Definitions

# 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/receivers.

## History

The traditional and most common type of piezoelectric resonator used in electronics was the quartz crystal, so oscillator circuits designed around them were called 'crystal oscillators'. Piezoelectricity was discovered by Jacques and Pierre Curie in 1880. Paul Langevin first investigated quartz resonators for use in sonar during World War I. The first crystal controlled oscillator, using a crystal of Rochelle salt, was built in 1917 and patented in 1918 by Alexander M. Nicholson at Bell Telephone Laboratories, although his priority was disputed by Walter Guyton Cady. Cady built the first quartz crystal oscillator in 1921. Other early innovators in quartz crystal oscillators include G. W. Pierce and Louis Essen.

Quartz crystal oscillators were developed for high-stability frequency references during the 1920's and 1930's. By 1926 quartz crystals were used to control the frequency of radio broadcasting stations and were popular with amateur radio operators. A number of firms started producing quartz crystals for electronic use during this time. Using what are now considered primitive methods, about 100,000 crystal units were produced in the United States during 1939. During WW2, demand for accurate frequency control of military radio equipment spurred rapid development of the crystal manufacturing industry. Suitable quartz became a critical war material, with much of it imported from Brazil.

Although crystal oscillators still most commonly use quartz crystals, devices using other materials are becoming more common, such as ceramic resonators.

## Operation

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 distort 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. (See RLC circuit.)

Quartz has the further advantage that its elastic constants and its size change in such a way that the frequency dependence on temperature can be very low. The specific characteristics will depend on the mode of vibration and the angle at which the quartz is cut (relative to its crystallographic axes)1 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 consumer devices such as wristwatches, clocks, radios, computers, and cellphones. Quartz crystals are also found inside test and measurement equipment, such as counters, signal generators, and oscilloscopes.

## Modeling

### Electrical model

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 (using the Laplace transform) the impedance of this network can be written as:

$Z\left(s\right) = left\left(\left\{frac\left\{1\right\}\left\{scdot C_1\right\}+scdot L_1+R_1\right\} right\right) || left\left(\left\{frac\left\{1\right\}\left\{scdot C_0\right\}\right\} right\right)$

or,

$Z\left(s\right) = frac\left\{s^2 + sfrac\left\{R_1\right\}\left\{L_1\right\} + \left\{omega_s\right\}^2\right\}\left\{\left(scdot C_0\right)\left[s^2 + sfrac\left\{R_1\right\}\left\{L_1\right\} + \left\{omega_p\right\}^2\right]\right\}$
$Rightarrow omega_s = frac\left\{1\right\}\left\{sqrt\left\{L_1 cdot C_1\right\}\right\}, quad omega_p = sqrt\left\{frac\left\{C_1+C_0\right\}\left\{L_1 cdot C_1 cdot C_0\right\}\right\} = omega_s sqrt\left\{1+frac\left\{C_1\right\}\left\{C_0\right\}\right\} approx omega_s left\left(1 + frac\left\{C_1\right\}\left\{2 C_0\right\}right\right) quad \left(C_0 >> C_1\right)$

where s is the complex frequency ($s=jomega$), $omega_s$ is the series resonant frequency in radians per second and $omega_p$ is the parallel resonant frequency in radians per second.

Adding additional capacitance across a crystal will cause the parallel resonance to shift downward. This can be used to adjust the frequency at which a crystal oscillator oscillates. 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 6 pF 32 kHz crystal has a parallel resonance frequency of 32,768 Hz when a 6.0 pF capacitor is placed across the crystal. Without this capacitance, the resonance frequency is higher than 32,768 Hz.

### Resonance modes

A quartz crystal provides both series and parallel resonance. The series resonance is a few kilohertz lower than the parallel one. Crystals below 30 MHz are generally operated between series and parallel resonance, which means that the crystal appears as an inductive reactance in operation. 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.

### 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 °C. 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 32 kHz tuning fork crystal is −0.04 ppm/°C².

$f = f_0\left[1-0.04 mbox\left\{ppm\right\}\left(T-T_0\right)^2\right]$

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

## Electrical oscillators

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. When the energy of the generated output frequencies matches the losses in the circuit, an oscillation can be sustained.

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 signals in the crystal's frequency band 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.

The output frequency of a quartz oscillator can be either the fundamental resonance or a multiple of the resonance, called an overtone frequency. High frequency crystals are often designed to operate at third, fifth, or seventh overtones.

A major reason for the wide use of crystal oscillators is their high Q factor. A typical Q for a quartz oscillator ranges from 104 to 106, compared to perhaps 102 for an LC oscillator. 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 megahertz.

One of the most important traits of quartz crystal oscillators is that they can exhibit very low phase noise. In many oscillators, any spectral energy at the resonant frequency will be amplified by the oscillator, resulting in a collection of tones at different phases. In a crystal oscillator, the crystal mostly vibrates in one axis. Therefore, only one phase is dominant. This property of low phase noise makes them particularly useful in telecommunications where stable signals are needed, and in scientific equipment where very precise time references are needed.

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 3.58 MHz, 10 MHz, 14.318 MHz, 20 MHz, 33.33 MHz, and 40 MHz. The vast popularity of the 3.58 MHz and 14.318 MHz crystals is attributed initially to low cost resulting from economies of scale resulting from the popularity of television and the fact that this frequency is involved in synchronizing to the colorburst signal necessary to display color on an NTSC or PAL based television set. Using frequency dividers, frequency multipliers and phase locked loop circuits, it is practical to derive a wide range of frequencies from one 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.

### Spurious frequencies

For crystals operated in series resonance, significant (and temperature-dependent) spurious responses may be experienced. These responses typically appear some tens of kilohertz 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 differences.

### Commonly used crystal frequencies

Frequency (MHz) Primary uses
0.032768 Real-time clocks, allows binary division to 1 Hz signal (215 × 1 Hz); also often used in low-speed low-power circuits
1.8432 UART clock; allows integer division to common baud rates
2.4576 UART clock; allows integer division to common baud rates up to 38400
3.2768 Allows binary division to 100 Hz (32768 × 100 Hz, or 215 × 100 Hz)
3.575611 PAL M color subcarrier
3.579545 NTSC M color subcarrier; very common and inexpensive, used in many other applications, eg. DTMF generators
3.582056 PAL N color subcarrier
3.686400 UART clock (2 × 1.8432 MHz); allows integer division to common baud rates
4.096000 Allows binary division to 1 kHz (212 × 1 kHz)
4.194304 Real-time clocks, divides to 1 Hz signal (222 × 1 Hz)
4.43361875 PAL B/D/G/H/I and NTSC M4.43 color subcarrier
4.9152 Used in CDMA systems; divided to 1.2288 MHz baseband frequency as specified by J-STD-008
5.068 Used in radio transceivers as an IF source
6.144 Digital audio systems - DAT, MiniDisc, sound cards; 128 × 48 kHz (27 × 48 kHz). Also allows integer division to common UART baud rates up to 38400.
6.5536 Allows binary division to 100 Hz (65536 × 100 Hz, or 216 × 100 Hz); used also in red boxes
7.15909 NTSC M color subcarrier (2 × 3.579545 MHz)
7.3728 UART clock (4 × 1.8432 MHz); allows integer division to common baud rates
8.86724 PAL B/G/H color subcarrier (2 × 4.433618 MHz)
9.216 Allows integer division to 1024 kHz and its halves (16 kHz, 32 kHz, 64 kHz...)
9.83040 Used in CDMA systems (2 × 4.9152); divided to 1.2288 MHz baseband frequency
10.245 Used in radio transceivers; mixes with 10.7 MHz subcarrier yielding 455 kHz signal, a common second IF for FM radio and first IF for AM radio
10.700 Used in radio transceivers as an IF source
11.0592 UART clock (6 × 1.8432 MHz); allows integer division to common baud rates
11.2896 Used in compact disc digital audio systems and CDROM drives; allows binary division to 44.1 kHz (256 × 44.1 kHz), 22.05 kHz, and 11.025 kHz
12.0000 Used in USB systems as the reference clock for the full-speed PHY rate of 12 Mbit/s, or multiplied up using a PLL to clock high speed PHYs at 480 Mbit/s
12.288 Digital audio systems - DAT, MiniDisc, sound cards; 256 × 48 kHz (28 × 48 kHz). Also allows integer division to common UART baud rates up to 38400.
13.500 Master clock for PAL/NTSC DVD players, Digital TV receivers etc. (13.5 MHz is an exact multiple of the PAL and NTSC line frequencies)
13.875 Used in some teletext circuits; 2 × 6.9375 MHz (clock frequency of PAL B teletext; SECAM uses 6.203125 MHz, NTSC M uses 5.727272 MHz, PAL G uses 6.2031 MHz, and PAL I uses 4.4375 MHz clock)
14.31818 NTSC M color subcarrier (4 × 3.579545 MHz). Common seed clock for modern PC motherboard clock generator chips, also common on VGA cards.
14.7456 UART clock (8 × 1.8432 MHz); allows integer division to common baud rates
16.368 Commonly used for down-conversion and sampling in GPS-receivers. Generates intermediate frequency signal at +4.092 MHz. 16.3676 or 16.367667 MHz are sometimes used to avoid perfect lineup between sampling frequency and GPS spreading code.
16.9344 Used in compact disc digital audio systems and CDROM drives; allows integer division to 44.1 kHz (384 × 44.1 kHz), 22.05 kHz, and 11.025 kHz. Also allows integer division to common UART baud rates.
17.734475 PAL B/G/H color subcarrier (4 × 4.433618 MHz)
18.432 UART clock (10 × 1.8432 MHz); allows integer division to common baud rates. Also allows integer division to 48 kHz (384 × 48 kHz), 96 kHz, and 192 kHz samplerates used in high-end digital audio.
19.6608 Used in CDMA systems (4 × 4.9152); divided to 1.2288 MHz baseband frequency
24.576 Digital audio systems - DAT, MiniDisc, AC'97, sound cards; 512 × 48 kHz (29 × 48 kHz)
25.000 Fast Ethernet MII clock (100 MHz / 4-bit nibble)
26.000 Commonly used as a reference clock for GSM and UMTS handsets. (26 MHz is exactly 96 × the GSM bit rate)
27.000 Master clock for PAL/NTSC DVD players, Digital TV receivers etc. (27 MHz is an exact multiple of the PAL and NTSC line frequencies)
29.4912 UART clock (16 × 1.8432 MHz); allows integer division to common baud rates

## Circuit notations and abbreviations

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:

• ATCXOanalog temperature controlled crystal oscillator
• CDXO —calibrated dual crystal oscillator
• MCXOmicrocomputer-compensated crystal oscillator
• OCVCXOoven-controlled voltage-controlled crystal oscillator
• OCXO — oven-controlled crystal oscillator
• RbXOrubidium 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
• VCTCXO — voltage controlled temperature compensated crystal oscillator
• VCXO — voltage-controlled crystal oscillator
• DTCXO — digital temperature compensated crystal oscillator