Quartz Resonators - Physical Properties
Modes of Vibration AT-Cut crystals have the ability to resonate at mechanical
overtones of the fundamental thickness shear mode. These overtone modes are enhanced
during the manufacturing process to make the crystal element resonate at higher
frequencies than would otherwise be possible. Using this technique frequencies up
to approx 250MHz can be obtained as in fig. 3
The Equivalent Circuit of a Quartz Crystal Since the crystal can be represented
as a resonant circuit, it will display a capacitive (C1) and Inductive (L1) reactance,
which will become equal and opposite at the resonant frequency, thereby leaving
only the purely resistive component (R)
The inductance (L1) relates to the mass of the quartz, and the dynamic capacitance
(C1) is analogous to the stiffness of the quartz. Within the equivalent circuit
(C0) is the physical capacity of the quartz crystal assembly. See fig. 4
If one where to apply a sweeping frequency from below the crystal’s resonant frequency
to one which is higher than that of the crystal, the result would be as appears
in fig. 5
Below F0, the crystal is observed to exhibit a reactance which is capacitive, and
opposes the applied AC current. At F0, the capacitive and inductive reactances are
equal and opposite and therefore exactly nullify each other leaving the crystal
purely resistive. This is known as the Series resonant condition.
As the applied frequency is increased above F0, the crystal becomes increasingly
inductive to the applied AC current, until point FA is reached, this is the Anti-Resonant
Condition (Sometimes called the parallel resonant condition). Beyond
that point the reactance again flips to being capacitive. The frequencies between
F0 to FA is where the crystal behaves inductively and is known as the crystal bandwidth.
It is over this bandwidth that the crystal can be pulled by varying the capacity
or inductance presented to the component.
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