The relationship between initial tolerance and frequency tolerance(crystal)

VVV said:

Frequency tolerance and initial tolerance are really the same thing. The crystal will have a certain frequency deviation from its stated frequency when first used (at 20°C). This is the initial tolerance or frequency tolerance.

However, the crystal ages and so the manufacturers specify ageing in ppm for the first year usually. That means that after one year the actual frequency deviation can be even worse than it was when you first started using that crystal (again at 20°C).

Temperature effects are described by another parameter, called frequency stability (usually given in ppm max over the -20°C to +60°C temperature range).

I am not sure what you mean by loading on the pins. If you are referring to the load capacitance, that is the capacitance the crystal needs to see in parallel with it to actually oscilate at the correct frequency (the frequency tolerance is guaranteed for a certain load capacitance only). When used in an oscillator, there are usually two caps connected, one at each end of the crystal. Their value has to be roughly twice the load capacitance, since they appear in series and the combination in parallel with the crystal. But since the actual oscillator (micro, etc.) has some capacitance per pin, that gets added to the effective capacitance of the previous caps, which means they are usually less than twice the requied load capacitance.

For example, for an 18pF crystal, the usual oscillator caps are 33pF. That gives you effectively 16.5pF load capacitance, plus another 3pF per each pin of the oscillator, for another 1.5pF total (these also appear in series for the crystal).
This results in approximately 18pF across the crystal, which is what you need.

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