A quartz crystal has a property called: piezoelectric effect.
This effect causes, by applying a mechanical pressure on the surface of the crystal, that a voltage is developed on the opposite sides.
In a similar manner, a voltage applied on the faces of the crystal produces a mechanical distortion on their surface.
An AC voltage causes mechanical vibration whose natural frequency is very stable and depends on the nature and carved crystal.
The equivalent circuit model of a quartz crystal (look at the picture below) is characterized by a very large inductance L (several Henrys), a very small capacitance Cs (<0.5pF) in series, and a series resistance r (a few hundred ohms), and a parallel capacity Cp (a few pF) which represents the electrostatic capacity between the two sides of the crystal.
The quality factor Q is high (> 20000). If r is neglected, the crystal impedance Z (jw) is given by
The equation above indicates that the crystal has two resonant frequencies: a series resonance "ws" and a parallel resonance "wp" given by the following equations
The last equation an be rewritten in the form
where wp> ws since Cp> Cp. A graphical representation of the reactance (impedance) Z (jw) is shown on picture above.
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Crystal oscillators. Series and parallel resonance >>
