks for sharing!

Fitting to the full model had limited improvements, the b coefficient was
quite large making it essentially equal to the ln(x) function you fitted in
excel. It is attached as "Lars_FitToMil55310.png".

So on further thought, the B term can't model a device aging even faster
than it should shortly after infancy. In the two extreme cases either B is
large and (Bt)>>1 so the be B term ends up just being an additive bias, or
B is small, and ln(x) is linearized (or slowed down) during the first bit
of time.

You can approximated the MIL 55310 between two points in time as

f(t2) - f(t1) = Aln(t2/t1)

A = ( f(t2) - f(t1) )/ln(t2/t1)

Looking at some of your plots it looks like between the end of year 1 and
year 10 you age from 20 ppb to 65 ppb,

A ~ 20

The next plot "Lars_ForceAcoef", is a fit with the A coefficient forced to
be 2 and 20. The 20 doesn't end-up fitting well on this time scale.

Looking at the data a little more, I wondered if the first 10 day are going
through some behavior that isn't representative of long-term aging, like
warm-up, retrace (I'm sure bob could name half a dozen more examples). So
the next two plots are fits of the 4 data points after day10, and seem to
fit well, "Lars_FitAfterDay10.png", "Lars_1Year.png".

If you are willing to share the next month, we can add that to the fit.

Cheers,

On Fri, Nov 18, 2016 at 1:26 PM, Lars Walenius lars.walenius@hotmail.com
wrote:

stable32 or matlab for this data set:

Hi Lars,

There are a few other pieces I have yet to fully appreciate. One of which
is that Aln(Bt+1) isn't a time-invariant model. In the most common case
(for the mfg) the time scale aligns with infancy of the OCXO, when it's hot
off the line. However after pre-aging, perhaps some service life, what time
reference is best? Sometime I will try adding an additional parameter for
infancy time and see how that goes.

A fit of the full ten year data-set, attached in the two plots
"Lars_10Year.png", "Lars_10Year_45Day.png".

I would agree to your description of 1/sqrt(t) aging for the first 1000
days, but sometime after, it follows 1/t. Attached is plot of age rate
"Lars_AgeRate.png". You can see during the first 1000 days the age rate
declines at 1 decade for 2 decades time indicating t^(-1/2), but eventually
it follows 1/t.

On Wed, Nov 23, 2016 at 3:57 PM, Lars Walenius lars.walenius@hotmail.com
wrote:

Hi

The biggest challenge is to take out the “early stuff”. One approach is to fit
the same equation twice with the time constant restricted to a range on each.
For most OCXO’s (90%) the equation when fit early represents an upper limit
to the drift. You might get a another element that comes in and is apparent
after a year or two. It might be replaced by another element after five or ten years.
They generally (~80%) represent a change in sign (negative drift vs positive).

If you look at the “other 10%” some have really poor aging and are not shipped.
Some are very erratic and simply can not be fit. Some of the 90% are fit with a
“upper limit” because they exhibit no measurable aging over the 30 days (or whatever)
of testing.

If you take the bad aging (out of spec) parts out of the pile, those are the ones
with the best fit. They have very pretty curves and they stick to those curves
for a long time. They have a single dominant cause for their aging ( = the defect).
The rest of the parts have all of the causes bashed down by the process so that
over a 20 or 30 year span, there probably is no single dominant cause.

Bob

On Thu, 24 Nov 2016 08:16:08 -0500
Bob Camp kb8tq@n1k.org wrote:

Then the question becomes: What would be a good fitting function for
the typical application of an OCXO that is regularly measured with
not too long time spans (e.g. GPSDO)? From the discussion it seems
that a second or third order Taylor would be sufficient to capture
aging for a span of 10-100 days.

		Attila Kinali

--
It is upon moral qualities that a society is ultimately founded. All
the prosperity and technological sophistication in the world is of no
use without that foundation.
-- Miss Matheson, The Diamond Age, Neil Stephenson

Sadly I don't think there is a concise answer to this, in reality you would
make the decision on the fly depending on how much data you have and which
model is the most well behaved.

I think it's a really interesting topic to see some of what goes into an
OCXO, a guaranteed limit on aging is one the many things.

Part of the reason that information on the topic is somewhat is scattered,
is if a commercial application genuinely needed 1e-12 stability for 100
days free-running, the answer without hesitation would be atomic. Then as
you dial back the long-term stability requirement how much NRE are you
willing to spend; which is also why there doesn't seem to plenty of worked
examples out there.

On Thu, Nov 24, 2016 at 10:49 AM, Attila Kinali attila@kinali.ch wrote:

Hi

Simple answer no. More complex answer: what are you trying to do? Depending
on the answer to that there may be other functions that are useful. In general
an unconstrained polynomial is great for fitting the data you have and awful
for predicting the future.

Bob

Hi

There has been a lot of research into these functions. The Frequency Control
Symposium archives have at least a few dozen papers on the why and how
of the functions working. They are now behind a paywall for me so those who have
the luxury of access will have to dig for them on their own.

Bob

On 11/24/2016 5:16 AM, Bob Camp wrote:

This excellent response channels what Jack Kusters used to say.  The
idea that aging follows any predicable pattern might have been true
decades ago.  For example, I remember being told in 1974 that
everyone knew that metal crystals aged downward and glass crystals
aged upward.  It was true at the time, but those aging processes
have been beat down.  According to Jack, 10811/E1938A aging is
primarily "stress relaxation".  It could be either direction and
a given crystal can change direction over time.  On top of that,
crystals have frequency "jumps" at unpredictable intervals.  At
HP, we had an "aging system" that watched crystals to try to reject
bad actors and find the well behaved ones.  The problem was that the
longer you watched an oscillator, the better chance of catching
it in the act of jumping.  They didn't necessarily get better
over time (over many months).  No matter how many crystals we
looked at, we never found one that had atomic like aging.

My observation is that the systematic (therefore predictable)
aging processes have been eliminated by improved manufacturing
techniques, leaving the true random (unpredictable) aging
processes.

The one thing I can say is that it is good to keep the crystal
ovenized at all times.  Even a momentary oven outage tends to
reboot aging.

Rick

Rick wrote:

That has been my observation, as well.  Same with mechanical shock and
with interruptions of oscillation (even if the oven remains undisturbed).

Charles