Frequency and Reactance in a Crystal Oscillator

The Crystal Oscillator

A crystal oscillator is an electronic circuit that uses the mechanical resonance of a vibrating crystal of piezoelectric material to create an electrical signal with a very precise frequency. It is widely used in various electronic devices such as radios, computers, and watches for accurate timekeeping and frequency generation.

Frequency of Oscillation

The frequency of oscillation of a crystal oscillator is determined by the mechanical properties of the crystal. When an alternating voltage is applied to the crystal, it undergoes mechanical vibrations at its resonant frequency. The crystal's resonant frequency is determined by its physical dimensions and material properties.

Reactance in a Crystal Oscillator

In an oscillating circuit, the crystal acts as a frequency-selective element, providing a specific frequency at which the circuit resonates. The crystal has a characteristic impedance, which is a combination of resistance and reactance. Reactance is the opposition offered by a circuit element to the flow of alternating current and can be either capacitive or inductive.

When the frequency of oscillation of the crystal oscillator becomes equal to the parallel resonance frequency of the crystal, the reactance of the crystal becomes infinite.

Parallel Resonance

Parallel resonance occurs in a circuit when the reactance of the inductive and capacitive elements cancel each other out. At resonance, the inductive and capacitive elements exhibit equal and opposite reactances, resulting in a net reactance of zero.

Reactance Becomes Infinite

When the frequency of oscillation of the crystal oscillator matches the parallel resonance frequency of the crystal, the inductive and capacitive reactances cancel each other out and the net reactance becomes zero. However, the crystal still possesses a small amount of resistance.

As the frequency deviates from the parallel resonance frequency, the crystal's reactance increases, and when the frequency becomes exactly equal to the parallel resonance frequency, the reactance becomes infinite.

This phenomenon is due to the crystal's mechanical vibrations being in phase with the alternating voltage applied, resulting in a resonance condition. At resonance, the crystal exhibits the maximum impedance, and the reactance becomes infinite.

Conclusion

When the frequency of oscillation of a crystal oscillator becomes equal to the parallel resonance frequency of the crystal, the reactance of the crystal becomes infinite. This occurs when the inductive and capacitive reactances of the crystal cancel each other out, resulting in a net reactance of zero. It is a critical condition for the proper operation of a crystal oscillator and is utilized for generating accurate and stable frequencies in electronic devices.