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. This frequency is commonly used to keep track of time (as in quartz wristwatches), to provide a stable clock signal for digital integrated circuits, and to stabilize frequencies for radio transmitters.

Using an amplifier and feedback, it is an especially accurate form of an electronic oscillator. The crystal used therein is sometimes called a "timing crystal". On schematic diagrams a crystal is sometimes labeled with the abbreviation XTAL.

Crystals for timing purposes

Inside construction of a modern high performance HC-49 package quartz crystal

A crystal is a solid in which the constituent atoms, molecules, or ions are packed in a regularly ordered, repeating pattern extending in all three spatial dimensions.

Almost any object made of an elastic material could be used like a crystal, with appropriate transducers, since all objects have natural resonant frequencies of vibration. For example, steel is very elastic and has a high speed of sound. It was often used in mechanical filters before quartz. The resonant frequency depends on size, shape, elasticity and the speed of sound in the material. High-frequency crystals are typically cut in the shape of a simple, rectangular plate. Low-frequency crystals, such as those used in digital watches, are typically cut in the shape of a tuning fork. For applications not needing very precise timing, a low-cost ceramic resonator is often used in place of a quartz crystal.

When a crystal of quartz is properly cut and mounted, it can be made to bend in an electric field, by applying a voltage to an electrode near or on the crystal. This property is known as piezoelectricity. When the field is removed, the quartz will generate an electric field as it returns to its previous shape, and this can generate a voltage. The result is that a quartz crystal behaves like a circuit composed of an inductor, capacitor and resistor, with a precise resonant frequency.

Quartz has the further advantage that its size changes very little with temperature. Therefore, the resonant frequency of the plate, which depends on its size, will not change much, either. This means that a quartz clock, filter or oscillator will remain accurate. For critical applications the quartz oscillator is mounted in a temperature-controlled container, called a crystal oven, and can also be mounted on shock absorbers to prevent perturbation by external mechanical vibrations.

Quartz timing crystals are manufactured for frequencies from a few tens of kilohertz to tens of megahertz. More than two billion (2×10⁹) crystals are manufactured annually. Most are small devices for wristwatches, clocks, and electronic circuits. However, quartz crystals are also found inside test and measurement equipment, such as counters, signal generators, and oscilloscopes.

Crystal Modelling

A quartz crystal can be modelled as an electrical network with a low impedance (series) and a high impedance (parallel) resonance point spaced closely together. Mathematically the impedance of this nework this can be written as:

 $Z(s)={\frac {s^{2} s{\frac {R_{1}}{L_{1}}} {\omega _{s}}^{2}}{s^{2} s{\frac {R_{1}}{L_{1}}} {\omega _{p}}^{2}}}$

where s is the complex frequency ( $s=j\omega$ ), $\omega _{s}$ is the series resonant frequency in radians and $\omega _{p}$ is the parallel resonant frequency in radians.

Adding additional capacitance across a crystal will cause the parallel resonance to shift downward. This can be used to adjust the frequency that a crystal oscillator oscillates at. Crystal manufacturers normally cut and trim their crystals to have a specified resonant frequency with a known 'load' capacitance added to the crystal. For example, a 6pF 32kHz crystal has a parallel resonance frequency of 32,768 Hz when a 6.0pF capacitor is placed across the crystal. Without this capacitance, the resonance frequency is higher than 32,768.

Temperature Effects

A crystal's frequency characteristic depends on the shape or 'cut' of the crystal. A tuning fork crystal is usually cut such that its frequency over temperature is a parabolic curve centered around 25 degC. This means that a tuning fork crystal oscillator will resonate close to its target frequency at room temperature, but will slow down when the temperature either increases or decreases from room temperature. A common parabolic coefficient for a 32kHz tuning fork crystal is -0.04ppm/degC^2.

 $f=f_{0}[1-0.04{\mbox{ppm}}(T-T_{0})^{2}]$

In a real application, this means that a clock built using a regular 32kHz tuning fork crystal will keep good time at room temperature, lose 2 minutes per year at 10 degrees above (or below) room temperature and lose 8 minutes per year at 20 degrees above (or below) room temperature.

Crystals and frequency

Schematic symbol and equivalent circuit for a quartz crystal in an oscillator

The crystal oscillator circuit sustains oscillation by taking a voltage signal from the quartz resonator, amplifying it, and feeding it back to the resonator. The rate of expansion and contraction of the quartz is the resonant frequency, and is determined by the cut and size of the crystal.

A regular timing crystal contains two electrically conductive plates, with a slice or tuning fork of quartz crystal sandwiched between them. During startup, the circuit around the crystal applies a random noise AC signal to it, and purely by chance, a tiny fraction of the noise will be at the resonant frequency of the crystal. The crystal will therefore start oscillating in synchrony with that signal. As the oscillator amplifies the signals coming out of the crystal, the crystal's frequency will become stronger, eventually dominating the output of the oscillator. Natural resistance in the circuit and in the quartz crystal filter out all the unwanted frequencies.

One of the most important traits of quartz crystal oscillators is that they can exhibit very low phase noise. In other words, the signal they produce is a pure tone. This makes them particularly useful in telecommunications where stable signals are needed, and in scientific equipment where very precise time references are needed.

The output frequency of a quartz oscillator is either the fundamental resonance or a multiple of the resonance, called an overtone frequency.

A typical Q for a quartz oscillator ranges from 10⁴ to 10⁶. The maximum Q for a high stability quartz oscillator can be estimated as Q = 1.6 × 10⁷/f, where f is the resonance frequency in MHz.

Environmental changes of temperature, humidity, pressure, and vibration can change the resonant frequency of a quartz crystal, but there are several designs that reduce these environmental effects. These include the TCXO, MCXO, and OCXO (defined below). These designs (particularly the OCXO) often produce devices with excellent short-term stability. The limitations in short-term stability are due mainly to noise from electronic components in the oscillator circuits. Long term stability is limited by aging of the crystal.

Due to aging and environmental factors such as temperature and vibration, it is hard to keep even the best quartz oscillators within one part in 10⁻¹⁰ of their nominal frequency without constant adjustment. For this reason, atomic oscillators are used for applications that require better long-term stability and accuracy.

Although crystals can be fabricated for any desired resonant frequency, within technological limits, in actual practice today engineers design crystal oscillator circuits around relatively few standard frequencies, such as 10 MHz, 20 MHz and 40 MHz. Using frequency dividers, frequency multipliers and phase locked loop circuits, it is possible to synthesize any desired frequency from the reference frequency.

Care must be taken to use only one crystal oscillator source when designing circuits to avoid subtle failure modes of metastability in electronics. If this is not possible, the number of distinct crystal oscillators, PLLs, and their associated clock domains should be rigorously minimized, through techniques such as using a subdivision of an existing clock instead of a new crystal source. Each new distinct crystal source needs to be rigorously justified, since each one introduces new, difficult to debug probabilistic failure modes, due to multiple crystal interactions, into equipment.

Series or parallel resonance

A quartz crystal provides both series and parallel resonance. The series resonance is a few kHz lower than the parallel one. Crystals below 30 MHz are generally operated at parallel resonance, which means that the crystal impedance appears infinite. Any additional circuit capacitance will thus pull the frequency down. For a parallel resonance crystal to operate at its specified frequency, the electronic circuit has to provide a total parallel capacitance as specified by the crystal manufacturer.

Crystals above 30 MHz (up to >200 MHz) are generally operated at series resonance where the impedance appears at its minimum and equal to the series resistance. For this reason the series resistance is specified (<100 Ω) instead of the parallel capacitance. For the upper frequencies, the crystals are operated at one of its overtones, presented as being a fundamental, 3rd, 5th, or even 7th overtone crystal. The oscillator electronic circuits usually provides additional LC circuits to select the wanted overtone of a crystal.

Spurious frequencies

For crystals operated in series resonance, significant (and temperature-dependent) spurious responses may be experienced. These responses typically appear some tens of kHz above the wanted series resonance. Even if the series resistances at the spurious resonances appear higher than the one at wanted frequency, the oscillator may lock at a spurious frequency (at some temperatures). This is generally avoided by using low impedance oscillator circuits to enhance the series resistance difference.

Notation

On electrical schematic diagrams, crystals are designated with the class letter "Y" (Y1, Y2, etc.) Oscillators, whether they are crystal oscillators or other, are designated with the class letter "G" (G1, G2, etc.) (See IEEE Std 315-1975, or ANSI Y32.2-1975) On occasion, one may see a crystal designated on a schematic with "X" or "XTAL", or a crystal oscillator with "XO", but these forms are deprecated.

Crystal oscillator types and their abbreviations:

ATCXO — analogue temperature-compensated crystal oscillator
CDXO —Calibrated Dual Crystal Oscillator
MCXO — microcomputer-compensated crystal oscillator
OCVCXO — oven-controlled voltage-controlled crystal oscillator
OCXO — oven-controlled crystal oscillator
RbXO — rubidium crystal oscillators (RbXO), a crystal oscillator (can be a MCXO) synchronized with a built-in rubidium standard which is run only occasionally to save power
TCVCXO — temperature-compensated voltage-controlled crystal oscillator
TCXO — temperature-compensated crystal oscillator
TSXO — temperature-sensing crystal oscillator, an adaptation of the TCXO
VCXO — voltage-controlled crystal oscillator
DTCXO — Digital Temperature Compensated crystal Oscillator - same as MCXO

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