# Calculate maximum deviation of quartz crystal

How can I calculate the maximum deviation of a quartz? This is from datasheet (12MHz):

Frequency Tolerance at +25° C => +- 30ppm

• temperature tolerance -20°~ + 70°C => +-50ppm

• aging (first year) => +- 2ppm

I want to calculate the maximum deviation for a specific period.

For example first quartz is at -20°C then the tolerance is 50 ppm or 50 ppm + 30 ppm? So +- 50 ppm or +-80ppm? The second quartz the same but it works at 70°C.

The following calculation is after one year so I add 2ppm. So when it is 82 ppm then the first quartz can operate at the worst case with 12MHz - 984 MHz and the second quartz is working with 12MHz+984MHz. Is this correct?

I am not sure because the frequency tolerance is at 25°C.

• Do you mean a quartz crystal? Could you edit your question for clarity? – TimWescott Jan 6 at 16:10

The correct estimate is a sum tolerance stackup of all variables for the crystal. (30+50+2 = 82ppm)

The 1st @ room temp is the just the initial tolerance of size of the crystal to the designed centre frequency.

The 2nd is the angle of the cut of the XTAL in minutes (1/60th) of a degree that only affects the 3rd order slope at room temp, so both are additive.

So a XTAL tolerance of +/82 ppm over temp in 1 year does not include shock & vibe nor C load error which adds to the room temp tolerance error and "could" be as little as 10 ppm with 10% caps but it depends on the slope of the cut and temp response.

## other

In the early 90's we wanted to make a $1 TCXO for 928Mhz synth, so I digitized all the AT cut curves, generated 3rd order polynominals to compute any of them and created a test process to bin them using a 30 second (foam insulated copper FPC with thermistor and 1/8W heater R around XTAL) "mini oven" that tested offset @ +40'C then +70'C which is a near "linear range". Then another guy created a tool to bin varicaps in 1 % bins, then when paired with the formulae, the TCXO could be compensated with DAC to Varicap within 1 PPM over -40~ +70'C range. I generated another 3rd Ord polynomial to compute any Xtal curve based on Δf(T=40'C to 70'C). The programmer used the formulae with thermistor readings to compute Varactor DAC voltage for$1 1ppm TCXO. Now you can buy them in bulk for this price.

• @Justme I meant 30 ppm, but anyway my answer is wrong (so I upvoted this answer) and deleted mine. – Michel Keijzers Jan 6 at 20:10
• does the frequency tolerance depends on temperature? Why the frequency tolerance is at 25°C and not between -20°C - 70°C? – wwwwwwwwwwww Jan 7 at 8:36
• Yes it depends on temperature. Like in your original post, tolerance is said both at 25°C (the 30ppm) so it is known how much tolerance is expected without temperature changes, and how much tolerance is expected to be added over the full temperature range (the 50ppm). – Justme Jan 7 at 9:00
• 1] initial Tolerance error is a fixed offset error tolerance so always done at 25’C , temperature stability depends on T range in spec and therefore slope and PPM difference..These always go thru 25’C because of 1] – Tony Stewart Sunnyskyguy EE75 Jan 7 at 17:01

To a first order of approximation, all the deviations add. So at the end of the first year, they're saying you can expect $$\\pm\$$82ppm.

It's a bit more complicated than that with quartz crystals. First because the specifications are only for the crystal in a super-precision oscillator circuit, and second because in general an AT-cut crystal that's designed for a specific temperature range will have a nominal temperature-vs-frequency characteristic that's 3rd-order. I would expect it to look like the picture (from IQD Frequency Products, who were clever enough to be the top result of a search).

So there's going to be some semi-predictable curve to the temperature characteristic, but it's probably wise to just assume that your product has to work well with a variation that's somewhere within $$\pm\$$ 82ppm. It's probably wiser to assume something outside of that, because the precision is only guaranteed for the crystal itself within the first year -- you're responsible for getting the circuit right, and your oscillator circuit design, component tolerances, component value shift over temperature, and part aging will all affect the oscillator frequency, possibly more than 80ppm if you're not careful.

Crystal tolerances are specified to be cumulative, so +/- 30ppm initial tolerance is at +25 °C only, and from that frequency it may change over the whole temperature range the max amount of +/- 50ppm, so deviation is +/- 80ppm in total. You must also notice that depending on the crystal type the maximum error may not be at the temperature extremes but somewhere in the middle. And during first year it can change up to 2ppm to any direction.