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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