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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 incorporating them became known as crystal oscillators, but other piezoelectric materials including polycrystalline ceramics are used in similar circuits. Quartz crystals are manufactured for frequencies from a few tens of kilohertz to hundreds of megahertz. More than two billion 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. Contents [hide]
1 History 2 Operation 3 Modeling o 3.1 Electrical model o 3.2 Resonance modes o 3.3 Temperature effects 4 Electrical oscillators o 4.1 Spurious frequencies 5 Commonly used crystal frequencies 6 Crystal structures and materials 7 Stability and aging 8 Crystal cuts 9 Circuit notations and abbreviations 10 See also 11 References 12 Further reading 13 External links
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 sonarduring 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 1920s and 1930s. Prior to crystals, radio stations controlled their frequency with tuned circuits, which could easily drift off frequency by 3-4 KHz. Since stations were assigned frequencies only 10 kHz apart, interference between adjacent stations due to frequency drift was common. In 1925 Westinghouse tried out a crystal oscillator in its flagship station KDKA, and by 1926 quartz crystals were used to control the frequency of many broadcasting stations and were popular with amateur radio operators. 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. With accuracies of up to 1 sec in 30 years (or 30 ms/year), quartz clocks became the world's most accurate timekeepers until atomic clocks were developed in the 1950s. 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.
100kHz crystal oscillators at the US National Bureau of Standards that served as the frequency standard for the United States in 1929.
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. Through World War II crystals were made from natural quartz crystal, virtually all from Brazil. Shortages of crystals during the war caused by the demand for accurate frequency control of military and naval radios and radars spurred postwar research into culturing synthetic quartz, and by 1950 a hydrothermal process for growing quartz crystals on a commercial scale was developed at Bell Laboratories. By the 1970s virtually all crystals used in electronics were synthetic. In 1968, Juergen Staudte invented a photolithographic process for manufacturing quartz crystal oscillators while working at North American Aviation (now Rockwell) that allowed them to be made small enough for portable products like watches.
Although crystal oscillators still most commonly use quartz crystals, devices using other materials are becoming more common, such asceramic resonators.
Crystal oscillation modes
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 resonantfrequencies 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 electrostriction or inverse 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). 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 Electrical model
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:
where s is the complex frequency ( resonant angular frequency and
is the series
is the parallel resonant angular frequency.
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. Adding additional inductance across a crystal will cause the resonance to shift upward. 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 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, this inductance forming a parallel resonant circuit with externally connected parallel capacitance. Any small additional capacitance in parallel with the crystal will thus pull the frequency downwards. Moreover, the effective inductive reactance of the crystal can be reduced by adding a capacitor in series with the crystal. This latter technique can provide a useful method of trimming the oscillatory frequency within a narrow range; in this case inserting a capacitor in series with the crystal will raise the frequency of oscillation. For a crystal to operate at its specified frequency, the electronic circuit has to be exactly that specified by the crystal manufacturer. Note that these points imply a subtlety concerning crystal oscillators in this frequency range: the crystal does not usually oscillate at precisely either of its resonant frequencies. 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 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.
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.
A crystal used in hobby radio controlequipment to select frequency.
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 controlling circuit places the crystal into an unstable equilibrium, and due to the positive feedback in the system, any tiny fraction of noise will start to get amplified, ramping up the oscillation. The crystal resonator can also be seen as a highly frequency-selective filter in this system: it will only pass a very narrow subband of frequencies around the resonant one, attenuating everything else. Eventually, only the resonant frequency will be active. 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 that of the fundamental resonance or of a multiple of that resonance, called
aharmonic frequency. Harmonics are an exact integer multiple of the fundamental frequency. But, like many other mechanical resonators, crystals exhibit several modes of oscillation, usually at approximately odd integer multiples of the fundamental frequency. These are termed "overtone modes", and oscillator circuits can be designed to excite them. The overtone modes are at frequencies which are approximate, but not exact odd integer multiples of that of the fundamental mode, and overtone frequencies are therefore not exact harmonics of the fundamental. 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 exciting the desired overtone frequency requires a slightly more complicated oscillator circuit. 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. 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.
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, such as 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 Main article: Crystal oscillator frequencies 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. For example, many (non-television) applications use 3.579545 MHz crystals since they are made in large quantities 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.
Crystal structures and materials
Common package types for quartz crystal products
Cluster of natural quartz crystals
A synthetic quartz crystal grown by the hydrothermal synthesis, about19 cm long and weighing about127 grams
Tuning fork crystal used in a modern quartz watch.
Simple quartz crystal
Inside construction of a modern high performance HC-49 packagequartz 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 60 USD/kg. 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. The
SiO4 tetrahedrons form parallel helices; the direction of twist of the helix determines the left- or right-hand orientation. The helixes are aligned along the z-axis and merged, 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. Quartz exists in several phases. At 573 °C at 1 atmosphere (and at higher temperatures and higher pressures) the α-quartz undergoesquartz 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. 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. 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. Y-bar crystals, or Z-plate crystals with long Y axis, have four growth regions usually called +X, -X, Z, and S. The distribution of impurities during growth is uneven; different growth areas contain different levels 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 a negative impact on radiation hardness, susceptibility to twinning, filter loss, and long and short term stability of the crystals. Different-cut seeds in different orientations may provide other kinds of growth regions. 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. Aluminium inclusions transform into color centers with gamma ray irradiation, causing a darkening of the crystal proportional to the dose and level of impurities; the presence of regions with different darkness reveals the different growth regions.