AVR Freaks

Wikipedia indeed has an explanation:

And if I'm not mistaken, the two load caps present a load to the crystal as if they were in series, e.g. two 22pF caps load the crystal with 11pF. Together with the pin and PCB capacitance you can trim this total capacity to the required/recommended capacitance of the particular crystal. Can take a bit of experimentation.

At work I did that once to trim a circuit to +/-1ppm (initial); of course you cannot measure the frequency on the crystal itself directly, you must use the digital output of the oscillator, as some AVRs provide on a CKOUT pin that be enabled with a fuse.

You don't necessarily need the CKOUT pin, at least on an Xmega. You can use a counter to divide it down a bit and wiggle an output compare pin. That can allow you to use a frequency counter on a cheap DMM that can't count above 500 kHz.

Ooooh, an excuse to give a long winded explanation.

Consider a quartz crystal as an electromechanical device. It is merely a slab of quite stiff piezoelectric matrial with a pair of electrodes on it. It has resonance at a specific frequency.

When you wish to design an oscillator, you create a positive feedback loop, and place a filter element in that loop. If you consider a simple transistor amplifier, the emitter resistor is a good place to affect the frequency response. If you substitute in your quartz crystal where the emitter resistor was, and somehow keep DC-biasing the transistor, at the resonant frequency of the slab it will act as a low-value resistor, and give you more amplification.
This is called series resonance. The oscillator is operating at the resonant frequency of the slab.

The amplifier in the AVR only shifts 180 degrees (it is an inverter), so we lack the additional 180 degrees of phase shift to get positive feedback. If we disregard crystals for a moment, there is a way to do this: construct a pi-stage from inductors and capacitors. So for a 16MHz filter with 180 degree phase, going from the output of the amplifier to the input, we pick a capacitance, say 16pF. We put 32pF on the input and the output, and put the inductor between the input and the output. The inductor sees the caps in series, 16pF. To get resonance at 16MHz we need an inductor of 6uH.
This would work (in reality the inductor becomes hard/impossible to manufacture). Only problem is, it is not all that stable, and it will be rather imprecise too.

Fortunately the quartz slab, when you apply a frequency that is slightly different from the resonant frequency, will have current that is no longer in phase with the applied voltage. It will be ahead or behind. When you have a component where the phase of the current lags the phase of the applied voltage, that is an inductor.
So, to get the 16MHz oscillator working, you call up your crystal supplier, and ask for "one that behaves as 6uH at 16MHz". What you usually say is "I want one that will have the inductance to match 16pF at 16MHz (which is 6uH if I bother to calculate it)".

The crystal supplier then cuts a crystal that is TOO THICK. The slab has resonance at a lower frequency than the one you asked for, and if you use it in a series resonant circuit, it will oscillate at that lower frequency. Let's say 15999800 Hz.

When you put it in the circuit, there is a point, 200Hz above the resonant frequency, where the crystal behaves as a 6uH inductor. At that frequency the pi-stage provides the additional 180 degrees shift, and low atenuation. Thus the circuit will oscillate at 16MHz, even though the crystal resonance is really at 15999800Hz.

This is called a 'parallel resonant crystal', even though really there is no such beast, and it is not operated at resonance. Close to, but not at resonance.

(Some details removed, as to not make this even longer. If you know what I left out, this was not meant for you:-)

/Kasper

Let me just add my thoughts on this.

The crystal is manufactured with such motional parameters so that it will work at the environment it is specified to.

So for a parallel resonant crystal, the crystal works in parallel resonant circuit (like with the AVR) at the rated frequency when it has the rated load capacitance over it. It means that the crystal is usually not operated exactly at the parallel resonant point where impedance is minimum (ESR only), but on the area of usual parallel resonance, the area between parallel resonant and series resonant points, where the crystal impedance looks a bit inductive, so therefore the exact oscillation frequency is set by the capacitors. And in a way having a variable amount of load capacitance can be used to fine-tune the frequency anyway.

And for a series resonant crystal, it works at the rated frequency in a series resonant circuit. The crystal will actually operate at the series resonance point where impedance is almost infinity.

So if you use a wrong type of crystal in wrong kind of circuit, or use a wrong amount of load capacitance, it will still work, but since the resonance type or load capacitance requirements are not right, the crystal just does not work at the specified frequency printed on it.

However the actual frequency usually so close to the frequency printed on it, so nobody usually sees they have series resonant crystal connected to AVR, unless they make a wall clock so the time always lags more than usually it is expected from a crystal oscillator.

And it is a completely different thing with what value capacitors the oscillator (AVR) works best with.

In short: It is the crystal that specifies the exact capacitor values (of course approximated stray capacitance taken into account as well). You have to see what range of capacitors AVR datasheet suggests, and then select a crystal with such capacitance requirement that fits the AVR requirements too.

Also other parameters are important if a crystal is suitable for a given oscillator at all, but the AVR datasheets and application notes do not specify these in great detail, like many other microcontroller datasheets. Sometimes you just need to select a crystal with smaller ESR or smaller load capacitance rating before the oscillator in microcontroller works reliably, and these are somewhat easily calculated if the oscillator transconductance (gain) is known. The dissipated power in crystal is much harder to calculate so usually it is just measured, but requires a current probe or FET voltage probe so it is also difficult to measure.