Geraldo Lino de Campos said the following on 10/09/2007 05:42 PM:

Hi Geraldo.  Welcome to the list!

I would suspect either the counter or the LPRO to be faulty.  Can you
check either against another device?

My reason for saying so is that the 9 digit number you gave us provides
resolution only to parts in 10e-9, and the last digit of most counters
is ambiguous by nature.

A typical Rb may have a total adjustment range of only a couple of parts
in 10e-9, so your counter resolution plus last digit ambiguity pretty
much hides any change that you might see.  If you can extend your gate
time by 10, that would add another digit of resolution and with that,
you should be able to see a change over the Rb tuning range.  (But note
that if you are clocking the counter directly from GPS, any gate time
shorter than thousands of seconds will have jitter measured in nanoseconds.)

I would not have been surprised if your counter read either 1 count
below 10 MHz, or 1 count above -- that would be expected due to the last
digit ambiguity.  But given the adjustment range, reading 2 counts low
with no change over the adjustment range does seem to indicate a problem
as that is (probably) out of the adjustment range.  However, unless we
can verify that the counter is in proper order, we can't tell whether
the problem is the counter or the Rb.

Hope this helps.

John

I was the person who posted the original comments.  My comments
were based on discussions with notable crystal guru, Jack Kusters,
who was merely an inventor of the SC cut.  He didn't have much
confidence in the various FCS papers Jeffrey was referring to.
Basically, he was aware of all those effects and if there were
any consistency to the proposed treatments, the HP crystal fab
would have been doing them.  For instance, the idea that, if
only you polish the crystal well enough, it won't age has been
debunked.  Some people currently making high quality crystals
learned much of what they are doing from Jack in the first place.
If any of them go beyond what Jack taught them, they might
publish at FCS.  Or they might not and keep it as a trade secret.

Rick Karlquist

(these are my personal opinions, and do not represent the official
position of Jack or HP.).

effrey Pawlan wrote:

Jeffrey Pawlan wrote:

Indeed, the observed crystal aging is a sum of a larger number of
physical processes.

• Some of them are stronger than others
• some of them decay faster or slower than other others
• many of them show a logarithmic frequency change over time
• a few of them have the shape of an exponential decay.
  The usual approximation used to predict frequency aging - as used in
  MIL-PRF55310 - is
  df/f = f0 + a1log(a2t+1),
  where a1 can be understood as a measure of the strenght of aging, and
  1/a2 is a kind of time constant, i.e. small a2 values stand for slowly
  aging processes and large ones for fast agers.
  A better approach to describe frequency aging would thus be a
  mathematical sum of several logarithmic terms as in the above equation.
  As nicely shown in John Vig's tutorial, you can easily get a reversal of
  the aging rate (i.e. a change from positive to negative aging or vice
  versa), if you simply superimpose a fast and weaker (positive) aging
  process with a slower but stronger negative aging process - see attached
  copy.

O.K. you now can say: why not make aging prediction by mathematical
fitting of a sum of logarithmic terms through the observed frequency
data over time?
Basically this would/could improve the degree of fitting, correct. BUT:
There is a big leveraging effect, if you make a mathematical prediction
over a long period of time from data taken over a relatively small time
period. In other words: If you just vary one or a few data points by a
very small amount (i.e. to eliminate jumps), the effect on the
extrapolated curve is enormous. Just try it using EXCEL's solver ...
I had published an example for that 10 years ago - see a copy of my
paper " Correlation of predicted and real aging behaviour" on our
website www.axtal.com.
In that paper I used data from about 9 months of aging, and compared the
predictions made from different time periods with the real aging.

From my standpoint the MIL-PRF55310 method of prediction is just a
standardized method to define how the aging numbers in a spec are
"verified" in a reasonable time of 4 weeks, It does not say: "This is
how the crystal will age over decades"

There is much more to say, but I will stop here, hoping that this
contribution gave some time nuts a better understanding - and may kill
their firm believe into aging predictions ;-)

Best regards

Bernd Neubig
DK1AG