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I am not sure If I have phrased the question right but if not please correct me

I want to know when Accuracy Parts per Million mentioned in the datasheet of voltage reference they say for example 5 ppm/c, which from my understanding, for every degree increased a 5 parts per million of the output voltage will increase

OK, but what is the base temperature that I should consider to calculate the drift ? is it the initial temp. when the Vref began its work, or the ambient temp which would be 25 degrees or the temp. which the manufacturer toke his original measurement in his laboratories ??

I want to calculate the voltage ref. drift that happens because of the temp. changes and after that try to make compensation in the software, it is still an idea I don't know if it is good or not but it worth trying it

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Typically the manufacturer will use a 'box' method and draw a rectangular box around the curve of output voltage vs. temperature. The quoted ppm/°C is the height of the box divided by the width of the box. The maximum and minimum temperatures used for this test should be (but are not always) specified. They may be the maximum/minimum operating temperatures or something inside those. Note that the maximum absolute value of the slope of the output voltage vs. temperature is typically not guaranteed, despite the units. It might actually be several times higher than the average if the curve looks like an 'S' or a more like a parabola.

Yes, you can characterize and compensate for some reference variations due to temperature. This is best used as a last resort after you've make everything else as good as it can be. Thermal testing is expensive and slow, and compensation can have ugly dynamic effects where slewing the temperature results in relatively large transient errors. I've done a two-dimensional curve (well, I guess surface) fitting to calibrate a very precise instrument (microKelvin-level) using an automated process in an environmental chamber but it's not for the faint of heart (or short of time).

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Data sheets for voltage regulators and references state initial accuracy at (normally) 25 degC. Any temperature related drift is based on the difference between this temperature and the actual operating temperature.

make compensation in the software

It can work - I'm doing a job right now that involves this idea.

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