Yes
First, have you done any long term studies on the crystal oscillators of different types?
Second, how did you fit a 3rd order polynomial with only 2 data points, or was it maybe the other way around (2nd order with 3 data points)?
Hi Al,
First, Yes but only briefly
Aging is a property of quality of materials and metallic diffusion of ions in to the crystal that can shift one way or another. It is also affected by excess heat, shock and vibration from holder movement. So the best crystals had high quality electrodes ( I forgot if they were gold plated but something that does not diffuse in to the crystal or oxidize Hence old crystal HC/U cans .were cold-welded ( Ultrasonic) an in a vacuum seal. For the last 20 years they have micro-sliced crystals in epoxy, which was notorious for being leaky to moisture and hence in the old days all plastic parts were only rated to 0'C due to pop-corn damage if any moisture go into the seal. Since moisture has a dielectric property of 60x it can add holder capacitance and lower the frequency. I don't have any vendor specific data any more, but you can always do well with some name brand crystals from Japan, like Epson.
Aging is typically 1 ppm/yr . It can slow down depending on quality of materials and process and factory source. But it never really stops as it is a slow chemical doping of crystal material from the metal holder, plus any other contaminants in contact or leaking inside.
I normally categorized all crystals with 3 numbers Tolerance/Stability/Aging per yr and temp range for stability
e.g. 25/25/1 -40~70'C
The polynomials I generated were manually computed with Microwave Journal's curve fitting program on DOS from digitized points all the AT temp curves which are S shaped 3rd order polynominials. Then I derived another polynomial to select which curve based on the ppm shift or slope from 40'C to 70'C because I discovered a linear relationship that could predict all the coefficients of the 3rd order polynomial for AT curves which are incremental for different crystal angle cuts in minutes ( 1/60th degree) as I recall. The crystal can micro-oven was a 2oz copper flex circuit with SMT heater resistors and SMT thermistor to sense and regulate the temperature inside a styrafoam shell. Insert XTAL, select temperature 40. wait 15 seconds. read Xtal within 0.1 ppm, switch to 70'C and repeat.. next Xtal. So they were all sorted according to angle cuts prediction by my linear PPM shift from 40~70'C then binned and paired with custom binned varistors for C1/C20V ratios so we could pair them and make a 1ppm VC-TCXO for under a dollar in parts. I don't know how others do it, but this worked.
It could also be done for other T1 to T2 temps.
The purpose was to control the RF transceiver freq within 1ppm from -40 to +50C for ISM Band 928MHz often used by hydro companies for our unique 2 way networked automated meter reading of residential utility meters. ( MOst still walk around and use a wireless handheld unit to read the automated meter, since Spread spectrum band is too short range and noisy. Ours was networked with repeaters and tied in directly to the utility company's database, for instant meter reading or scheduled routine readings.