Equivalent circuit of a quartz crystal resonator

To analyse the electrical response of a quartz crystal resonator, it is very often useful to depict it as the equivalent electrical components that would be needed to replace it. This equivalent circuit is can then be used to analyse its response and predict its performance as in the diagram below:

The equivalent circuit given below is often called the 4-parameter crystal model and it is sufficient for many calculations and to illustrate the operation of the crystal.

(Quartz crystal resonator equivalent circuit)

It is possible to equate these theoretical constituent components to real physical attributes of the crystal:

Ø L:  The inductance arises from the mass of the material.

Ø C1:  This capacitance arises from the compliance of the crystal.

Ø R:  This element arises from the losses in the system. The largest of these arises from the frictional losses of the mechanical vibration of the crystal.

Ø C  This capacitance in the theoretical quartz crystal equivalent circuit arises from the capacitance between the electrodes of the crystal element. This is often refered to as the shunt capacitance.

Apart from their use in oscillators, quartz crystals find uses in filters. Here they offer levels of performance that cannot be achieved by other forms of filter. Often several crystals may be used in one filter to provide the correct shape.