Quartz Crystal Oscillator: Working Principle, Piezoelectric Effect, Equivalent Circuit & Applications

Introduction

Quartz crystal oscillators are designed to overcome many of the frequency stability problems found in conventional oscillators. Common factors that affect oscillator stability include variations in power supply voltage, temperature changes, and load variations.

Although careful selection of components in LC and RC oscillators can improve stability, there is a practical limit to how stable these circuits can be. To achieve extremely high frequency stability, a quartz crystal is used as the frequency-determining element, forming what is known as a Quartz Crystal Oscillator (XO).

Piezoelectric Effect

A quartz crystal operates based on the piezoelectric effect. When an electrical voltage is applied across a thin slice of quartz, it physically changes shape. Conversely, when a mechanical force is applied to the crystal, an electrical charge is generated.

This bidirectional energy conversion—electrical to mechanical and mechanical to electrical—makes quartz crystals act as transducers. The mechanical vibrations generated by this effect replace the LC tank circuit used in traditional oscillators.

Quartz Crystal Construction

Quartz is one of the most widely used crystal materials in electronic circuits due to its high mechanical strength and excellent frequency stability. A quartz crystal oscillator uses a very thin wafer of precisely cut quartz.

Both flat surfaces of the crystal are metallized to form electrical connections. The crystal’s physical dimensions and thickness determine its fundamental frequency, also known as its characteristic frequency.

Once a crystal is cut and fabricated, it can operate only at its designed frequency. The characteristic frequency is inversely proportional to the thickness of the crystal between its metallized surfaces.

Equivalent Electrical Model of Quartz Crystal

A vibrating quartz crystal can be represented by an equivalent electrical circuit consisting of:

• A small resistance (R)
• A large inductance (L)
• A very small capacitance (C)

This series RLC circuit represents the mechanical vibrations of the crystal. It is connected in parallel with a capacitance C_p, which represents the electrical capacitance of the crystal mounting and electrodes.

Modes of Resonance

Series Resonant Frequency

Quartz crystal oscillators typically operate at their series resonant frequency. At this frequency, the inductance (L_s) and capacitance (C_s) of the crystal resonate in series, resulting in minimum impedance.

This frequency is known as the series resonant frequency (f_s).

Parallel Resonant Frequency

In addition to the series resonance, a second resonant frequency exists due to the interaction between the series RLC branch and the parallel capacitance C_p.

The parallel resonant frequency (f_p) occurs when the reactance of the series LC circuit equals the reactance of the parallel capacitance.

Microprocessor Oscillator Application

Most microprocessors, microcontrollers, and PIC devices include two oscillator pins, typically labeled OSC1 and OSC2. These pins allow connection to an external quartz crystal, RC oscillator, or ceramic resonator.

In microprocessor-based systems, the quartz crystal oscillator generates a continuous square-wave signal. The fundamental frequency of this signal is determined entirely by the crystal.

This frequency controls the system clock, instruction execution rate, and overall timing of the processor, making quartz crystal oscillators essential for accurate and stable digital system operation.

Advantages of Quartz Crystal Oscillators

• Extremely high frequency stability
• Low frequency drift with temperature changes
• Excellent accuracy and repeatability
• Low phase noise
• Widely used as system clocks

Applications

• Microprocessors and microcontrollers
• Digital clocks and watches
• Communication systems
• Frequency synthesizers
• Computers and embedded systems