What is a Crystal Oscillator || How to Construct a Crystal Oscillator

A crystal oscillator is an electronic oscillator which uses the mechanical resonance of a vibrating crystal composed of a piezoelectric material to create an electrical signal of a constant frequency. When a small voltage is applied to a thin piece of quartz crystal, it changes its shape. This phenomenon is known as the piezoelectric effect. The most common type of piezoelectric resonator in use is the quartz crystal. The oscillators that implement these crystals for oscillation are called the crystal oscillators.

Properties of a Quartz Crystal
A quartz crystal produces a slight change in shape by application of voltage on the surface or through an electrode, called electrostriction. These piezoelectric materials that transform its shape are called as transducers. When the voltage is removed, the crystal returns back to its original shape generating a small voltage. The quartz crystal produces mechanical vibrations or oscillations at a specific resonant frequency to which it is designed. The behavior of a crystal is similar to an RLC circuit with higher quality or Q factor. Thus a quartz crystal can be used as a tuned circuit in an LC oscillator.

The quartz used in crystal oscillators is very thin and the electrical connections are taken from its two surfaces. The resonant frequency of the quartz crystal depends on the physical shape, size, thickness and elasticity of the material. The typical quartz crystal is cut and shaped to attain it's specific frequency.

The elastic vibrational nature of the quartz crystal has less dependence on the temperature, and thus has more stability. The stability of the quartz crystal makes them more acceptable as oscillators in receivers, transmitters, clocks, microcontrollers etc.

Equivalent Circuit of a Quartz Crystal
The equivalent circuit of a quartz crystal consists of a series resistance, inductance and capacitance (RLC) circuit with a low resistance Rs, large inductance Ls, and a small capacitance Cs. It also has a parallel capacitance Cp. Thus the resonant frequency of the crystal is determined by
A series resonant circuit, which is composed of Rs, Ls and the Cs.
A parallel resonant circuit, which is composed of Ls and Cs resonating parallel with the capacitor Cp. 

Calculation of Series and Parallel Resonant Frequency of a Quartz Crystal 

Calculation to find out the series resonance in a quartz crystal is given by the formula

Fs = 1/2π√LsCs

Calculation to find out the parallel resonance in a quartz crystal is given by the formula

Fp = 1/2π√Ls(CpCs/Cp+Cs)

 Applications of Crystal Oscillators

1. A crystal oscillator is used in generating an oscillator signal in radio and television.
2. It is used to generate a stable oscillator signal in transmitters.
3. It is used in communication systems, tracking and guidance systems.
4. It is used as a stable clock signal in digital frequency synthesizers, microcontrollers and other integrated circuits.
5. It is used as a local oscillator in frequency converters and doublers.
6. It is used in quartz watches and clocks for precise time measurements.

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