AN2441 Datasheet, PDF (4/14 Pages) STMicroelectronics – Low cost effective oscillator for STR71x MCUs

Quartz crystal characteristics
2
Quartz crystal characteristics
AN2441
A quartz crystal is a piezoelectric device transforming electrical energy to mechanical
energy and vice versa. The transformation occurs at the resonant frequency. It can be
modeled as follows:
Figure 2. Quartz equivalent circuitry
R
L
C
C₀
Where:
C₀ represents the shunt capacitance resulting from the capacitor formed by the
electrodes and the parasites of the contacts.
L (motional inductance) represents the vibrating mass of the crystal.
C (motional capacitance) represents the elasticity of the crystal
R represents the circuit losses.
Because R is normally negligible, the impedance of this circuitry is given by the following
equation:
Z
=
--^j- × --------------^w----²---^L----^C------–----¹----------------
w _{(C0 + C) – w}²_LCC0
The following figure represents the quartz reactance across its operating frequency:
Figure 3. Quartz crystal reactance across frequency
Impedance
Area of usual parallel
resonance
Anti Resonance
F_a
0
Frequency
Series Resonance
F_s
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