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

Bob Stewart bob at evoria.net
Sat Nov 12 17:49:41 EST 2016

```So, are you measuring OCXO stability or EFC stability?
Bob
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From: Tom Van Baak <tvb at LeapSecond.com>
To: Discussion of precise time and frequency measurement <time-nuts at febo.com>
Sent: Saturday, November 12, 2016 3:54 PM
Subject: [time-nuts] quartz drift rates, linear or log

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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