Quartz: Properties, Parameters, and Applications

This page explains what quartz is and covers the basics of quartz crystal oscillators. A link to a quartz calculator is also provided.

The technical formula for quartz is SiO2, composed of two elements: silicon and oxygen. Amorphous forms of quartz are found in rocks and sand. While quartz is abundant in nature, highly pure forms are needed for manufacturing quartz crystal units.

Quartz is a piezoelectric material used for high-frequency oscillation, making it a vital component in the modern electronics industry. Quartz crystals are used to generate precise frequencies and are widely used in clocks, computers, processors, and watches.

Quartz resonators consist of a piece of piezoelectric material fitted across crystallographic axes. These wafers have conductive electrodes formed by vacuum evaporation. The piezoelectric effect occurs when an electric field (E-field) is applied between these electrodes, causing the wafer to vibrate. Figure 1 depicts a quartz crystal’s equivalent circuit, where:

• Ls is the inductance
• Cs is the series capacitance
• Cp is the parallel capacitance
• Rs is the series resistance

Crystal oscillators can operate in two modes: series and parallel.

Quartz Crystal Parameters

• Q-factor: The equation/formula for the Q-factor is shown in the image above. Crystals offer very high Q-factors, approximately 100,000.
• Resonance: Resonance occurs when the voltage across an electronic circuit is in phase with the current supplied to the circuit. At resonance, the circuit behaves like a resistive circuit, and the power factor of the circuit is equal to one.
• Series Resonance: This condition is achieved using a series connection of a capacitor and an inductor. The formula for series resonance frequency is mentioned above.
• Parallel Resonance: This condition is achieved using a parallel connection of a capacitor and an inductor. The formula for parallel resonance frequency is also mentioned above.

Equations for Series and Parallel Resonance

The series resonant frequency ($f_s$) is given by:

${f_s} = \frac{1}{2\pi\sqrt{L_sC_s}}$

The parallel resonant frequency ($f_p$) is given by:

${f_p} = \frac{1}{2\pi\sqrt{L_s \frac{C_s C_p}{C_s+C_p}}}$

Manufacturing Quartz Crystals

The following steps are involved in manufacturing quartz crystals:

• Cutting the wafers
• Lapping them
• Cleaning them
• Checking orientation
• Rounding
• Cleaning and etching of blanks
• Base plating
• Mounting
• Bonding
• Final adjustment of frequency using vacuum deposition of silver/gold
• Sealing the holder to the can
• Prevention of electrode oxidation
• High-temperature cycling
• High-vacuum bake cycling
• Frequency control and sorting