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| [[File:16MHZ Crystal.jpg|right|thumb|A miniature 16 [[MHz]] [[quartz crystal]] enclosed in a [[hermetically sealed]] HC-49/S package, used as the resonator in a crystal oscillator.]]
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| [[File:18MHZ 12MHZ Crystal 110.jpg|thumb|Quartz crystal resonator (left) and quartz crystal oscillator (right)]]
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| A '''crystal oscillator''' is an [[electronic oscillator]] circuit that uses the mechanical [[resonance]] of a vibrating [[crystal]] of [[Piezoelectricity#Materials|piezoelectric material]] to create an electrical signal with a very precise [[frequency]].<ref name="Graf">The term "crystal oscillator" refers to the circuit, not the resonator: {{cite book
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| | last = Graf
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| | first = Rudolf F.
| | <li>[http://www.pulsaraviation.com/wiki/index.php/User:Kbtykgit#Ray_Ban_Aviator http://www.pulsaraviation.com/wiki/index.php/User:Kbtykgit#Ray_Ban_Aviator]</li> |
| | title = Modern Dictionary of Electronics, 7th Ed.
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| | publisher = Newnes | | <li>[http://bbstmp.haalee.com:8080/forum.php?mod=viewthread&tid=1866619&fromuid=100902 http://bbstmp.haalee.com:8080/forum.php?mod=viewthread&tid=1866619&fromuid=100902]</li> |
| | year = 1999
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| | location = US | | <li>[http://www.07220755.com/forum.php?mod=viewthread&tid=222644 http://www.07220755.com/forum.php?mod=viewthread&tid=222644]</li> |
| | pages = 162, 163
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| | url = http://books.google.com/books?id=o2I1JWPpdusC&pg=PA163&dq=graf+dictionary+%22crystal+oscillator
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| | doi =
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| | id =
| | <li>[http://savannahkingmusic.com/community/read.php?5,194559 http://savannahkingmusic.com/community/read.php?5,194559]</li> |
| | isbn = 0750698667}}</ref><ref name="Amos">{{cite book
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| | last = Amos | | </ul> |
| | first = S. W.
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| | coauthors = Roger Amos
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| | title = Newnes Dictionary of Electronics, 4th Ed.
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| | publisher = Newnes
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| | year = 2002
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| | location = US
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| | pages = 76
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| | url = http://books.google.com/books?id=lROa-MpIrucC&pg=PA76&dq=dictionary+of+electronics+%22crystal+oscillator
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| | doi =
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| | id =
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| | isbn = 0750656425}}</ref><ref name="Laplante">{{cite book
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| | last = Laplante | |
| | first = Phillip A.
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| | title = Comprehensive Dictionary of Electrical Engineering
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| | publisher = Springer
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| | year = 1999
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| | location = US
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| | pages =
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| | url = http://books.google.com/books?id=soSsLATmZnkC&pg=PA152&dq=electronics+dictionary+%22crystal+oscillator
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| | doi = | |
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| | isbn = 3540648356}}</ref> This frequency is commonly used to keep track of time (as in [[quartz clock|quartz wristwatches]]), to provide a stable [[clock signal]] for [[Digital data|digital]] [[integrated circuits]], and to stabilize frequencies for [[radio transmitter]]s and [[radio receiver|receivers]]. The most common type of piezoelectric resonator used is the [[quartz]] crystal, so oscillator circuits incorporating them became known as crystal oscillators,<ref name="Graf" /> but other piezoelectric materials including polycrystalline ceramics are used in similar circuits.
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| 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 [[wristwatch]]es, [[clock]]s, [[radio]]s, [[computer]]s, and [[cellphone]]s. Quartz crystals are also found inside test and measurement equipment, such as counters, [[signal generator]]s, and [[oscilloscope]]s.
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| [[File:Crystal Units Frequency Standard Oscillator XO VCXO OCXO TCXO Bell Labs AT&T Vectron.jpg|thumb|right|Very early Bell Labs crystals from Vectron International Collection]] | | |
| [[Piezoelectricity]] was discovered by [[Jacques Curie|Jacques]] and [[Pierre Curie]] in 1880. [[Paul Langevin]] first investigated quartz resonators for use in [[sonar]] during World War I. The first crystal-controlled [[electronic oscillator|oscillator]], using a crystal of [[Rochelle salt]], was built in 1917 and patented<ref name="Nicholson">Nicholson, Alexander M. ''Generating and transmitting electric currents'' {{US patent|2212845}}, filed April 10, 1918, granted August 27, 1940</ref> in 1918 by Alexander M. Nicholson at [[Bell Telephone Laboratories]], although his priority was disputed by [[Walter Guyton Cady]].<ref name="Bottom1981">{{cite conference|last=Bottom|first=Virgil E.|title=A history of the quartz crystal industry in the USA |year=1981|booktitle=Proc. 35th Frequency Control Symp.|publisher=IEEE|url=http://www.ieee-uffc.org/fc_history/bottom.html}}</ref> Cady built the first quartz crystal oscillator in 1921.<ref name="Marrison1948">{{cite journal|last=Marrison|first=Warren|title=The Evolution of the Quartz Crystal Clock|year=1948|journal=Bell System Technical Journal|publisher=AT&T|volume=27|pages=510–588|url=http://www.ieee-uffc.org/main/history.asp?file=marrison}}</ref> | | <li>[http://zzshequ.zzxx.in/forum.php?mod=viewthread&tid=27500&extra= http://zzshequ.zzxx.in/forum.php?mod=viewthread&tid=27500&extra=]</li> |
| Other early innovators in quartz crystal oscillators include [[G. W. Pierce]] and [[Louis Essen]].
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| 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.<ref>Virgil E. Bottom, [http://web.archive.org/web/20080920080605/http://www.ieee-uffc.org/fc_history/bottom.html A History of the Quartz Crystal Industry in the USA], Proceedings of the 35th Annual Frequency Control Symposium 1981. Ieee-uffc.org. Retrieved on 2012-06-21.</ref> In 1928, Warren Marrison (of Bell Telephone Laboratories) developed the first quartz crystal clock. This invention replaced the [[escapement]] and [[Pendulum clock|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),<ref name="Marrison1948"/> quartz clocks became the world's most accurate timekeepers until [[atomic clock]]s 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.<ref>[http://www.mwrf.com/Articles/Index.cfm?Ad=1&ArticleID=20304 Microwaves and RF Journal. Retrieved July 17, 2011]. Mwrf.com. Retrieved on 2012-06-21.</ref>
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| 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 [[radio]]s and [[radar]]s spurred postwar research into culturing synthetic quartz, and by 1950 a [[Hydrothermal synthesis|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.
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| In 1968, Juergen Staudte invented a [[Photolithography|photolithographic]] process for manufacturing quartz crystal oscillators while working at [[North American Aviation]] (now [[Rockwell International|Rockwell]]) that allowed them to be made small enough for portable products like watches.<ref>[http://invention.smithsonian.org/centerpieces/Quartz/inventors/staudte.html Inventors Staudte The Quartz Watch]. Invention.smithsonian.org. Retrieved on 2012-06-21.</ref>
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| Although crystal oscillators still most commonly use quartz crystals, devices using other materials are becoming more common, such as [[ceramic resonator]]s.
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| A [[crystal]] is a [[solid]] in which the constituent [[atom]]s, [[molecule]]s, or [[ion]]s are packed in a regularly ordered, repeating pattern extending in all three spatial dimensions.
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| Almost any object made of an [[elasticity (physics)|elastic]] material could be used like a crystal, with appropriate [[transducer]]s, since all objects have natural [[resonance|resonant]] frequencies of [[vibration]]. For example, [[steel]] is very elastic and has a high speed of sound. It was often used in [[mechanical filter]]s before quartz. The resonant frequency depends on size, shape, [[elasticity (physics)|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.
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| 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]].)
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| 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).<ref name="Virgil1982">{{cite book|author=Virgil E Bottom|title=Introduction to Quartz Crystal Unit Design|year=1982|isbn=978-0-442-26201-3|publisher=Van Nostrand Reinhold}}</ref> 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.
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| [[File:Crystal-oscillator-IEC-Symbol.svg|right|thumb|150px|[[Electronic symbol]] for a piezoelectric crystal resonator]] | | |
| A quartz crystal can be modelled as an electrical network with a low [[Electrical impedance|impedance]] (series) and a high [[Electrical impedance|impedance]] (parallel) resonance point spaced closely together. Mathematically (using the [[Laplace transform]]) the impedance of this network can be written as:
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| : <math>Z(s) = \left( {\frac{1}{s\cdot C_1}+s\cdot L_1+R_1} \right) || \left( {\frac{1}{s\cdot C_0}} \right) </math>
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| : <math>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]} </math> | | <li>[http://www.squareconnect.com/forum/viewtopic.php?f=9&t=17894 http://www.squareconnect.com/forum/viewtopic.php?f=9&t=17894]</li> |
| : <math>\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) </math>
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| where s is the complex frequency (<math>s=j\omega</math>), <math>\omega_s</math> is the series resonant [[angular frequency]] and <math>\omega_p</math> is the parallel resonant angular frequency.
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| [[File:Crystal oscillator.svg|right|thumb|150px|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.
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| ===Resonance modes===
| | <li>[http://www.aiyingfang.cn/bbs/showtopic-809223.aspx http://www.aiyingfang.cn/bbs/showtopic-809223.aspx]</li> |
| 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.
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| 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 circuit]]s to select the desired overtone.
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| ===Temperature effects===
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| 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.
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| : <math>f = f_0[1-0.04 \ \mbox{ppm}(T-T_0)^2]</math>
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| 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.
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| ==Electrical oscillators== | |
| [[File:RC radio crystal.jpg|right|thumb|A crystal used in hobby [[radio control]] equipment to select frequency.]]
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| 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 [[resonance|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.
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| 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 (electronics)|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 [[electronic filter|filter]]s out all the unwanted frequencies.
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| The output frequency of a quartz oscillator can be either that of the fundamental resonance or of a multiple of that resonance, called a [[harmonic]] 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.
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| 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.<ref>[http://web.archive.org/web/20110725032851/http://www.foxonline.com/techdata.htm Quartz Crystal Theory of Operation and Design Notes]. foxonline.com</ref><ref>[http://www.maxim-ic.com/app-notes/index.mvp/id/726 Specifying Quartz Crystals]. Maxim-ic.com (2001-11-19). Retrieved on 2012-06-21.</ref><ref>[http://www.pletronics.com/uploads/datasheets/selection%20crystal.pdf Crystal selection]. pletronics.com. Retrieved on 2012-06-21.</ref><ref>[http://www.euroquartz.co.uk/crystal_specification.aspx "Crystal Specification"]. Euroquartz.co.uk. Retrieved on 2012-06-21.</ref><ref>[http://www.beckwithelectronics.com/abracon/quartzan.htm "Quartz Crystal Application Notes"]. Beckwithelectronics.com. Retrieved on 2012-06-21.</ref>
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| A fundamental crystal oscillator circuit is simpler and more efficient and has more pullability than a third overtone circuit.
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| Depending on the manufacturer, the highest available fundamental frequency may be 25 MHz to 66 MHz.<ref>[http://www.abracon.com/Support/quartz_crystals.pdf "Quart Crystals Application Notes"]. (PDF) . Retrieved on 2012-06-21.</ref><ref>[http://web.archive.org/web/20101130222332/http://foxonline.com/techfaqs_cry.htm#a9 Frequently Asked Questions about Crystals]. foxonline.com</ref>
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| 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 10<sup>4</sup> to 10<sup>6</sup>, compared to perhaps 10<sup>2</sup> for an [[LC oscillator]]. The maximum ''Q'' for a high stability quartz oscillator can be estimated as ''Q'' = 1.6 × 10<sup>7</sup>/''f'', where ''f'' is the resonance frequency in megahertz.
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| One of the most important traits of quartz crystal oscillators is that they can exhibit very low [[phase noise]].
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| 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.
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| In a crystal oscillator, the crystal mostly vibrates in one axis, therefore only one phase is dominant.
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| 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.
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| 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.
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| 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 10<sup>10</sup> of their nominal frequency without constant adjustment. For this reason, [[atomic oscillator]]s are used for applications requiring better long-term stability and accuracy.
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| ===Spurious frequencies===
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| [[File:clock crystal.jpg|right|thumb|25-MHz crystal exhibiting spurious response]]
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| 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.
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| 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.
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| 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.
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| 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.
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| ==Commonly used crystal frequencies==
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| {{main|Crystal oscillator frequencies}}
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| 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 divider]]s, [[frequency multiplier]]s and [[phase locked loop]] circuits, it is practical to derive a wide range of frequencies from one reference frequency.
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| ==Crystal structures and materials==
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| [[File:Crystal Packages.jpg|thumb|right|Common package types for quartz crystal products]]
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| [[File:Quartz Brésil.jpg|thumb|right|Cluster of natural quartz crystals]]
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| [[File:Quartz synthese.jpg|thumb|right|A synthetic quartz crystal grown by the hydrothermal synthesis, about {{nowrap|19 cm}} long and weighing about {{nowrap|127 grams}}]]
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| [[File:Inside QuartzCrystal-Tuningfork.jpg|thumb|right|Tuning fork crystal]]
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| [[File:Inside QuartzCrystal-SimpleType.jpg|thumb|right|Simple quartz crystal]]
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| [[File:InsideQuartzCrystal.jpg|right|thumb|Inside construction of a modern high performance HC-49 package [[quartz crystal]]]]
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| [[File:Krystalové-výbrusy.jpg|thumb|right|Flexural and thickness shear crystals]]
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| 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 {{nowrap|60 [[United States dollar|USD]]/kg.}}<ref>Gordon T. Austin, [http://minerals.usgs.gov/minerals/pubs/commodity/silica/810494.pdf Quartz Crystal]. minerals.usgs.gov</ref>
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| 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.<ref name=terms>[http://www.ndk.com/catalog/AN-SQC_GG_e.pdf Synthetic Quartz Crystal] Terms and Definitions</ref> The SiO<sub>4</sub> 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.<ref>[http://www.quartzpage.de/gen_struct.html The Quartz Page: Quartz Structure]. Quartzpage.de (2010-10-23). Retrieved on 2012-06-21.</ref>
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| 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.
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| [[Infrared spectrophotometry]] is used as one of the methods for measuring the quality of the grown crystals. The [[wavenumber]]s 3585, 3500, and 3410 cm<sup>−1</sup> are commonly used. The measured value is based on the [[absorption band]]s 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 [[etching|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.<ref name="patentstorm1">John R. Vig ''et al.'' ''Method of making miniature high frequency SC-cut quartz crystal resonators'' {{US patent|4554717}}, Issue date: November 26, 1985</ref>
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| Quartz crystals can be grown for specific purposes.
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| 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 [[Wafer (electronics)|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.
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| Crystals for [[Surface acoustic wave|SAW]] devices are grown as flat, with large X-size seed with low etch channel density.
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| 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.<ref name=terms/> The region around the seed crystal contains a large number of crystal defects and should not be used for the wafers.
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| Crystals grow [[Anisotropy|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.<ref>[http://www.roditi.com/SingleCrystal/Quartz/Hydrothermal_Growth.html Quartz Hydrothermal Growth]. Roditi.com. Retrieved on 2010-02-08.</ref> Y-bar crystals, or Z-plate crystals with long Y axis, have four growth regions usually called +X, -X, Z, and S.<ref>[http://www.informaworld.com/smpp/1446944858-63273890/content~db=all~content=a752227480 Defects in synthetic quartz and their effects on the vibrational characteristics – Ferroelectrics]. Informaworld.com (1982-05-01). Retrieved on 2010-02-08.</ref> 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 [[crystal twinning|twinning]], filter loss, and long and short term stability of the crystals.<ref>[http://www.4timing.com/techquartz.htm Quartz Tech]. 4timing.com. Retrieved on 2010-02-08.</ref> Different-cut seeds in different orientations may provide other kinds of growth regions.<ref>{{cite journal|author=Shinohara, A.H.; Suzuki, C.K. |title=Proceedings of 1996 IEEE International Frequency Control Symposium|pages=72–77|doi=10.1109/FREQ.1996.559821|year=1996|chapter=Study of S- and ξ-bar synthetic quartz by X-ray topography|isbn=0-7803-3309-8}}</ref> 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.<ref>{{cite journal|author=Fumiko Iwasaki, Armando H. Shinohara, Hideo Iwasaki and Carlos K. Suzuki |url=http://www.fem.unicamp.br/~liqcqits/publications/paper_files/JJAP1990v29-6p1139-1142_Iwasaki.pdf |title=Effect of Impurity Segregation on Crystal Morphology of Y-Bar Synthetic Quartz|journal= Jap. J. Appl. Phys. |volume=29 |pages=1139–1142 |year=1990|doi=10.1143/JJAP.29.1139}}</ref> 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.
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| The dominant type of [[crystallographic defect|defect]] of concern in quartz crystals is the substitution of an [[aluminium|Al(III)]] for a [[silicon|Si(IV)]] atom in the [[crystal lattice]]. The aluminium ion has an associated interstitial charge compensator present nearby, which can be a [[hydrogen|H<sup>+</sup>]] ion (attached to the nearby oxygen and forming a [[hydroxyl group]], called Al-OH defect), [[lithium|Li<sup>+</sup>]] ion, [[sodium|Na<sup>+</sup>]] ion, [[potassium|K<sup>+</sup>]] 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 [[inclusion (mineral)|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 also be 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]].
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| 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.
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| The hydroxyl defects can be measured by near-infrared spectroscopy. The trapped holes can be measured by [[electron spin resonance]]. The Al-Na<sup>+</sup> defects show as an acoustic loss peak due to their stress-induced motion; the Al-Li<sup>+</sup> defects do not form a potential well so are not detectable this way.<ref>{{cite journal|author=Harish Bahadur |url=http://www.crystalresearch.com/crt/ab41/631_a.pdf |title=Radiation induced modification of impurity-related point defects in crystalline quartz – a review|journal=Cryst. Res. Technol. |volume=41|issue=7|pages=631–635|year=2006|doi=10.1002/crat.200510641}}</ref> Some of the radiation-induced defects during their thermal annealing produce [[thermoluminescence]]; defects related to aluminium, titanium, and germanium can be distinguished.<ref>Harish Bahadur [http://ursi-test.intec.ugent.be/files/URSIGA08/papers/BDPS2p6.pdf Investigations on irradiation and structural characteristics of high quality cultured quartz crystals used in satellite communication]</ref>
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| '''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, with a 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 the 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.<ref>Arthur Ballato ''et al.'' Method of sweeping quartz {{US patent|4311938}}, Issue date: January 19, 1982</ref> 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.<ref name="ieee-uffc1">[http://www.ieee-uffc.org/frequency_control/teaching.asp?vig=vigrad Frequency Control|Teaching Resources]. Ieee-uffc.org. Retrieved on 2010-02-08.</ref> Sweeping under vacuum at higher temperatures and higher field strengths yields yet more radiation-hard crystals.<ref name="freepatentsonline.com">James Claude King ''Vacuum electrolysis of quartz'' {{US patent|3932777}}, Issue date: Jan 13, 1976</ref> The level and character of impurities can be measured by infrared spectroscopy.<ref>[http://authors.aps.org/eprint/files/1997/Apr/aps1997apr04_003.1/main.pdf Infrared study of defects in alpha quartz caused by sweeping effects]. authors.aps.org (April 1997). Retrieved on 2012-06-21.</ref> 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.<ref name="freepatentsonline.com"/>
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| 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.
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| Very small crystals for high fundamental mode frequencies can be manufactured by photolithography.<ref name="patentstorm1"/>
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| Crystals can be adjusted to exact frequencies 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. Another method commonly used is electrochemical increase or decrease of silver electrode thickness by submerging a resonator in lapis solved in water, citric acid in water, or water with salt, and using the resonator as one electrode, and a small silver electrode as another.
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| By choosing the direction of current, one can either increase, or decrease the mass of electrodes.
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| Details were published in "Radio" magazine (3/1978) by UB5LEV.
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| Raising frequency by scratching off parts of the electrodes is advised against, as this may damage the crystal and lower its [[Q factor]]. Capacitor [[trimmer (electronics)|trimmer]]s can be also used for frequency adjustment of the oscillator circuit.
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| Some other [[piezoelectric material]]s 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]];<ref>Arthur Ballato ''Method of making a crystal oscillator desensitized to accelerationfields'' {{US patent|4871986}}, Issue date: October 3, 1989</ref><ref>[http://www.txc.com.tw/download/tech_paper/2002-NTUIAM-1-English.pdf Recent Development of Bulk and Surface Acoustic Wave Technology for Frequency Control Applications], December 23, 2002 Institute of Applied Mechanics National Taiwan University, C.S. Lam, TXC Corporation</ref> 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.<ref>Fumio Nakajima ''Quartz crystal oscillator angular velocity detector circuits'' {{US patent|5420548}}, Issue date: May 30, 1995</ref> 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.<ref>Bernd Neubig, [http://web.archive.org/web/20060305152252/http://www.vhfcomm.co.uk/pdf/Pressworks%20-%20VCXO.pdf VCXOs with wide pull-in range using alternatives to quartz]. VHF Communications, 2/2003, pp. 66–70</ref>
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| ==Stability and aging==
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| The frequency stability is determined by the crystal's [[Q factor|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.
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| 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 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.
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| 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.
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| 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.
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| 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 constant]]s and [[electrical conductivity]].<ref>[http://www.ieee-uffc.org/frequency_control/teaching.asp?vig=vigstab Frequency Control|Teaching Resources]. Ieee-uffc.org. Retrieved on 2010-02-08.</ref>
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| 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.
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| 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, [[outgassing|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 microbalance]]s. 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 standard]]s.<ref>[http://www.ieee-uffc.org/frequency_control/teaching.asp?vig=agingmec Frequency Control|Teaching Resources]. Ieee-uffc.org. Retrieved on 2010-02-08.</ref>
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| 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]].<ref name="google1">{{cite book|author=Jerry C. Whitaker|title=The electronics handbook|url=http://books.google.com/books?id=08wHm9EqX20C&pg=PA198|accessdate=26 April 2011|date=23 December 1996|publisher=CRC Press|isbn=978-0-8493-8345-8|pages=198–}}</ref> 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.
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| 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.
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| 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.
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| Crystals are sensitive to [[shock (mechanics)|shock]]. The mechanical stress causes a short-term 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 in 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-force|g]].<ref>[http://www.ieee-uffc.org/frequency_control/teaching.asp?vig=vigaccel Frequency Control|Teaching Resources]. Ieee-uffc.org. Retrieved on 2010-02-08.</ref>
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| [[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 N<sup>2</sup>. 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 [[Frequency-shift keying|FSK]] technologies.
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| 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 a hydrogen-free atmosphere in an electric field of at least 500 V/cm for at least 12 hours. Such swept crystals have a very low response to steady ionizing radiation. Some [[silicon|Si(IV)]] atoms are replaced with [[aluminium|Al(III)]] impurities, each having a compensating [[lithium|Li<sup>+</sup>]] or [[sodium|Na<sup>+</sup>]] 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<sup>+</sup> and Na<sup>+</sup> ions from the lattice, reducing this effect. The Al<sup>3+</sup> site can also trap hydrogen atoms. All crystals have a transient negative frequency shift after exposure to an [[X-ray]] pulse; the frequency then shifts gradually back; natural quartz reaches stable frequency after 10–1000 seconds, with a negative offset to pre-irradiation frequency, artificial crystals return to a 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.<ref name="freepatentsonline.com"/> 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.<ref>John R. Vig ''Method and apparatus for compensating for neutron induced frequency shifts in quartz resonators'' {{US patent|5512864}}, Issue date: Apr 30, 1996</ref> 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 levels of alkali metal impurities lose Q with irradiation; Q of swept artificial crystals is unaffected. Irradiation with higher doses (over 10<sup>5</sup> 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 the finite number of impurity sites that can be affected.<ref name="ieee-uffc1"/>
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| [[Magnetic field]]s have little effect on the crystal itself, as quartz is [[diamagnetic]]; [[eddy current]]s or AC voltages can however be induced into the circuits, and magnetic parts of the mounting and housing may be influenced.
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| 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 to reach 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.<ref>[http://www.ieee-uffc.org/frequency_control/teaching.asp?vig=vigwarm Frequency Control|Teaching Resources]. Ieee-uffc.org. Retrieved on 2010-02-08.</ref>
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| Crystals have no inherent failure mechanisms; some have operated 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.<ref>[http://www.am1.us/Papers/U11625%20VIG-TUTORIAL.PDF Quartz crystal resonators and oscillators for frequency control and timing applications]: a tutorial by John R. Vig, U.S. Army Communications-Electronics Command</ref> Crystals can be also damaged by overdriving.
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| The crystals have to be driven at the appropriate drive level. While AT cuts tend to be fairly forgiving, with only their electrical parameters, stability and aging characteristics being 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.<ref name="actcrystals1">[http://www.actcrystals.com/techinfo/crystalterminology_txt.html Crystal Terminology]. Actcrystals.com. Retrieved on 2010-02-08.</ref> 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]].<ref>[http://www.axtal.com/data/publ/ukw1979_e.pdf Design of crystal oscillator circuits], a course by B. Neubig</ref>
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| 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.
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| Aging decreases logarithmically with time, the largest changes occurring shortly after manufacture. Artificially aging a crystal by prolonged storage at 85 to 125 °C can increase its long-term stability.
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| A badly designed oscillator circuit may suddenly begin oscillating on an overtone. In 1972, a train in [[Fremont, California]] crashed due to a faulty oscillator. 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 slow down.<ref>[http://www.edn.com/article/CA6636507.html Making oscillator selection crystal clear – 2/19/2009]. EDN (2008-07-20). Retrieved on 2010-02-08.</ref>
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| ==Crystal cuts==
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| 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.
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| [http://www.mazepath.com/uncleal/quartz.gif Image of several crystal cuts]<ref>[http://www.mazepath.com/uncleal/eotvos.htm Eotvos and Novel Equivalence Principle Tests]. Mazepath.com (2007-07-03). Retrieved on 2010-02-08.</ref>
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| {| class="wikitable sortable"
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| |-
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| ! Cut
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| ! Frequency range
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| ! Mode
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| ! Angles
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| ! Description
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| |-
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| | '''AT'''
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| | 0.5–300 MHz
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| | thickness shear (c-mode, slow quasi-shear)
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| | 35°15', 0° (<25 MHz)<br />35°18', 0°(>10 MHz)
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| | The most common cut, developed in 1934. The plate contains the crystal's x axis and is inclined by 35°15' from the z (optic) axis. The frequency-temperature curve is a sine-shaped curve with [[inflection point]] at around 25–35 °C. Has frequency constant 1.661 MHz⋅mm.<ref name="nelfc1">[http://www.nelfc.com/pdf/pdfapp/9113.pdf Crystals and oscillators] By Jerry A. Lichter</ref> Most (estimated over 90%) of all crystals are this variant. Used for oscillators operating in wider temperature range, for range of 0.5 to 200 MHz; also used in oven-controlled oscillators.<ref>[http://www.icmfg.com/glossary.html#AT_cut Crystal and frequency control glossary]. Icmfg.com. Retrieved on 2010-02-08.</ref> Sensitive to mechanical stresses, whether caused by external forces or by temperature gradients. Thickness-shear crystals typically operate in fundamental mode at 1–30 MHz, 3rd [[overtone]] at 30–90 MHz, and 5th overtone at 90–150 MHz;<ref>[http://www.4timing.com/techcrystal.htm Crystal Technology]. 4timing.com. Retrieved on 2010-02-08.</ref> according to other source they can be made for fundamental mode operation up to 300 MHz, though that mode is usually used only to 100 MHz<ref>[http://www.oscilent.com/esupport/TechSupport/ReviewPapers/IntroQuartz/vigqrtz.htm Introduction to Quartz Frequency Standards – Quartz and the Quartz Crystal Unit]. Oscilent.com. Retrieved on 2010-02-08.</ref> and according to yet another source the upper limit for fundamental frequency of the AT cut is limited to 40 MHz for small diameter blanks.<ref name="nelfc1"/> Can be manufactured either as a conventional round disk, or as a strip resonator; the latter allows much smaller size. The thickness of the quartz blank is about (1.661 mm)/(frequency in MHz), with the frequency somewhat shifted by further processing.<ref>[http://hoffmanmaterials.com/product/quartz-blanks Quartz Blanks]. Hoffman Materials. Retrieved on 2010-02-08.</ref> The third overtone is about 3 times the fundamental frequency; the overtones are higher than the equivalent multiple of the fundamental frequency by about 25 kHz per overtone. Crystals designed for operating in overtone modes have to be specially processed for plane parallelism and surface finish for the best performance at a given overtone frequency.<ref name="actcrystals1"/>
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| | '''SC'''
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| | 0.5–200 MHz
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| | thickness shear
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| | 35°15', 21°54'
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| | A special cut (Stress Compensated) developed in 1974, is a double-rotated cut (35°15' and 21°54') for oven-stabilized oscillators with low [[phase noise]] and good aging characteristics. Less sensitive to mechanical stresses. Has faster warm-up speed, higher Q, better close-in phase noise, less sensitivity to spatial orientation against the vector of gravity, and less sensitivity to vibrations.<ref>[http://www.commsdesign.com/main/9805fe4.htm CSD – May 1998 – Making it Crystal Clear: Crystal Oscillators in Communications]. Commsdesign.com. Retrieved on 2010-02-08.</ref> Its frequency constant is 1.797 MHz⋅mm. Coupled modes are worse than the AT cut, resistance tends to be higher; much more care is required to convert between overtones. Operates at the same frequencies as the AT cut. The frequency-temperature curve is a third order downward parabola with inflection point at 95 °C and much lower temperature sensitivity than the AT cut. Suitable for OCXOs in e.g. space and GPS systems. Less available than AT cut, more difficult to manufacture; the order-of-magnitude improvement of parameters is traded for an order of magnitude tighter crystal orientation tolerances.<ref name="patentstorm2">Alfred Kahan ''Cut angles for quartz crystal resonators'' {{US patent|4499395}}, Issue date: Feb 12, 1985</ref> Aging characteristics are 2 to 3 times better than of the AT cuts. Less sensitive to drive levels. Far fewer activity dips. Less sensitive to plate geometry. Requires an oven, does not operate well at ambient temperatures as the frequency rapidly falls off at lower temperatures. Has several times lower motional capacitance than the corresponding AT cut, reducing the possibility to adjust the crystal frequency by attached capacitor; this restricts usage in conventional TCXO and VCXO devices, and other applications where the frequency of the crystal has to be adjustable.<ref>[http://www.ofc.com/products/ocxo/ocxos.htm OCXO Application Notes – OCXOs – Oven Controlled Crystal Oscillators]. Ofc.com. Retrieved on 2010-02-08.</ref><ref>[http://commsdesign.com/main/9805fe4.htm CSD – May 1998 – Making it Crystal Clear: Crystal Oscillators in Communications]. Commsdesign.com. Retrieved on 2010-02-08.</ref> The temperature coefficients for the fundamental frequency is different than for its third overtone; when the crystal is driven to operate on both frequencies simultaneously, the resulting beat frequency can be used for temperature sensing in e.g. microcomputer-compensated crystal oscillators. Sensitive to electric fields. Sensitive to air damping, to obtain optimum Q it has to be packaged in vacuum.<ref name="google1"/> Temperature coefficient for b-mode is −25 ppm/°C, for dual mode 80 to over 100 ppm/°C.<ref name="uncirimag">{{cite book|author=Paul W. Kruse|title=Uncooled infrared imaging arrays and systems|url=http://books.google.com/books?id=5zXS_By-nQ8C&pg=PA273|accessdate=26 April 2011|year=1997|publisher=Academic Press|isbn=978-0-12-752155-8|pages=273–}}</ref>
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| | '''BT'''
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| | 0.5–200 MHz
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| | thickness shear (b-mode, fast quasi-shear)
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| | −49°8', 0°
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| | A special cut, similar to AT cut, except the plate is cut at 49° from the z axis. Operates in thickness shear mode, in b-mode (fast quasi-shear). It has well known and repeatable characteristics.<ref>[http://www.icmfg.com/crystalglossaryb.html#BT_cut Crystal and frequency control glossary]. Icmfg.com. Retrieved on 2010-02-08.</ref> Has frequency constant 2.536 MHz⋅mm. Has poorer temperature characteristics than the AT cut. Due to the higher frequency constant, can be used for crystals with higher frequencies than the AT cut, up to over 50 MHz.<ref name="nelfc1"/>
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| | '''IT'''
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| | thickness shear
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| | A special cut, is a double-rotated cut with improved characteristics for oven-stabilized oscillators. Operates in thickness shear mode. The frequency-temperature curve is a third order downward parabola with inflection point at 78 °C. Rarely used. Has similar performance and properties to the SC cut, more suitable for higher temperatures.
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| | '''FC'''
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| | thickness shear
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| | A special cut, a double-rotated cut with improved characteristics for oven-stabilized oscillators. Operates in thickness shear mode. The frequency-temperature curve is a third order downward parabola with inflection point at 52 °C. Rarely used. Employed in oven-controlled oscillators; the oven can be set to lower temperature than for the AT/IT/SC cuts, to the beginning of the flat part of the temperature-frequency curve (which is also broader than of the other cuts); when the ambient temperature reaches this region, the oven switches off and the crystal operates at the ambient temperature, while maintaining reasonable accuracy. This cut therefore combines the power saving feature of allowing relatively low oven temperature with reasonable stability at higher ambient temperatures.<ref>Bruce R. Long ''Low power temperature-controlled frequency-stabilized oscillator'' {{US patent|4985687}}, Issue date: Jan 15, 1991</ref>
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| | '''AK'''
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| |
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| | thickness shear
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| | a double rotated cut with better temperature-frequency characteristics than AT and BT cuts and with higher tolerance to crystallographic orientation than the AT, BT, and SC cuts (by factor 50 against a standard AT cut, according to calculations). Operates in thickness-shear mode.<ref name="patentstorm2"/>
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| |-
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| | '''CT'''
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| | 300–900 kHz
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| | face shear
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| | 38°, 0°
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| | The frequency-temperature curve is a downward parabola.
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| |-
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| | '''DT'''
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| | 75–800 kHz
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| | face shear
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| | −52°, 0°
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| | Similar to CT cut. The frequency-temperature curve is a downward parabola. The temperature coefficient is lower than the CT cut; where the frequency range permits, DT is preferred over CT.<ref name="nelfc1"/>
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| |-
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| | '''SL'''
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| | face-shear
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| | −57°, 0°
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| |-
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| | '''GT'''
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| | 0.1–3 MHz
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| | width-extensional
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| | 51°7'
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| | Its temperature coefficient between −25..+75 °C is near-zero, due to cancelling effect between two modes.<ref name="nelfc1"/>
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| |-
| |
| | '''E''', '''5°X'''
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| | 50–250 kHz
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| | longitudal
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| |
| |
| | Has reasonably low temperature coefficient, widely used for low-frequency crystal filters.<ref name="nelfc1"/>
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| |-
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| | '''MT'''
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| | 40–200 kHz
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| | longitudal
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| |
| |
| |
| |
| |-
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| | '''ET'''
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| |
| |
| |
| |
| | 66°30'
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| |
| |
| |-
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| | '''FT'''
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| |
| |
| |
| |
| | −57°
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| |-
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| | '''NT'''
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| | 8–130 kHz
| |
| | length-width flexure (bending)
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| |
| |
| |
| |
| |-
| |
| | '''XY''', '''tuning fork'''
| |
| | 3–85 kHz
| |
| | length-width flexure
| |
| |
| |
| | The dominant low-frequency crystal, as it is smaller than other low-frequency cuts, less expensive, has low impedance and low Co/C1 ratio. The chief application is the 32.768 kHz RTC crystal. Its second overtone is about six times the fundamental frequency.<ref name="actcrystals1"/>
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| |-
| |
| | '''H'''
| |
| | 8–130 kHz
| |
| | length-width flexure
| |
| |
| |
| | Used extensively for wideband filters. The temperature coefficient is linear.
| |
| |-
| |
| | '''J'''
| |
| | 1–12 kHz
| |
| | length-thickness flexure
| |
| |
| |
| | J cut is made of two quartz plates bonded together, selected to produce out of phase motion for a given electrical field.
| |
| |-
| |
| | '''RT'''
| |
| |
| |
| |
| |
| |
| |
| | A double rotated cut.
| |
| |-
| |
| | '''SBTC'''
| |
| |
| |
| |
| |
| |
| |
| | A double rotated cut.
| |
| |-
| |
| | '''TS'''
| |
| |
| |
| |
| |
| |
| |
| | A double rotated cut.
| |
| |-
| |
| | '''X 30°'''
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| |
| |
| |
| |
| |
| |
| | A double rotated cut.
| |
| |-
| |
| | '''LC'''
| |
| |
| |
| | thickness shear
| |
| | 11.17°/9.39°
| |
| | A double rotated cut ("Linear Coefficient") with a linear temperature-frequency response; can be used as a sensor in crystal thermometers.<ref>Bikash K. Sinha ''Stress-compensated quartz resonators'' {{US patent|4419600}}, Issue date: Dec 6, 1983</ref> Temperature coefficient is 35.4 ppm/°C.<ref name="uncirimag" />
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| |-
| |
| | '''AC'''
| |
| |
| |
| |
| |
| | 31°
| |
| | Temperature-sensitive, can be used as a sensor. Single mode with steep frequency-temperature characteristics.<ref name="patentstorm3">John R. Vig ''High sensitivity temperature sensor and sensor array'' {{US patent|5686779}}, Issue date: Nov 11, 1997</ref> Temperature coefficient is 20 ppm/°C.<ref name="uncirimag" />
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| |-
| |
| | '''BC'''
| |
| |
| |
| |
| |
| | −60°
| |
| | Temperature-sensitive.<ref name="patentstorm3"/>
| |
| |-
| |
| | '''NLSC'''
| |
| |
| |
| |
| |
| |
| |
| | Temperature-sensitive.<ref name="patentstorm3"/> Temperature coefficient is about 14 ppm/°C.<ref name="uncirimag" />
| |
| |-
| |
| | '''Y'''
| |
| |
| |
| |
| |
| |
| |
| | Temperature-sensitive, can be used as a sensor. Single mode with steep frequency-temperature characteristics.<ref name="patentstorm3"/> The plane of the plate is perpendicular to the Y axis of the crystal.<ref>[http://www.engineersedge.com/engineering/Engineering_Terms_Glossary/Y/y_cut_crystal_4074.htm Y Cut Crystal]. Engineersedge.com (2009-08-25). Retrieved on 2010-02-08.</ref> Also called '''parallel''' or '''30-degree'''. Temperature coefficient is about 90 ppm/°C.<ref name="uncirimag" />
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| |-
| |
| | '''X'''
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| |
| |
| |
| |
| |
| |
| | Used in one of the first crystal oscillators in 1921 by W.G. Cady, and as a 50 kHz oscillator in the first crystal clock by Horton and Marrison in 1927.<ref name="ieee-uffc2">[http://www.ieee-uffc.org/main/history.asp?file=frerking UFFC|History]. Ieee-uffc.org (1959-03-23). Retrieved on 2010-02-08.</ref> The plane of the plate is perpendicular to the X axis of the crystal. Also called '''perpendicular''', '''normal''', '''Curie''', '''zero-angle''', or '''ultrasonic'''.<ref>[http://www.minsocam.org/ammin/AM30/AM30_461.pdf Glossary of terms used in the quartz oscillator-plate industry]. minsocam.org. Retrieved on 2012-06-21.</ref>
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| |}
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| 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.
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| The high frequency cuts are mounted by their edges, usually on springs; the stiffness of the spring has to be optimal, as if it is too stiff, mechanical shocks could be transferred to the crystal and cause it to break, 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.<ref>[http://www.icmfg.com/crystalfaqs.html Quartz crystal FAQs from International Crystal]. Icmfg.com. Retrieved on 2010-02-08.</ref>
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| 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 on the thin wires makes the assembly sensitive to mechanical shocks and vibrations.<ref name="nelfc1"/>
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| 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.
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| 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),<ref>[http://www.mail-archive.com/time-nuts@febo.com/msg10485.html Re: [time-nuts] Super stable BVA Quartz resonators... BVA??]. Mail-archive.com (2007-12-07). Retrieved on 2010-02-08.</ref> 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 the 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.<ref>[http://www.mail-archive.com/time-nuts@febo.com/msg10505.html Re: [time-nuts] Super stable BVA Quartz resonators... BVA??]. Mail-archive.com (2007-12-08). Retrieved on 2010-02-08.</ref> 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.<ref>[http://www.oscilloquartz.ch/file/pdf/8600.pdf 8600 Oven Crystal Oscillator]. oscilloquartz.ch. Retrieved on 2012-06-21.</ref> 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.<ref>[http://www.ieee-uffc.org/main/history.asp?file=norton UFFC|History]. Ieee-uffc.org (1957-10-04). Retrieved on 2010-02-08.</ref>
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| 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, at the cost of a lowered Q.<ref>[http://www.edn.com/blog/1470000147/post/580024458.html Crystal grinding: When electronics were REALLY hands-on – PowerSource – Blog on EDN – 1470000147]. Edn.com. Retrieved on 2010-02-08.</ref>
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| 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.<ref>[http://www.edn.com/archives/1997/112097/24cs.htm EDN Access-11.20.97 Crystal Oscillators: Looking Good In Wireless Systems]. Edn.com. Retrieved on 2010-02-08.</ref>
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| ==Circuit notations and abbreviations==
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| 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 [[Institute of Electrical and Electronics Engineers|IEEE]] Std 315-1975, or [[American National Standards Institute|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.
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| Crystal oscillator types and their abbreviations:
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| *'''ATCXO''' — [[Analog temperature controlled crystal oscillator]]
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| *'''CDXO''' — Calibrated dual crystal oscillator
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| *'''DTCXO''' — Digital temperature compensated crystal oscillator
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| *'''EMXO''' — Evacuated miniature crystal oscillator
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| *'''GPSDO''' — [[GPSDO|Global positioning system disciplined oscillator]]
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| *'''MCXO''' — [[Microcomputer]]-compensated crystal oscillator
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| *'''OCVCXO''' — [[Crystal oven|oven-controlled]] voltage-controlled crystal oscillator
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| *'''OCXO''' — [[Crystal oven|Oven-controlled crystal oscillator]]
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| *'''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
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| *'''TCVCXO''' — Temperature-compensated [[voltage-controlled oscillator|voltage-controlled crystal oscillator]]
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| *'''TCXO''' — Temperature-compensated crystal oscillator
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| *'''TMXO''' – Tactical miniature crystal oscillator<ref name="ieee-uffc2"/>
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| *'''TSXO''' — Temperature-sensing crystal oscillator, an adaptation of the TCXO
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| *'''VCTCXO''' — Voltage-controlled temperature-compensated crystal oscillator
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| *'''VCXO''' — Voltage-controlled crystal oscillator
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| ==See also==
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| *[[Clock drift]] – Clock drift measurements of crystal oscillators can be used to build [[random number generator]]s.
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| *[[Crystal filter]]
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| *[[Erhard Kietz]] work on electronic tuning forks and with quartz crystals for precise signal frequencies
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| *[[Pierce oscillator]]
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| *[[VFO]] — variable-frequency oscillator
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| ==References==
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| {{Reflist|colwidth=30em}}
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| ==Further reading==
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| *Ulrich L. Rohde "Microwave and Wireless Synthesizers: Theory and Design ", John Wiley & Sons, August 1997, ISBN 0-471-52019-5
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| ==External links==
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| {{Commons category|Crystal oscillators}}
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| *[http://www.ieee-uffc.org/frequency_control/teaching.asp?name=vigtoc Introduction to quartz frequency standards]
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| *{{cite web
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| |title = What is a quartz crystal device?
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| |work = QIAJ
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| |publisher = Quartz Crystal Industry Assoc. of Japan
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| |year = 2007
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| |url = http://www.qiaj.jp/pages/frame20/page01-e.html
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| |accessdate = 2008-08-10}}
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| *{{cite conference
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| |first = Frerking
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| |last = Marvin E.
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| |title = Fifty years of progress in quartz crystal frequency standards
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| |booktitle = Proc. 1996 IEEE Frequency Control Symposium
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| |pages = 33–46
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| |publisher = Institute of Electrical and Electronic Engineers
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| |year = 1996
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| |location =
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| |url = http://www.ieee-uffc.org/main/history.asp?file=frerking
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| |accessdate = 2009-03-31}}
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| *[http://www.frequencycontrolsolutions.com/2009/11/distortions-in-crystal-oscillators.html Distortions in Crystal Oscillators]
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| *[http://www.am1.us/Papers/U11625%20VIG-TUTORIAL.PDF Quartz crystal resonators and oscillators]
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| {{Electronic components}}
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| {{DEFAULTSORT:Crystal Oscillator}}
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| [[Category:Electrical components]]
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| [[Category:Oscillators]]
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Abercrombie And Fitch Dk ex parte deordinationis
Holde ud og få en belønning, efter at være kommet så langt du kan bare give op. Ibelieve det. Det er fordi gravide kvinder kan spare tid og igen også som for temmelig meget øjeblik. På grund af e-handel shopping kultur består af specifik i retning af de længes og som et resultat ville virkelig gerne inde befolkning.
Vi havde besøgt Upstate New York hjem sted Buckley MI5/FBI muldvarp David Rupert, og havde fået bevis for, at han er en Abercrombie And Fitch Dk livslang kriminel (også fremgår af en NY State Police affidavit). Vi gav også forsvaret med fire konkurs høvle af Rupert, alle falske.
Siden begyndelsen af 1990'erne og udvikling af underholdning enemærker såsom Melbournes King Street, har der været meget arbejde, som industrien, lovgivere, lokale myndigheder og lokalsamfundet i håndteringen lokale bekymringer om vold og den offentlige sikkerhed. Som en tidligere politibetjent og derefter konsulent i området over de sidste 20 år, jeg har været vidne til et førstehåndsvidne praksis, der har påvirket af niveauet for alkoholrelaterede og natklub vold.
Men denne intensitet er hvad der gør ham kryds. Det er det brændstof, der skubber ham til at forbedre og aldrig sige die på banen. Bryster slikke anerkendt spændt vasket gik kunne hvile hvorfor. Røv ben. Original og Nike Roshe Run Woven faktisk synd udmærker sig ved den måde, hvorpå de er frivillige (tidl. Parte actus); dødelig og tilgivelige synd ved den måde, hvorpå de påvirker vores forhold til Gud (ex parte deordinationis).
Når du køber smykker som kommer op. Michael Kors Tasker Når du køber en perforeret til dine offentlige præsentation, færdigheder og svagheder. Hvis du vil købe ejendomme fra bankerne, er det vigtigt at have dine penge og hold linet op før tid. Du skal være parat til at bevæge sig hurtigt..
Ved at skrive om din forskning, er du konstant placere dig selv ofte i forhold til arbejdet i andre forskere, men også i forhold til dine egne data. Diskutere resultater og drage konklusioner indebærer at foretage påstande om fortolkning, betydning og anvendelighed.
Aware Parenting er både forebyggende og reparerende. Den præventive del af filosofien lærer forældre hvordan de kan opfylde børnenes legitime behov og hvordan man kan genkende og undgå kilder til stress og traumer, især i de tidlige år, hvor børn er ekstremt sårbare.
Nogle yderligere detaljer. Jeg købte den 17., 4 dage tidligere den samme fyr solgte Nike Air Max 90 en del af ejendommen (de 11 fod) til den nu nabo. Maj. Dagens begivenheder starter med en skål for hr. Sidst, har jeg bemærket, at en sjov ting sker, når jeg afskedige dommen: Aron og jeg er mere tilbøjelige til at være åben for at prøve den anden tilgang. Det betyder, at han kunne læse om buksetrold adfærd, eller jeg vil gøre et spil ud af at børste Sylvias tænder, i stedet for grusning mine.
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Selvom det stadig klart, at producenterne vil ikke have flere guitarspil pop rocker til at vinde American Idol. De fleste af disse fyre er R-sangere eller land. Jeg hørte, at Gov / CFPB håndhævere vil trold fra servicevirksomheden tilbage til långiveren (os), så vi kan sætte i Nike Roshe Run Woven servicevirksomheden setup doc eventuelle Nike Air Force One noter, at dette lån er Dodd Frank-kompatibel. Tak for dine kommentarer.
Men til dato, er der stadig ingen 100% automatiseret system. Så hvis du er en ny på erfaren internet-iværksætter lige er startet ud, hvordan du besvarer spørgsmål, når de kommer op? Det er, hvor den støtteordning kommer i. Det centrale er, at du er nødt til at finde det tidligt, og den eneste måde du kommer til at finde det tidligt er at være proaktiv omkring dit helbred og at bo på toppen af din lægebesøg. Hvis du går efter en mammografi hvert andet eller tredje år, kan det være for sent, når du finder din brystkræft.
Men det mærkelige var, de så også en tredje person, der står mellem dem. Det lignede en lille pige omkring 9 eller 10 år gammel. Hende, jeg var med til ligesom 4 måneder indtil hun brød det ud med mig, tilsyneladende uden grund. Vi hadn haft nogen dårlige slagsmål eller noget, alt syntes fint.
Da bundkortet spændingsregulering moduler, der giver strøm til CPU'en får deres strøm fra strømforsyningen er +12 V jernbane, kan disse søvntilstand dramatisk reducere belastningen på strømforsyningen er +12 V rail.According til Intels præsentation ved IDF, de nye Haswell processorer indtaste en dvaletilstand kaldet C7, der kan falde processor strømforbrug så lavt som 0.05A. Selv om den sovende CPU er den eneste belastning på +12 V jernbane, kan de fleste strømforsyninger håndtere Longchamp Denmark en belastning denne lave.
Som enhver projektionsskærm de skal også renses og plejes på en regelmæssig basis for at sikre, at de er rene og vil vare. Ralph Lauren Danmark De gør en fantastisk tilføjelse til et bestyrelseslokale eller hjemmebiograf og kan være ganske dramatisk, når den hæves til at begynde en præsentation.
En meget udbredt ængstelse til en national kanon register har ført til forbud mod ATF og lokale retshåndhævende fra adgang til digitale databaser med henblik på identifikation af salgsstedet for våben inddrevet gerningssteder. [7] [8] [9 ]. Har du brug for at vise Nord-og Sydpolen, hvis du ikke tror, du nogensinde gå der? Sandsynligvis ikke. '.
Ingen enkelt blodprøve er diagnostisk, men hvis dit A1C er reproducerbart over 6,0%, så ville du have tidlig diabetes. Begreber som unormal glukosetolerance, præ diabetiker, og borderline diabetiker er forældet. Kommer snart! Gratis adgang til kun 1 ting Konkurrencen på ITV. Der vil også være et andet nyt gameshow på luft snart kaldet Twisted.
Louis Vuitton Taske i de to sæt
Care konkurrere Som jeg sagde før, jeg har gjort denne træning; Jeg kan ikke gøre op træning og derefter aldrig prøve dem Louis Vuitton Taske selv. Denne ene er virkelig fyrer op dine ben! Så lad os få en venskabelig konkurrence. Når du har prøvet denne træning, poste dine resultater i en kommentar.
Hævder, at han parkerede sin bil i et område, der ikke blev blokeret. Han hævder, at han troede, jogging stadig var okay. Blev mødt af to bevæbnede park rangers og slået med en billet.. Stormen blev rapporteret at være nord for Key West den 6. September, [6], og i de tidlige morgentimer fredag 7. September Weather Bureau kontor i New Orleans, Louisiana, udsendte en rapport om store skader langs Louisiana og Mississippi kyster.
Ada Marie blev udskrevet fra hospitalet i meget svag tilstand, og med mainstream lægehjælp i stand til at hjælpe videre, vendte hun sig til sin barndom skolegang. Hun begyndte sin eget program for selvhealing at komme sig, hun har lidt. Gennem disse var hun i stand til ikke kun at helbrede hendes krop, men hendes sind, hendes ånd og hendes livsglæde, for at leve!.
'Som mange af jer allerede kender (men måske nogle nye medlemmer af denne blog ikke) Jeg bor i Phoenix, Arizona. Hvor du bor her, bestemmer (i høj grad) din økonomiske velbefindende. Dem i' Øst Valley 'Chandler, Gilbert, Scottsdale, osv. Problemet i det argument er den antagelse, at fordi hvert af disse to sæt kun indeholder én farve af heste, det oprindelige sæt indeholdt også kun én farve Nike Roshe Run Dame af heste. Fordi der er ingen fælles elementer (heste) i de to sæt, er det uvist, om de to heste deler den samme farve. Beviset Nike Air Force 1 Dame danner en falsidical paradoks; det synes at vise noget åbenbart falsk ved gyldig begrundelse, men i virkeligheden den argumentation er fejlagtig..
Flytningen kommer som administrationens selvpåtvungne 30 nov frist for fastsættelse af webstedet er blot få dage væk, og embedsmænd erkender det kan ikke være fuldt operationelt inden da. Pilotprogram af CMS annonceret i første omgang iværksætte for beboere i Ohio, Florida og Texas, og er den seneste indsats for at give brugerne et alternativ til den urolige site. Er endnu en måde, vi arbejder på at tilbyde Nike Roshe forbrugerne en række forskellige måder at tilmelde sig overkommelige dækning, 'agentur talskvinde Julie Bataille sagde i at annoncere pilotprojektet.' Ved at styrke flere kanaler at tilmelde dig i kvalitet, overkommelige dækning sikrer vi, at alle amerikaner, der ønsker det, kan få adgang til disse nye dækning muligheder.
Beats By Dre Solo men vi bare gå ud og gøre det med ånd
1971: Den værste brand i Stouffville er 94 år historie ødelagde en hel virksomhed blok på hjørnet af Main og marked gader. Borgmester Ken Laushway og brandchef Smith havde en mirakuløs flugt fra alvorlig skade, når den forreste af de vigtigste struktur kollapsede.
Superior Courts: Hver provins og territorium har to niveauer af fineste domstol, at man høre forsøg og den anden til at behandle klager. Superior domstolene behandler lovovertrædelser, skilsmisser, civile sager, der involverer store mængder af penge og Charter udfordringer, og gennemgå de afgørelser truffet Beats By Dre Solo af administrative domstole og nogle lavere retsinstanser.
Tilføj løg og kog under omrøring lejlighedsvis, for 2 3 minutter eller indtil blødgjort. Tilsæt kylling og kog, drejning, for 3 4 minutter eller indtil Ray Ban Sunglasses gyldent. 'Johnny Manziel deltog i nogle af aktiviteterne i 2013 Manning Passing Academy som et kollegium rådgiver / coach,' lejr embedsmænd sagde i en erklæring sagde. 'Efter mangler og blive sent til praksis opgaver, forklarede Johnny, at han havde følt sig syg.
Placer bacon i et enkelt lag på tilberedt bakken. Grill, dreje en gang for 6 7 minutter eller til de er gyldne og sprøde. Han nødvendigheden af grænser, begrænsninger, nøjsomhed. Han er den balance til Zeus ekspansion, og han er nødvendige for os alle for Abercrombie Danmark at holde jordet.
'De lærte os en masse om pacing og pack kørende og viste mig som individ, Longchamp København hvordan du kører et løb,' siger Dacorte. 'Det er svært at sætte ord på det, men vi bare gå ud og gøre det med ånd, og som kommer fra al den uddannelse, vi gør, og fra at være sammen.'.
Århundrede amerikansk kunst og samtidskunst. På view er malerier og værker på papir af amerikanske mestre George Caleb Bingham, George Catlin, John La Farge, John Singer Sargent, Mary Cassatt, Winslow Homer, George Inness, Thomas Wilmer Dewing, Edward Hopper og Georgien O skulpturer af Augustus Saint Gaudens , Frederick Remington, og Alexander Calder.
Under den føderale tilgang, vil det centrale mål for forhandlingerne er at indgå aftaler om selvstyre i modsætning til juridiske definitioner af naturlig ret. Efter denne metode kan den række af spørgsmål, som den føderale regering ville se som emner for forhandling omfatte alle, nogle eller dele af følgende: vedtagelse og børns velfærd.
Picnik er meget funktionel og meget populære. Redaktionel note: Unforunately denne tjeneste sluttede April 19, 2012.. Tænk nederdel steak og filet mignon (gnide både i groft salt før tilberedning). Og da dagens argentinere elsker noget slankende, kaste på nogle skind kyllingebryster eller faste hvide fisk steaks (hellefisk, for eksempel)..
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Når motion og spise. Jeg forsøger ikke Nike Air Max 90 at spise alle mine kalorier tilbage, men nogle gange er jeg bare så freaking sulten. Naturligvis sker dette projekt for at være på pacific, så 1 pacific stadig lyder temmelig 'markedsføring' og kan meget vel være i overensstemmelse med resten af partiet, men Vancouver har et par Nike Roshe Run andre, der er nævnt i samme vene (i projekter om Seymour, Howe, Richards, Cordova, vand, main) og generelt, man fornemmer et skift fra den supereksklusive af noget lignende 'Vancouvers turn' eller 'Shangri La' i flere af de seneste projekter, ligesom Rolston eller mærket (hvilken slags refererer til gamle vandmærke). Berusende dage, Vancouver, holde det op..
Som en prædikant, han står for personificeringen af personlig transformation og NLP ekspert. Han har personligt instrueret præsidenter, berømte sportsstjerner og ledere i alle evner. Følgende artikel er et uddrag fra bogen, Michael Kors Danmark det er for dyrene! En stamme er en skade på en muskel eller sene, hvor muskelfibrene rive som følge af overstrækning. En stamme er også i daglig tale kendt som en trukket muskel.
Så delte vi en lejlighed, så en anden lejlighed, og derefter flyttede ind i et lille kontor. Endelig et par år siden, vi landede i den nyeste Panic kontoret fik vi at designe og bygge ud fra bunden, fra tom rå shell til færdigt produkt. Sandsynligvis den bedste ting jeg gjorde var en yoga træ på min højre side foran et spejl, og sørg for mine hofter er niveau. Når jeg havde det mestrer, jeg startede med at lave overliggende tricep extensions skiftes til en front raise (med vægte).
Under den delegerede uddannelse, opstod en række andre spørgsmål, der kræver telefonopkald. Heldigvis var ikke jeg præsentere, så jeg kunne smutte ind og ud af veldrevet begivenhed (takket være den store FBEU personale og embedsmænd til stede). Tilskudsdokumenterne nedskæringer kommer midt Internationale Valutafond pres på Sudan til at dæmme Longchamp Denmark op for udgifterne og tilbagebetale gæld. Tilsvarende IMF bakkes stramninger annonceret sidste år udløste også protester, der blev hurtigt sat ned.
Enhver, der gør ikke forstå, at dette stadig er en fodgængerovergang, bør have deres licens taget væk og aldrig givet tilbage. Og som for dem her, at gøre indsigelse mod, hvad det står for, jeg ikke engang gider længere; hvis du tilflugtssted regnet det ud nu, så bare trække sig tilbage til komforten i dit hjem og holde hovedet i kattegrus.
Bedste Svar: Jeg har revet sener / ledbånd i min fod før, og jeg har i øjeblikket en brud på samme fod (to separate skader og donw to år Toe senesmerter Fødderne er komplekse strukturer, der består af snesevis af knogler, muskler og.. Sener, der er udviklet til at modstå bærer kroppens vægt.
Louis Vuitton Pung Den indeholder specifikke strategier
Det Hvide Hus havde nået ud til Teheran tidligere i denne måned for at tilbyde et møde på sidelinjen af FN Generalforsamling på mandag eller tirsdag, men Rouhani faldt på det tidspunkt. Fakultetet er kendt for at gennemføre innovative forskningsprojekter og yder et væsentligt bidrag til viden om hvordan man kan forbedre uddannelsesmuligheder og resultater for børn, unge og voksne fra forskellige baggrunde og omstændigheder..
Den indeholder specifikke strategier, du kan bruge i Louis Vuitton Pung dag for at begynde at forberede dine børn for den sværeste opgave af deres liv: Dyrkning up.Childhood er short.Adulthood dog Longchamp Le Pliage er for en meget lang tid. For nu, dette begreb ser lige så død som Spire, men måske i en fjern fremtid en anden udvikler (gerne sige, Fordham Company) kunne ansætte den spanske starchitect at blænde med sin akvarel hav shells.Spire ser Nike Air Force One død; oprindelige udvikler siger Calatrava stadig kunne Ray Ban Sunglasses forme hjemmeside [Trib] Chicago Spire Developer Hit med $ 77 millioner Afskærmning Suit [bremset].
De fleste klausuler, at skriftlig meddelelse skal gøres gældende inden for 30 dage fra datoen for modtagelsen af en skriftlig ordre. Reglerne kræver også, at sikker, computer genererede, er tidsstemplede revisionsspor anvendes til at registrere dato og tidspunkt for operatør indgange og handlinger, der skaber, ændre eller slette elektroniske registre.
Så i stedet for at fokusere på Abbott / Gillard Bout planlagt til september 14 måske skulle jeg tage mit udgangspunkt denne kommentar fra Avlen:. Against Spørgsmålstegn forblive i Chelseas fremad linje, på trods af Fernando Torres viser glimt af hans pre selv i de seneste uger, og Samuel Eto'o er en anden, hvis ry i øjeblikket vejer tungere end hans bidrag.
Don blive overrasket, hvis elementer af country, sigøjner jazz og swing formår at snige sig ind i handling så godt. Vi vil se en behandling derefter få det udviklet på normal vis. New York Tyler J. Ikke desto mindre, Khoo sagde, at skrive indholdet ikke kunne være af interesse for alle.
Jeg kender dig og dine kammerater tror track parter er redet med hårdt stofmisbrug. Virksomhedens officielle talte på betingelse af anonymitet, sagde han for nylig flyttede sin virksomhed offshore undgå retssager eller ophøre og afstå bekendtgørelser..
En Associated Press reporter kørte gennem byen for omkring 7 km (4 miles) på onsdag og så mere end 40 lig. På grund af alder overvejelser (jeg være 60 i 5 år) og min personlige forudsigelse af den næste top, tænkte jeg 2018 eller når jeg følte at tiden var inde alvorlige opgørelse stiger, osv.
Nike Roshe Run Woven herunder en masse siden sidst den 24.
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Noget, der slår mig som mærkeligt i dette område er der er mange tvangsauktioner og REO ejendomme til rådighed, men nye hjem bygherrer er stadig drive forretning der sælger de nye boliger. Det er som om boblen aldrig sket i nogle tilfælde.. Nu ejendomsadministration er en stor luns af, at 50%. Ca.
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Ifølge Kieran McLaughlin, en direktør for Jones Lang LaSalle, sammen med en betydelig hævning i pant godkendelser op 25% siden januar og den fornyede fremkomsten af de 95% realkreditlån fra udbydere som Halifax, har disse initiativer styrket markedets tillid. Faktisk aktiekurserne på de vigtigste hus bygning PLC'er er steget med 50% i gennemsnit siden begyndelsen af året..
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