Hi

If you have a *really bad* crystal, it will follow a very nice log aging cure. 
A good crystal is much less predictable. The reason is fairly simple, the bad 
crystal has a single dominant cause for it's aging. It missed a step somewhere 
along the line and it's got a problem. A precision part is going to be run 
through a process that results in no single effect being dominant. 

Bob

On Jun 24, 2010, at 2:40 PM, Don Cross wrote:

> 
> Hi, my name is Don.  I have been lurking on this list for a while, so here is 
> my first post.
> I am a hobbyist who has just built my second home-made quartz digital clock.  
> Both are based on a microcontroller that counts timer interrupts and uses 
> software tricks to allow me to tune the clock rate based on comparison with 
> atomic time via NTP.  The second clock uses a temperature sensor and a heater 
> (a grid of resistors) enclosed with the microcontroller board in a glass jar 
> to regulate its own temperature.
> Of course, I am noticing a drift in the clock rate over time due to crystal 
> aging.  The frequency of the crystal is gradually increasing over time.  For 
> example, on June 2, the frequency was 15.99927052 MHz.  As of yesterday it is 
> hovering around 15.99927796 MHz.
> I have read through several online resources, including the very interesting 
> one that was posted here recently:
> http://www.am1.us/Papers/U11625%20VIG-TUTORIAL.PDF
> On page 4-7 of that document there is a slide titled "Typical Aging 
> Behaviors" where it shows that long-term crystal aging can be represented as 
> a sum of logarithmic functions.  I was wondering if this is just an 
> approximation, or if there is a theoretical reason why logarithms would 
> describe such phenomena?  Looking at the causes of aging, they seem to do 
> with changes in the bonding with the electrodes, deposition or oxidation of 
> the components inside the crystal enclosure, etc.
> I am thinking about trying to measure the aging process over the coming 
> months, and then try to model and even predict future aging.  If I can get 
> that to work, perhaps I can even incorporate the formula for predicted aging 
> right into my software.  Any insights on this would be much appreciated.
> FYI, here is a link to what I did on my first clock.  I have not yet finished 
> the web page for the second clock, but I will get around to it, eventually.
> http://cosinekitty.com/digitalclock/
> I do have the firmware for my second clock online, along with some crude 
> schematics, if anyone is interested:
> http://cosinekitty.com/thermalclock/thermal_clock_firmware.cpphttp://cosinekitty.com/thermalclock/main_board_schematic.pnghttp://cosinekitty.com/thermalclock/heater_switch.png
> - Don                                           
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