[time-nuts] quartz drift rates, linear or log

Bob Camp kb8tq at n1k.org
Sat Nov 12 22:53:14 EST 2016


Exact info on mass transfer is a bit complicated. A 5 MHz 5th overtone is 
a bit thicker and more massive than a 100 MHz 5th. Both are thicker (and 
more massive) than a 100 MHz fundamental.  On top of that the blank is not
equally sensitive to mass at all points on it’s surface. Finally, gold has a bit more
mass than hydrogen. A layer of one is not quite the same as a layer of the other. 

All that said, The standard “gee wiz” number is that 1 ppb is an atomic layer
on a 5 MHz thrid. Given all of the hand waving, it’s a back calculated number 
based on calibrating the crystal with a thin film of gold (under these conditions …. 
on that design … calculated after XXX beers ...). 


> On Nov 12, 2016, at 8:56 PM, Scott Stobbe <scott.j.stobbe at gmail.com> wrote:
> Those are wonderful plots :)
> I vaguely recall that a 1ppm frequency shift is approximately equivalent to
> the mass transfer of one molecular layer of a crystal. So at some point
> your counting atoms if there was no noise, thermal disturbance, mechanical
> disturbance...
> On Sat, Nov 12, 2016 at 5:00 PM Tom Van Baak <tvb at leapsecond.com> wrote:
>> There were postings recently about OCXO ageing, or drift rates.
>> I've been testing a batch of TBolts for a couple of months and it provides
>> an interesting set of data from which to make visual answers to recent
>> questions. Here are three plots.
>> 1) attached plot: TBolt-10day-fit0-e09.gif (
>> http://leapsecond.com/pages/tbolt/TBolt-10day-fit0-e09.gif )
>> A bunch of oscillators are measured with a 20-channel system. Each
>> frequency plot is a free-running TBolt (no GPS, no disciplining). The
>> X-scale is 10 days and the Y-scale is 1 ppb, or 1e-9 per Y-division. What
>> you see at this scale is that all the OCXO are quite stable. Also, some of
>> them show drift.
>> For example, the OCXO frequency in channel 14 changes by 2e-9 in 10 days
>> for a drift rate of 2e-10/day. It looks large in this plot but its well
>> under the typical spec, such as 5e-10/day for a 10811A. We see a variety of
>> drift rates, including some that appear to be zero: flat line. At this
>> scale, CH13, for example, seems to have no drift.
>> But the drift, when present, appears quite linear. So there are two things
>> to do. Zoom in and zoom out.
>> 2) attached plot: TBolt-10day-fit0-e10.gif (
>> http://leapsecond.com/pages/tbolt/TBolt-10day-fit0-e10.gif )
>> Here we zoom in by changing the Y-scale to 1e-10 per division. The X-scale
>> is still 10 days. Now we can see the drift much better. Also at this level
>> we can see instability of each OCXO (or the lab environment). At this
>> scale, channels CH10 and CH14 are "off the chart". An OCXO like the one in
>> CH01 climbs by 2e-10 over 10 days for a drift rate of 2e-11/day. This is
>> 25x better than the 10811A spec. CH13, mentioned above, is not zero drift
>> after all, but its drift rate is even lower, close to 1e-11/day.
>> For some oscillators the wiggles in the data (frequency instability) are
>> large enough that the drift rate is not clearly measurable.
>> The 10-day plots suggests you would not want to try to measure drift rate
>> based on just one day of data.
>> The plots also suggest that drift rate is not a hard constant. Look at any
>> of the 20 10-day plots. Your eye will tell you that the daily drift rate
>> can change significantly from day to day to day.
>> The plots show that an OCXO doesn't necessarily follow strict rules. In a
>> sense they each have their own personality. So one needs to be very careful
>> about algorithms that assume any sort of constant or consistent behavior.
>> 3) attached plot: TBolt-100day-fit0-e08.gif (
>> http://leapsecond.com/pages/tbolt/TBolt-100day-fit0-e08.gif )
>> Here we look at 100 days of data instead of just 10 days. To fit, the
>> Y-scale is now 1e-8 per division. Once a month I created a temporary
>> thermal event in the lab (the little "speed bumps") which we will ignore
>> for now.
>> At this long-term scale, OCXO in CH09 has textbook logarithmic drift. Also
>> CH14 and CH16. In fact over 100 days most of them are logarithmic but the
>> coefficients vary considerably so it's hard to see this at a common scale.
>> Note also the logarithmic curve is vastly more apparent in the first few
>> days or weeks of operation, but I don't have that data.
>> In general, any exponential or log or parabolic or circular curve looks
>> linear if you're looking close enough. A straight highway may look linear
>> but the equator is circular. So most OCXO drift (age) with a logarithmic
>> curve and this is visible over long enough measurements. But for shorter
>> time spans it will appear linear. Or, more likely, internal and external
>> stability issues will dominate and this spoils any linear vs. log
>> discussion.
>> So is it linear or log? The answer is it depends. Now I sound like Bob ;-)
>> /tvb
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