keble
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The crystal manufacturer specifies the resonant frequency at a specific capacitance load across the crystal. At any other value of loading the frequency will be different - incidentally that provides a way of changing frequency slightly. So if you want the frequency to be on spec you need to have the right capacitance.
The inverter provides some transconductance - for a given set of electrical parameters it is possible to work out how much you need to get oscillation to occur.
See E. Vittoz, High-Performance Crystal Oscillator circuits: Theory and Application IEEE Journal of Solid state circuits, vol. 23, No. June 1988 pp.774- 783.
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