A miniature 4 MHz quartz crystal enclosed in a hermetically sealed HC-49/US package, used as the resonator in a crystal oscillator.

A crystal oscillator is an electronic oscillator 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 and receivers. The most common type of piezoelectric resonator used is the quartz crystal, so oscillator circuits designed around them became known as "crystal oscillators."

Quartz 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 used 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.

History[link]

Very early Bell Labs crystals from Vectron International Collection

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^[1] in 1918 by Alexander M. Nicholson at Bell Telephone Laboratories, although his priority was disputed by Walter Guyton Cady.^[2] Cady built the first quartz crystal oscillator in 1921.^[3] 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 1920s and 1930s. By 1926 quartz crystals were used to control the frequency of radio broadcasting stations and were popular with amateur radio operators.^[4] In 1928, Warren Marrison (of Bell Telephone Laboratories) developed the first quartz crystal clock. This invention replaced the escapement and pendulum (as the timing reference), relying instead on the natural vibrations occurring in the quartz crystal as the oscillator. This improved timing accuracies to 1 sec in 30 years (or 30 ms/year).^[5] Utilizing the early work at Bell Labs, AT&T eventually established their Frequency Control Products division, later spun off and known today as Vectron International.^[6]

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 World War II, the demand for accurate frequency control of military and naval radios and radars spurred rapid development of the quartz crystal manufacturing industry. Suitable types of quartz became a critical war material, and much of it was eventually supplied by Brazil.

In 1968, Juergen Staudte invented a process for manufacturing quartz crystal oscillators while working at North American Aviation (now Rockwell). Staudte patented his invention, which used a photolithographic process that is similar to the way integrated circuits are made. In 1970 he left North American Aviation to start his own company, Statek, in Orange, California. Statek began manufacturing and marketing the quartz oscillators in 1971.^[7]

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

Crystal oscillation modes

Operation[link]

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).^[8] 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.

Modeling[link]

Electrical model[link]

Electronic symbol for a piezoelectric crystal resonator

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:

Failed to parse (Missing texvc executable; please see math/README to configure.): Z(s) = \left( {\frac{1}{s\cdot C_1}+s\cdot L_1+R_1} \right) || \left( {\frac{1}{s\cdot C_0}} \right)

or,

Failed to parse (Missing texvc executable; please see math/README to configure.): Z(s) = \frac{s^2 + s\frac{R_1}{L_1} + {\omega_s}^2}{(s\cdot C_0)[s^2 + s\frac{R_1}{L_1} + {\omega_p}^2]}

Failed to parse (Missing texvc executable; please see math/README to configure.): \Rightarrow \omega_s = \frac{1}{\sqrt{L_1 \cdot C_1}}, \quad \omega_p = \sqrt{\frac{C_1+C_0}{L_1 \cdot C_1 \cdot C_0}} = \omega_s \sqrt{1+\frac{C_1}{C_0}} \approx \omega_s \left(1 + \frac{C_1}{2 C_0}\right) \quad (C_0 \gg C_1)

where s is the complex frequency (Failed to parse (Missing texvc executable; please see math/README to configure.): s=j\omega ), Failed to parse (Missing texvc executable; please see math/README to configure.): \omega_s

is the series resonant frequency in radians per second and Failed to parse (Missing texvc executable; please see math/README to configure.): \omega_p
is the parallel resonant frequency in radians per second.

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

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 oscillates. Crystal manufacturers normally cut and trim their crystals to have a specified resonance frequency with a known 'load' capacitance added to the crystal. For example, a crystal intended for a  6 pF load has its specified parallel resonance frequency when a 6.0 pF capacitor is placed across it. Without this capacitance, the resonance frequency is higher.

Resonance modes[link]

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 these crystals the series resistance is specified (<100 Ω) instead of the parallel capacitance. To reach higher frequencies, a crystal can be made to vibrate at one of its overtone modes, which occur near multiples of the fundamental resonant frequency. Only odd numbered overtones are used. Such a crystal is referred to as a 3rd, 5th, or even 7th overtone crystal. To accomplish this, the oscillator circuit usually includes additional LC circuits to select the desired overtone.

Temperature effects[link]

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.

Failed to parse (Missing texvc executable; please see math/README to configure.): 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 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[link]

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.

An oscillator crystal has 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. The narrow resonance band of the quartz crystal filters 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. Manufacturers have difficulty producing crystals thin enough to produce fundamental frequencies over 30 MHz. To produce higher frequencies, manufacturers make overtone crystals tuned to put the 3rd, 5th, or 7th overtone at the desired frequency, because they are thicker and therefore easier to manufacture than a fundamental crystal that would produce the same frequency—although getting the desired overtone frequency requires a slightly more complicated oscillator circuit.^{[9][10][11][12][13]} A fundamental crystal oscillator circuit is simpler and more efficient and has more pullability than a third overtone circuit. Depending on the manufacturer, the highest available fundamental frequency may be 25 MHz to 66 MHz.^[14][15]

A major reason for the wide use of crystal oscillators is their high Q factor. A typical Q value 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 difficult to keep even the best quartz oscillators within one part in 10¹⁰ of their nominal frequency without constant adjustment. For this reason, atomic oscillators are used for applications requiring better long-term stability and accuracy.

Spurious frequencies[link]

25-MHz crystal exhibiting spurious response

For crystals operated at series resonance or pulled away from the main mode by the inclusion of a series inductor or capacitor , significant (and temperature-dependent) spurious responses may be experienced. Though most spurious modes are typically some tens of kilohertz above the wanted series resonance their temperature coefficient will be different from the main mode and the spurious response may move through the main mode at certain temperatures. Even if the series resistances at the spurious resonances appear higher than the one at wanted frequency a rapid change in the main mode series resistance can occur at specific temperatures when the two frequencies are coincidental. A consequence of these activity dips is that the oscillator may lock at a spurious frequency (at specific temperatures). This is generally minimized by ensuring that the maintaining circuit has insufficient gain to activate unwanted modes.

Spurious frequencies are also generated by subjecting the crystal to vibration this modulates the resonance frequency to a small degree by the frequency of the vibrations. SC-cut crystals are designed to minimize the frequency effect of mounting stress and they are therefore less sensitive to vibration. Acceleration effects including gravity are also reduced with SC cut crystals as is frequency change with time due to long term mounting stress variation. There are disadvantages with SC cut shear mode crystals, these are the need for the maintaining oscillator to discriminate against other closely related unwanted modes and increased frequency change due to temperature when subject to a full ambient range. SC cut crystals are most advantageous where temperature control at their temperature of zero temperature coefficient (turnover) is possible under these circumstances an overall stability performance from premium units can approach the stability of Rubidium frequency standards.

Commonly used crystal frequencies[link]

Crystal oscillator circuits are often designed around relatively few standard frequencies, such as 3.579545 MHz, 4.433619 MHz, 10 MHz, 14.318182 MHz, 17.734475 MHz, 20 MHz, 33.33 MHz, and 40 MHz. The popularity of the 3.579545 MHz crystals is due to low cost since they are used for NTSC color television receivers. Using frequency dividers, frequency multipliers and phase locked loop circuits, it is practical to derive a wide range of frequencies from one reference frequency. 14.318182 MHz (four times 3.579545 MHz) is used in computer video displays to generate a bitmapped video display for NTSC color monitors, such as the CGA used with the original IBM PC. (The IBM PC used 14.318182 MHz, divided by three, as its 4.77 MHz clock source, using one crystal for two purposes.) The 4.433619 MHz and 17.734475 MHz values are used in PAL color television equipment and devices intended to produce PAL signals.

Crystals can be manufactured for oscillation over a wide range of frequencies, from a few kilohertz up to several hundred megahertz. Many applications call for a crystal oscillator frequency conveniently related to some other desired frequency, so hundreds of standard crystal frequencies are made in large quantities and stocked by electronics distributors.

Common package types for quartz crystal products

Crystal structures and materials[link]

Cluster of natural quartz crystals

A synthetic quartz crystal grown by the hydrothermal synthesis, about 19 cm long and weighing about 127 grams.

Tuning fork crystal

Simple quartz crystal

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

Flexural and thickness shear crystals

The most common material for oscillator crystals is quartz. At the beginning of the technology, natural quartz crystals were used; now synthetic crystalline quartz grown by hydrothermal synthesis is predominant due to higher purity, lower cost, and more convenient handling. One of the few remaining uses of natural crystals is for pressure transducers in deep wells. During World War II and for some time afterwards, natural quartz was considered a strategic material by the USA. Large crystals were imported from Brazil. Raw "lascas", the source material quartz for hydrothermal synthesis, are imported to USA or mined locally by Coleman Quartz. The average value of as-grown synthetic quartz in 1994 was USD60/kg.^[16]

Two types of quartz crystals exist: left-handed and right-handed, differing in the optical rotation but identical in other physical properties. Both left and right-handed crystals can be used for oscillators, if the cut angle is correct. In manufacture, right-handed quartz is generally used.^[17] The SiO₄ tetrahedrons form parallel helixes; the direction of twist of the helix determines the left- or right-hand orientation. The helixes are aligned along the z-axis and merged together, sharing atoms. The mass of the helixes forms a mesh of small and large channels parallel to the z-axis; the large ones are large enough to allow some mobility of smaller ions and molecules through the crystal.^[18]

Quartz exists in several phases. At 573 °C at 1 atmosphere (and at higher temperatures and higher pressures) the α-quartz undergoes quartz inversion, transforms reversibly to β-quartz. The reverse process however is not entirely homogeneous and crystal twinning occurs. Care has to be taken during manufacture and processing to avoid the phase transformation. Other phases, e.g. the higher-temperature phases tridymite and cristobalite, are not significant for oscillators. All quartz oscillator crystals are the α-quartz type.

Infrared spectrophotometry is used as one of the methods for measuring the quality of the grown crystals. The wavenumbers 3585, 3500, and 3410 cm⁻¹ are commonly used. The measured value is based on the absorption bands of the OH radical and the infrared Q value is calculated. The electronic grade crystals, grade C, have Q of 1.8 million or above; the premium grade B crystals have Q of 2.2 million, and special premium grade A crystals have Q of 3.0 million. The Q value is calculated only for the z region; crystals containing other regions can be adversely affected. Another quality indicator is the etch channel density; when the crystal is etched, tubular channels are created along linear defects. For processing involving etching, e.g. the wristwatch tuning fork crystals, low etch channel density is desirable. The etch channel density for swept quartz is about 10–100 and significantly more for unswept quartz. Presence of etch channels and etch pits degrades the resonator's Q and introduces nonlinearities.^[19]

Quartz crystals can be grown for specific purposes.

Crystals for AT-cut are the most common in mass production of oscillator materials; the shape and dimensions are optimized for high yield of the required wafers. High-purity quartz crystals are grown with especially low content of aluminium, alkali metal and other impurities and minimal defects; the low amount of alkali metals provides increased resistance to ionizing radiation. Crystals for wrist watches, for cutting the tuning fork 32768 Hz crystals, are grown with very low etch channel density.

Crystals for SAW devices are grown as flat, with large X-size seed with low etch channel density.

Special high-Q crystals, for use in highly stable oscillators, are grown at constant slow speed and have constant low infrared absorption along the entire Z axis. Crystals can be grown as Y-bar, with a seed crystal in bar shape and elongated along the Y axis, or as Z-plate, grown from a plate seed with Y-axis direction length and X-axis width.^[17] The region around the seed crystal contains a large number of crystal defects and should not be used for the wafers.

Crystals grow anisotropically; the growth along the Z axis is up to 3 times faster than along the X axis. The growth direction and rate also influences the rate of uptake of impurities.^[20] Y-bar crystals, or Z-plate crystals with long Y axis, have four growth regions usually called +X, -X, Z, and S.^[21] The distribution of impurities during growth is uneven; different growth areas contain different level of contaminants. The z regions are the purest, the small occasionally present s regions are less pure, the +x region is yet less pure, and the -x region has the highest level of impurities. The impurities have negative impact on radiation hardness, susceptibility to twinning, filter loss, and long and short term stability of the crystals.^[22] Different-cut seeds in different orientations may provide other kinds of growth regions.^[23] The growth speed of the -x direction is slowest due to the effect of adsorption of water molecules on the crystal surface; aluminium impurities suppress growth in two other directions. The content of aluminium is lowest in z region, higher in +x, yet higher in -x, and highest in s; the size of s regions also grows with increased amount of aluminium present. The content of hydrogen is lowest in z region, higher in +x region, yet higher in s region, and highest in -x.^[24] Aluminium inclusions transform to color centers with a gamma ray irradiation, causing darkening of the crystal proportional to the dose and level of impurities; presence of regions with different darkness reveals the different growth regions.

The dominant type of defect of concern in quartz crystals is the substitution of Al(III) for Si(IV) atom in the crystal lattice. The aluminium ion has an associated interstitial charge compensator present nearby, which can be a H⁺ ion (attached to the nearby oxygen and forming a hydroxyl group, called Al-OH defect), Li⁺ ion, Na⁺ ion, K⁺ ion (less common), or an electron hole trapped in a nearby oxygen atom orbital. The composition of the growth solution, whether it is based on lithium or sodium alkali compounds, determines the charge compensating ions for the aluminium defects. The ion impurities are of concern as they are not firmly bound and can migrate through the crystal, altering the local lattice elasticity and the resonant frequency of the crystal. Other common impurities of concern are e.g. iron(III) (interstitial), fluorine, boron(III), phosphorus(V) (substitution), titanium(IV) (substitution, universally present in magmatic quartz, less common in hydrothermal quartz), and germanium(IV) (substitution). Sodium and iron ions can cause inclusions of acnite and elemeusite crystals. Inclusions of water may be present in fast-grown crystals; interstitial water molecules are abundant near the crystal seed. Another defect of importance is the hydrogen containing growth defect, when instead of a Si-O-Si structure a pair of Si-OH HO-Si groups is formed; essentially a hydrolyzed bond. Fast-grown crystals contain more hydrogen defects than slow-grown ones. These growth defects source as supply of hydrogen ions for radiation-induced processes and forming Al-OH defects. Germanium impurities tend to trap electrons created during irradiation; the alkali metal cations then migrate towards the negatively charged center and form a stabilizing complex. Matrix defects can be also present; oxygen vacancies, silicon vacancies (usually compensated by 4 hydrogens or 3 hydrogens and a hole), peroxy groups, etc. Some of the defects produce localized levels in the forbidden band, serving as charge traps; Al(III) and B(III) typically serve as hole traps while electron vacancies, titanium, germanium, and phosphorus atoms serve as electron traps. The trapped charge carriers can be released by heating; their recombination is the cause of thermoluminescence.

The mobility of interstitial ions depends strongly on temperature. Hydrogen ions are mobile down to 10 K, but alkali metal ions become mobile only at temperatures around and above 200 K. The hydroxyl defects can be measured by near-infrared spectroscopy. The trapped holes can be measured by electron spin resonance. The Al-Na⁺ defects show as an acoustic loss peak due to their stress-induced motion; the Al-Li⁺ defects do not form a potential well so are not detectable this way.^[25] Some of the radiation induced defects during their thermal annealing produce thermoluminescence; defects related to aluminium, titanium, and germanium can be distinguished.^[26]

Swept crystals are crystals that have undergone a solid-state electrodiffusion purification process. Sweeping involves heating the crystal above 500 °C in a hydrogen-free atmosphere, and the voltage gradient of at least 1 kilovolt/cm, for several (usually over 12) hours. The migration of impurities and the gradual replacement of alkali metal ions with hydrogen (when swept in air) or electron holes (when swept in vacuum) causes a weak electric current through the crystal; decay of this current to a constant value signals end of the process. The crystal is then left to cool, while the electric field is maintained. The impurities are concentrated at the cathode region of the crystal, which is cut off afterwards and discarded.^[27] Swept crystals have increased resistance to radiation, as the dose effects are dependent on the level of alkali metal impurities; they are suitable for use in devices exposed to ionizing radiation, e.g. for nuclear and space technology.^[28] Sweeping under vacuum at higher temperatures and higher field strengths yields yet more radiation-hard crystals.^[29] The level and character of impurities can be measured by infrared spectroscopy.^[30] Quartz can be swept in both α and β phase; sweeping in β phase is faster, but the phase transition may induce twinning. Twinning can be mitigated by subjecting the crystal to compression stress in the X direction, or an AC or DC electric field along the X axis while the crystal cools through the phase transformation temperature region.^[29]

Sweeping can be also used to introduce one kind of an impurity into the crystal. Lithium, sodium, and hydrogen swept crystals are used for e.g. studying quartz behavior.

Very small crystals for high fundamental mode frequencies can be manufactured by photolithography.^[19]

Crystals can be adjusted to exact frequency by laser trimming. A technique used in the world of amateur radio for slight decrease of the crystal frequency may be achieved by exposing crystals with silver electrodes to vapors of iodine, which causes a slight mass increase on the surface by forming a thin layer of silver iodide; such crystals however had problematic long-term stability.^[31] Another method commonly used is electrochemical increase or decrease of silver electrode thickness by submerging resonator in lapis solved in water, citric acid in water, or water with salt, and using resonator as one electrode, and small silver electrode as another.

By choosing direction of current, one can either increase, or decrease mass of electrodes. Details were published in "Radio" magazine (3/1978) by UB5LEV.

Raising frequency by scratching off parts of the electrodes is advised against, as this may damage the crystal and lower its Q factor.^[32] Capacitor trimmers can be also used for frequency adjustment of the oscillator circuit.

Some other piezoelectric materials than quartz can be employed; e.g. single crystals of lithium tantalate, lithium niobate, lithium borate, berlinite, gallium arsenide, lithium tetraborate, aluminium phosphate, bismuth germanium oxide, polycrystalline zirconium titanate ceramics, high-alumina ceramics, silicon-zinc oxide composite, or dipotassium tartrate;^[33][34] some materials may be more suitable for specific applications. An oscillator crystal can be also manufactured by depositing the resonator material on the silicon chip surface.^[35] Crystals of gallium phosphate, langasite, langanite and langanate are about 10 times more pullable than the corresponding quartz crystals, and are used in some VCXO oscillators.^[36]

Stability and aging[link]

The frequency stability is determined by the crystal's Q. It is inversely dependent on the frequency, and on the constant that is dependent on the particular cut. Other factors influencing Q are the overtone used, the temperature, the level of driving of the crystal, the quality of the surface finish, the mechanical stresses imposed on the crystal by bonding and mounting, the geometry of the crystal and the attached electrodes, the material purity and defects in the crystal, type and pressure of the gas in the enclosure, interfering modes, and presence and absorbed dose of ionizing and neutron radiation.

Temperature influences the operating frequency; various forms of compensation are used, from analog compensation (TCXO) and microcontroller compensation (MCXO) to stabilization of the temperature with a crystal oven (OCXO). The crystals possess temperature hysteresis; the frequency at a given temperature achieved by increasing the temperature is not equal to the frequency on the same temperature achieved by decreasing the temperature. The temperature sensitivity depends primarily on the cut; the temperature compensated cuts are chosen as to minimize frequency/temperature dependence. Special cuts can be made with a linear temperature characteristics; the LC cut is used in quartz thermometers. Other influencing factors are the overtone used, the mounting and electrodes, impurities in the crystal, mechanical strain, crystal geometry, rate of temperature change, thermal history (due to hysteresis), ionizing radiation, and drive level.

Crystals tend to suffer anomalies in their frequency/temperature and resistance/temperature characteristics, known as activity dips. These are small downward (in frequency) or upward (in resistance) excursions localized at certain temperatures, with their temperature position dependent on the value of the load capacitors.

Mechanical stresses also influence the frequency. The stresses can be induced by mounting, bonding, and application of the electrodes, by differential thermal expansion of the mounting, electrodes, and the crystal itself, by differential thermal stresses when there is a temperature gradient present, by expansion or shrinkage of the bonding materials during curing, by the air pressure that is transferred to the ambient pressure within the crystal enclosure, by the stresses of the crystal lattice itself (nonuniform growth, impurities, dislocations), by the surface imperfections and damage caused during manufacture, and by the action of gravity on the mass of the crystal; the frequency can therefore be influenced by position of the crystal. Other dynamic stress inducing factors are shocks, vibrations, and acoustic noise. Some cuts are less sensitive to stresses; the SC (Stress Compensated) cut is an example. Atmospheric pressure changes can also introduce deformations to the housing, influencing the frequency by changing stray capacitances.

Atmospheric humidity influences the thermal transfer properties of air, and can change electrical properties of plastics by diffusion of water molecules into their structure, altering the dielectric constants and electrical conductivity.^[37]

Other factors influencing the frequency are the power supply voltage, load impedance, magnetic fields, electric fields (in case of cuts that are sensitive to them, e.g. SC), the presence and absorbed dose of γ-particles and ionizing radiation, and the age of the crystal.

Crystals undergo slow gradual change of frequency with time, known as aging. There are many mechanisms involved. The mounting and contacts may undergo relief of the built-in stresses. Molecules of contamination either from the residual atmosphere, outgassed from the crystal, electrodes or packaging materials, or introduced during sealing the housing can be adsorbed on the crystal surface, changing its mass; this effect is exploited in quartz crystal microbalances. The composition of the crystal can be gradually altered by outgassing, diffusion of atoms of impurities or migrating from the electrodes, or the lattice can be damaged by radiation. Slow chemical reactions may occur on or in the crystal, or on the inner surfaces of the enclosure. Electrode material, e.g. chromium or aluminium, can react with the crystal, creating layers of metal oxide and silicon; these interface layers can undergo changes in time. The pressure in the enclosure can change due to varying atmospheric pressure, temperature, leaks, or outgassing of the materials inside. Factors outside of the crystal itself are e.g. aging of the oscillator circuitry (and e.g. change of capacitances), and drift of parameters of the crystal oven. External atmosphere composition can also influence the aging; hydrogen can diffuse through nickel housing. Helium can cause similar issues when it diffuses through glass enclosures of rubidium standards.^[38]

Gold is a favored electrode material for low-aging resonators; its adhesion to quartz is strong enough to maintain contact even at strong mechanical shocks, but weak enough to not support significant strain gradients (unlike chromium, aluminium, and nickel). Gold also does not form oxides; it adsorbs organic contaminants from the air, but these are easy to remove. However, gold alone can undergo delamination; a layer of chromium is therefore sometimes used for improved binding strength. Silver and aluminium are often used as electrodes; however both form oxide layers with time that increases the crystal mass and lowers frequency. Silver can be passivated by exposition to iodine vapors, forming a layer of silver iodide. Aluminium oxidizes readily but slowly, until about 5 nm thickness is reached; increased temperature during artificial aging does not significantly increase the oxide forming speed; a thick oxide layer can be formed during manufacture by anodizing.^[39] Exposition of silver-plated crystal to iodine vapors can be also used in amateur conditions for lowering the crystal frequency slightly; the frequency can be also increased by scratching off parts of the electrodes, but that carries risk of damage to the crystal and loss of Q.

A DC voltage bias between the electrodes can accelerate the initial aging, probably by induced diffusion of impurities through the crystal. Placing a capacitor in series with the crystal and a several-megohm resistor in parallel can minimize such voltages.

Crystals suffer from minor short-term frequency fluctuations as well. The main causes of such noise are e.g. thermal noise (which limits the noise floor), phonon scattering (influenced by lattice defects), adsorption/desorption of molecules on the surface of the crystal, noise of the oscillator circuits, mechanical shocks and vibrations, acceleration and orientation changes, temperature fluctuations, and relief of mechanical stresses. The short-term stability is measured by four main parameters: Allan variance (the most common one specified in oscillator data sheets), phase noise, spectral density of phase deviations, and spectral density of fractional frequency deviations. The effects of acceleration and vibration tend to dominate the other noise sources; surface acoustic wave devices tend to be more sensitive than bulk acoustic wave (BAW) ones, and the stress-compensated cuts are even less sensitive. The relative orientation of the acceleration vector to the crystal dramatically influences the crystal's vibration sensitivity. Mechanical vibration isolation mountings can be used for high-stability crystals.

Crystals are sensitive to shock. The mechanical stress causes short-time change in the oscillator frequency due to the stress-sensitivity of the crystal, and can introduce a permanent change of frequency due to shock-induced changes of mounting and internal stresses (if the elastic limits of the mechanical parts are exceeded), desorption of contamination from the crystal surfaces, or change in parameters of the oscillator circuit. High magnitudes of shocks may tear the crystals off their mountings (especially the case of large low-frequency crystals suspended on thin wires), or cause cracking of the crystal. Crystals free of surface imperfections are highly shock-resistant; chemical polishing can produce crystals able to survive tens of thousands g.^[40]

Phase noise plays significant role in frequency synthesis systems using frequency multiplication; a multiplication of a frequency by N increases the phase noise power by N². A frequency multiplication by 10 times multiplies the magnitude of the phase error by 10 times. This can be disastrous for systems employing e.g. PLL or FSK technologies.

Crystals are somewhat sensitive to radiation damage. Natural quartz is much more sensitive than artificially grown crystals, and sensitivity can be further reduced by sweeping the crystal – heating the crystal to at least 400 °C in hydrogen-free atmosphere in electric field of at least 500 V/cm for at least 12 hours. Such swept crystals have very low response to steady ionizing radiation. Some Si(IV) atoms are replaced with Al(III) impurities, each having a compensating Li⁺ or Na⁺ cation nearby. Ionization produces electron-hole pairs; the holes are trapped in the lattice near the Al atom, the resulting Li and Na atoms are loosely trapped along the Z axis; the change of the lattice near the Al atom and the corresponding elastic constant then causes a corresponding change in frequency. Sweeping removes the Li⁺ and Na⁺ ions from the lattice, reducing this effect. The Al³⁺ site can also trap hydrogen atoms. All crystals have transient negative frequency shift after exposition to an X-ray pulse; the frequency then shifts gradually back; natural quartz reaches stable frequency after 10–1000 seconds, with negative offset to pre-irradiation frequency, artificial crystals return to frequency slightly lower or higher than pre-irradiation, swept crystals anneal virtually back to original frequency. The annealing is faster at higher temperatures. Sweeping under vacuum at higher temperatures and field strength can further reduce the crystal's response to X-ray pulses.^[29] Series resistance of unswept crystals increases after an X-ray dose, and anneals back to a somewhat higher value for a natural quartz (requiring a corresponding gain reserve in the circuit) and back to pre-irradiation value for synthetic crystals. Series resistance of swept crystals is unaffected. Increase of series resistance degrades Q; too high increase can stop the oscillations. Neutron radiation induces frequency changes by introducing dislocations into the lattice by knocking out atoms, a single fast neutron can produce many defects; the SC and AT cut frequency increases roughly linearly with absorbed neutron dose, while the frequency of the BT cuts decreases.^[41] Neutrons also alter the temperature-frequency characteristics. Frequency change at low ionizing radiation doses is proportionally higher than for higher doses. High-intensity radiation can stop the oscillator by inducing photoconductivity in the crystal and transistors; with a swept crystal and properly designed circuit the oscillations can restart within 15 microseconds after the radiation burst. Quartz crystals with high level of alkali metal impurities lose Q with irradiation; Q of swept artificial crystals is unaffected. Irradiation with higher doses (over 10⁵ rad) lowers sensitivity to subsequent doses. Very low radiation doses (below 300 rad) have disproportionately higher effect, but this nonlinearity saturates at higher doses. At very high doses, the radiation response of the crystal saturates as well, due to finite number of impurity sites that can be affected.^[28]

Magnetic fields have low effect on the crystal itself, as quartz is diamagnetic; eddy currents or AC voltages can however be induced into the circuits, and magnetic parts of the mounting and housing may be influenced.

After the power-up, the crystals take several seconds to minutes to "warm up" and stabilize their frequency. The oven-controlled OCXOs require usually 3–10 minutes for heating up and reaching thermal equilibrium; the oven-less oscillators stabilize in several seconds as the few milliwatts dissipated in the crystal cause a small but noticeable level of internal heating.^[42]

Crystals have no inherent failure mechanisms; some are operating in devices for decades. Failures may be however introduced by faults in bonding, leaky enclosures, corrosion, frequency shift by aging, breaking the crystal by too high mechanical shock, or radiation induced damage when nonswept quartz is used.^[43] Crystals can be also damaged by overdriving.

The crystals have to be driven at the appropriate drive level. While AT cuts tend to be fairly forgiving, and only their electrical parameters, stability and aging characteristics are degraded when overdriven, low-frequency crystals, especially flexural-mode ones, may fracture at too high drive levels. The drive level is specified as the amount of power dissipated in the crystal. The appropriate drive levels are about 5 microwatts for flexural modes up to 100 kHz, 1 microwatt for fundamental modes at 1–4 MHz, 0.5 microwatts for fundamental modes 4–20 MHz, and 0.5 microwatts for overtone modes at 20–200 MHz.^[44] Too low drive level may cause problems with starting the oscillator. Low drive levels are better for higher stability and lower power consumption of the oscillator. Higher drive levels, in turn, reduce the impact of noise by increasing the signal-to-noise ratio.^[45]

The stability of AT cut crystals decreases with increasing frequency. For more accurate higher frequencies it is better to use a crystal with lower fundamental frequency, operating at an overtone.

Aging decreases logarithmically with time, the highest changes occurring shortly after manufacture. Artificially aging the crystal by its prolonged storage at between 85–125 °C can be done for increasing long-term stability.

A badly designed oscillator circuit may suddenly become oscillating on an overtone; in 1972, a train in Fremont, California crashed. An inappropriate value of the tank capacitor caused the crystal in a control board to be overdriven, jumping to an overtone, and causing the train to speed up instead of slowing down.^[46]

Crystal cuts[link]

The resonator plate can be cut from the source crystal in many different ways. The orientation of the cut influences the crystal's aging characteristics, frequency stability, thermal characteristics, and other parameters. These cuts operate at bulk acoustic wave (BAW); for higher frequencies, surface acoustic wave (SAW) devices are employed.

Image of several crystal cuts^[47]

The T in the cut name marks a temperature-compensated cut, a cut oriented in a way that the temperature coefficients of the lattice are minimal; the FC and SC cuts are also temperature-compensated.

The high frequency cuts are mounted by their edges, usually on springs; the stiffness of the spring has to be optimal, as too stiff could transfer mechanical shocks to the crystal and cause its breaking, and too little stiffness may allow the crystal to collide with the inside of the package when subjected to a mechanical shock, and break. Strip resonators, usually AT cuts, are smaller and therefore less sensitive to mechanical shocks. At the same frequency and overtone, the strip will have less pullability, higher resistance, and higher temperature coefficient.^[65]

The low frequency cuts are mounted at the nodes where they are virtually motionless; thin wires are attached at such points on each side between the crystal and the leads. The large mass of the crystal suspended the thin wires makes the assembly sensitive to mechanical shocks and vibrations.^[48]

The crystals are usually mounted in hermetically sealed glass or metal cases, filled with a dry and inert atmosphere, usually vacuum, nitrogen, or helium. Plastic housings can be used as well, but those are not hermetic and another secondary sealing has to be built around the crystal.

Several resonator configurations are possible, in addition to the classical way of directly attaching leads to the crystal. E.g. the BVA resonator (Boîtier à Vieillissement Amélioré, Enclosure with Improved Aging),^[66] developed in 1976; the parts that influence the vibrations are machined from a single crystal (which reduces the mounting stress), and the electrodes are deposited not on the resonator itself but on inner sides of two condenser discs made of adjacent slices of the quartz from the same bar, forming a three-layer sandwich with no stress between the electrodes and the vibrating element. The gap between the electrodes and the resonator act as two small series capacitors, making the crystal less sensitive to circuit influences.^[67] The architecture eliminates the effects of the surface contacts between the electrodes, the constraints in the mounting connections, and the issues related to ion migration from the electrodes into the lattice of the vibrating element.^[68] The resulting configuration is rugged, resistant to shock and vibration, resistant to acceleration and ionizing radiation, and has improved aging characteristics. AT cut is usually used, though SC cut variants exist as well. BVA resonators are often used in spacecraft applications.^[69]

In the 1930s to 1950s, it was fairly common for people to adjust the frequency of the crystals by manual grinding. The crystals were ground using a fine abrasive slurry, or even a toothpaste, to increase their frequency. A slight decrease by 1–2 kHz when the crystal was overground was possible by marking the crystal face with a pencil lead, for the price of lowering the Q.^[70]

The frequency of the crystal is slightly adjustable ("pullable") by modifying the attached capacitances. A varactor, a diode with capacitance depending on applied voltage, is often used in voltage-controlled crystal oscillators, VCXO. The crystal cuts are usually AT or rarely SC, and operate in fundamental mode; the amount of available frequency deviation is inversely proportional to the square of the overtone number, so a third overtone will have only one ninth of the pullability of the fundamental mode. SC cuts, while more stable, are significantly less pullable.^[71]

Circuit notations and abbreviations[link]

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 — Analog temperature controlled crystal oscillator
• CDXO — Calibrated dual crystal oscillator
• DTCXO — Digital temperature compensated crystal oscillator
• EMXO — Evacuated miniature crystal oscillator
• GPSDO — Global positioning system disciplined 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 an 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
• TMXO – Tactical miniature crystal oscillator^[63]
• TSXO — Temperature-sensing crystal oscillator, an adaptation of the TCXO
• VCTCXO — Voltage-controlled temperature-compensated crystal oscillator
• VCXO — Voltage-controlled crystal oscillator

See also[link]

• Clock drift – Clock drift measurements of crystal oscillators can be used to build random number generators.
• Erhard Kietz work on electronic tuning forks and with quartz crystals for precise signal frequencies
• Pierce oscillator
• VFO — variable-frequency oscillator

References[link]

Further reading[link]

• Ulrich L. Rohde "Microwave and Wireless Synthesizers: Theory and Design ", John Wiley & Sons, August 1997, ISBN 0-471-52019-5

External links[link]

Wikimedia Commons has media related to: Crystal oscillators

• Introduction to quartz frequency standards
• "What is a quartz crystal device?". QIAJ. Quartz Crystal Industry Assoc. of Japan. 2007. http://www.qiaj.jp/pages/frame20/page01-e.html. Retrieved 2008-08-10. 
• Marvin E., Frerking (1996). "Fifty years of progress in quartz crystal frequency standards". Proc. 1996 IEEE Frequency Control Symposium. Institute of Electrical and Electronic Engineers. pp. 33–46. http://www.ieee-uffc.org/main/history.asp?file=frerking. Retrieved 2009-03-31. 
• Distortions in Crystal Oscillators
• Quartz crystal resonators and oscillators