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for a piezoelectric crystal resonatorA
crystal oscillator is an
electronic circuit that uses the mechanical resonance of a vibrating crystal of
Piezoelectricity#Materials to create an electrical signal with a very precise
frequency. This frequency is commonly used to keep track of time (as in quartz clock), to provide a stable
clock signal for
digital integrated circuits, and to stabilize frequencies for
radio transmitters.
Using an amplifier and feedback, it is an especially accurate form of an
electronic oscillator. The crystal used therein is sometimes called a "timing crystal". On schematic a crystal is labeled
Y.
Crystals for timing purposes
quartz crystal enclosed in an
hermetically sealed HC-49/US package, used as the resonator in a crystal oscillator.
A crystal is a
solid in which the constituent
atoms, molecules, or ions are packed in a regularly ordered, repeating pattern extending in all three spatial dimensions.
Almost any object made of an elastic material could be used like a crystal, with appropriate transducers, since all objects have natural resonance frequencies of vibration. For example, steel is very elastic and has a high speed of sound. It was often used in mechanical filters before quartz. The resonant frequency depends on size, shape, elasticity (physics), and the speed of sound in the material. High-frequency crystals are typically cut in the shape of a simple, rectangular plate. Low-frequency crystals, such as those used in digital watches, are typically cut in the shape of a
tuning fork. For applications not needing very precise timing, a low-cost ceramic resonator is often used in place of a quartz crystal.
When a crystal of quartz is properly cut and mounted, it can be made to distort in an electric field by applying a
voltage to an
electrode near or on the crystal. This property is known as piezoelectricity. When the field is removed, the quartz will generate an electric field as it returns to its previous shape, and this can generate a voltage. The result is that a quartz crystal behaves like a circuit composed of an
inductor, capacitor and
resistor, with a precise resonant frequency. (See RLC circuit.)
Quartz has the further advantage that its elastic constants and its size change in such a way that the frequency dependence on temperature can be very low. The specific characteristics will depend on the mode of vibration and the angle at which the quartz is cut (relative to its crystallographic axes)1 Therefore, the resonant frequency of the plate, which depends on its size, will not change much, either. This means that a quartz clock, filter or oscillator will remain accurate. For critical applications the quartz oscillator is mounted in a temperature-controlled container, called a crystal oven, and can also be mounted on shock absorbers to prevent perturbation by external mechanical vibrations.
Quartz timing crystals are manufactured for frequencies from a few tens of
kilohertz to tens of megahertz. More than two billion (2×109) crystals are manufactured annually. Most are small devices for consumer devices such as
wristwatches, clocks,
radios, computers, and cellphones. Quartz crystals are also found inside test and measurement equipment, such as counters,
signal generators, and
oscilloscopes.
Crystal modelling
A quartz crystal can be modelled as an electrical network with a low
Electrical impedance (series) and a high
Electrical impedance (parallel) resonance point spaced closely together. Mathematically the impedance of this network can be written as:
Z(s) = \left( {\frac{1}{s\cdot C_1}+s\cdot L_1+R_1} \right) || \left( {\frac{1}{s\cdot C_0--> \right)
or,
Z(s) = \frac{s^2 + s\frac{R_1}{L_1} + {\omega_s}^2}{s + s\frac{R_1}{L_1} + {\omega_p}^2} \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-->
where s is the complex frequency (s=j\omega), \omega_s is the series resonant frequency in
radians per second and \omega_p is the parallel resonant frequency in radians per second.
Adding additional capacitance across a crystal will cause the parallel resonance to shift downward. This can be used to adjust the frequency that a crystal oscillator oscillates at. Crystal manufacturers normally cut and trim their crystals to have a specified resonant frequency with a known 'load' capacitance added to the crystal. For example, a 6 pF 32 kHz crystal has a parallel resonance frequency of 32,768 Hz when a 6.0 pF capacitor is placed across the crystal. Without this capacitance, the resonance frequency is higher than 32,768 Hz.
Temperature effects
A crystal's frequency characteristic depends on the shape or 'cut' of the crystal. A tuning fork crystal is usually cut such that its frequency over temperature is a parabolic curve centered around 25 °C. This means that a tuning fork crystal oscillator will resonate close to its target frequency at room temperature, but will slow down when the temperature either increases or decreases from room temperature. A common parabolic coefficient for a 32 kHz tuning fork crystal is −0.04 ppm/°C².
f = f_0 \ \mbox{ppm}(T-T_0)^2
In a real application, this means that a clock built using a regular 32 kHz tuning fork crystal will keep good time at room temperature, lose 2 minutes per year at 10 degrees Celsius above (or below) room temperature and lose 8 minutes per year at 20 degrees Celsius above (or below) room temperature.
Crystals and frequency
equipment to select frequency.
The crystal oscillator circuit sustains oscillation by taking a voltage signal from the quartz resonator, amplifying it, and feeding it back to the resonator. The rate of expansion and contraction of the quartz is the resonance frequency, and is determined by the cut and size of the crystal.
A regular timing crystal contains two electrically conductive plates, with a slice or tuning fork of quartz crystal sandwiched between them. During startup, the circuit around the crystal applies a random noise
Alternating current signal to it, and purely by chance, a tiny fraction of the noise will be at the resonant frequency of the crystal. The crystal will therefore start oscillating in synchrony with that signal. As the oscillator amplifies the signals coming out of the crystal, the crystal's frequency will become stronger, eventually dominating the output of the oscillator. Natural resistance in the circuit and in the quartz crystal electronic filter out all the unwanted frequencies.
One of the most important traits of quartz crystal oscillators is that they can exhibit very low phase noise. In other words, the signal they produce is a
pure tone. This makes them particularly useful in telecommunications where stable signals are needed, and in scientific equipment where very precise time references are needed.
The output frequency of a quartz oscillator is either the fundamental resonance or
harmonic, called an
overtone frequency.
A typical
Q factor for a quartz oscillator ranges from 104 to 106. The maximum
Q for a high stability quartz oscillator can be estimated as
Q = 1.6 × 107/
f, where
f is the resonance frequency in megahertz.
Environmental changes of temperature, humidity, pressure, and vibration can change the resonant frequency of a quartz crystal, but there are several designs that reduce these environmental effects. These include the TCXO, MCXO, and OCXO (defined below). These designs (particularly the OCXO) often produce devices with excellent short-term stability. The limitations in short-term stability are due mainly to noise from electronic components in the oscillator circuits. Long term stability is limited by aging of the crystal.
Due to aging and environmental factors such as temperature and vibration, it is hard to keep even the best quartz oscillators within one part in 10−10 of their nominal frequency without constant adjustment. For this reason,
atomic oscillators are used for applications that require better long-term stability and accuracy.
Although crystals can be fabricated for any desired resonant frequency, within technological limits, in actual practice today engineers design crystal oscillator circuits around relatively few standard frequencies, such as 3.58 MHz, 10 MHz, 14.318 MHz, 20 MHz, 33.33 MHz, and 40 MHz. The vast popularity of the 3.58MHz and 14.318MHz crystals is attributed initially to low cost resulting from mass production resulting from the popularity of television and the fact that this frequency is involved in synchronizing to the colorburst signal necessary to display color on an
NTSC or
PAL based
television set. Using frequency dividers, frequency multipliers and
phase locked loop circuits, it is possible to synthesize any desired frequency from the reference frequency.
Care must be taken to use only one crystal oscillator source when designing circuits to avoid subtle failure modes of metastability in electronics. If this is not possible, the number of distinct crystal oscillators, PLLs, and their associated clock domains should be rigorously minimized, through techniques such as using a subdivision of an existing clock instead of a new crystal source. Each new distinct crystal source needs to be rigorously justified, since each one introduces new, difficult to debug probabilistic failure modes, due to multiple crystal interactions, into equipment.
Commonly used crystal frequencies
{| class="wikitable sortable"! Frequency (MHz)! Primary uses|-| 32.768 kHz| Real-time clocks, allows binary division to 1 Hz signal (215 x 1 Hz); also often used in low-speed low-power circuits] clock; allows integer division to common baud rates] clock; allows integer division to common baud rates up to 38400|-| 3.2768| allows binary division to 100 Hz (32768x 100 Hz, or 215 x 100 Hz)|-| 3.575611|
PAL Broadcast television systems#ITU identification scheme color subcarrier M color subcarrier; very common and inexpensive, used in many other applications, eg. [DTMF generators] Broadcast television systems#ITU identification scheme color subcarrier|-|
3.686400|
UART clock (2x 1.8432 MHz); allows integer division to common baud rates]s, clearly divides to 1 Hz signal (222 x 1 Hz)|-| 4.433618|
PAL Broadcast television systems#ITU identification scheme and NTSC M4.43 color subcarrier|-| 4.9152| Used in
CDMA systems; divided to 1.2288 MHz baseband frequency as specified by J-STD-008] source|-| 6.144| digital audio systems -
digital audio tape, MiniDisc, sound cards; 128x 48 kHz (27 x 48 kHz). Also allows integer division to common UART baud rates up to 38400.]es|-|
7.15909| NTSC M color subcarrier (2x 3.579545 MHz)|-|
7.3728|
UART clock (4x 1.8432 MHz); allows integer division to common
baud rates] systems (2x 4.9152); divided to 1.2288 MHz baseband frequency|-| 10.245| used in radio transceivers; mixes with 10.7 MHz subcarrier yielding 455 kHz signal, a common second
intermediate frequency for FM radio and first IF for AM radio source|-|
11.0592| [UART clock (6x 1.8432 MHz); allows integer division to common baud rates] digital audio systems and CDROM drives; allows binary division to 44.1 kHz (256x 44.1 kHz), 22.05 kHz, and 11.025 kHz], MiniDisc, sound cards; 256x 48 kHz (28 x 48 kHz). Also allows integer division to common UART baud rates up to 38400.] circuits; 2x 6.9375 MHz (clock frequency of PAL B teletext; SECAM uses 6.203125 MHz, NTSC M uses 5.727272 MHz, PAL G uses 6.2031 MHz, and PAL I uses 4.4375 MHz clock)|-|
14.3182| NTSC M color subcarrier (4x 3.579545 MHz). Also common on
VGA cards.] clock (8x 1.8432 MHz); allows integer division to common baud rates|-| 16.368| Commonly used for down-conversion and sampling in GPS-receivers. Generates
Intermediate_frequency signal at +4.092 MHz. 16.3676 or 16.367667 MHz are sometimes used to avoid perfect lineup between sampling frequency and GPS
CDMA.|-| 16.9344| Used in
compact disc digital audio systems and CDROM drives; allows integer division to 44.1 kHz (384x 44.1 kHz), 22.05 kHz, and 11.025 kHz. Also allows integer division to common UART baud rates.] clock (10x 1.8432 MHz); allows integer division to common baud rates. Also allows integer division to 48 kHz (384x 48 kHz), 96 kHz, and 192 kHz samplerates used in high-end digital audio.|-|
19.6608| Used in
CDMA systems (4x 4.9152); divided to 1.2288 MHz baseband frequency],
MiniDisc,
sound cards; 512x 48 kHz (29 x 48 kHz)] clock (16x 1.8432 MHz); allows integer division to common baud rates|}
Series or parallel resonance
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 at parallel resonance, which means that the crystal impedance appears infinite. Any additional circuit capacitance will thus pull the frequency down. For a parallel resonance crystal to operate at its specified frequency, the electronic circuit has to provide a total parallel capacitance as specified by the crystal manufacturer.
Crystals above 30 MHz (up to >200 MHz) are generally operated at series resonance where the impedance appears at its minimum and equal to the series resistance. For this reason the series resistance is specified (
for a piezoelectric crystal resonatorA
crystal oscillator is an electronic circuit that uses the mechanical resonance of a vibrating crystal of Piezoelectricity#Materials to create an electrical signal with a very precise
frequency. This frequency is commonly used to keep track of time (as in
quartz clock), to provide a stable clock signal for
digital integrated circuits, and to stabilize frequencies for radio transmitters.
Using an amplifier and
feedback, it is an especially accurate form of an electronic oscillator. The crystal used therein is sometimes called a "timing crystal". On schematic a crystal is labeled
Y.
Crystals for timing purposes
quartz crystal enclosed in an hermetically sealed HC-49/US package, used as the resonator in a crystal oscillator.
A
crystal is a solid in which the constituent atoms,
molecules, or
ions are packed in a regularly ordered, repeating pattern extending in all three spatial dimensions.
Almost any object made of an elastic material could be used like a crystal, with appropriate transducers, since all objects have natural
resonance frequencies of vibration. For example, steel is very elastic and has a high speed of sound. It was often used in mechanical filters before quartz. The resonant frequency depends on size, shape, elasticity (physics), and the speed of sound in the material. High-frequency crystals are typically cut in the shape of a simple, rectangular plate. Low-frequency crystals, such as those used in digital watches, are typically cut in the shape of a
tuning fork. For applications not needing very precise timing, a low-cost ceramic resonator is often used in place of a quartz crystal.
When a crystal of
quartz is properly cut and mounted, it can be made to distort in an electric field by applying a
voltage to an electrode near or on the crystal. This property is known as piezoelectricity. When the field is removed, the quartz will generate an electric field as it returns to its previous shape, and this can generate a voltage. The result is that a quartz crystal behaves like a circuit composed of an inductor,
capacitor and
resistor, with a precise resonant frequency. (See RLC circuit.)
Quartz has the further advantage that its elastic constants and its size change in such a way that the frequency dependence on temperature can be very low. The specific characteristics will depend on the mode of vibration and the angle at which the quartz is cut (relative to its crystallographic axes)1 Therefore, the resonant frequency of the plate, which depends on its size, will not change much, either. This means that a quartz clock, filter or oscillator will remain accurate. For critical applications the quartz oscillator is mounted in a temperature-controlled container, called a
crystal oven, and can also be mounted on shock absorbers to prevent perturbation by external mechanical vibrations.
Quartz timing crystals are manufactured for frequencies from a few tens of
kilohertz to tens of megahertz. More than two billion (2×109) crystals are manufactured annually. Most are small devices for consumer devices such as wristwatches, clocks, radios, computers, and
cellphones. Quartz crystals are also found inside test and measurement equipment, such as counters, signal generators, and
oscilloscopes.
Crystal modelling
A quartz crystal can be modelled as an electrical network with a low
Electrical impedance (series) and a high
Electrical impedance (parallel) resonance point spaced closely together. Mathematically the impedance of this network can be written as:
Z(s) = \left( {\frac{1}{s\cdot C_1}+s\cdot L_1+R_1} \right) || \left( {\frac{1}{s\cdot C_0--> \right)
or,
Z(s) = \frac{s^2 + s\frac{R_1}{L_1} + {\omega_s}^2}{s + s\frac{R_1}{L_1} + {\omega_p}^2} \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-->
where s is the complex frequency (s=j\omega), \omega_s is the series resonant frequency in radians per second and \omega_p is the parallel resonant frequency in radians per second.
Adding additional capacitance across a crystal will cause the parallel resonance to shift downward. This can be used to adjust the frequency that a crystal oscillator oscillates at. Crystal manufacturers normally cut and trim their crystals to have a specified resonant frequency with a known 'load' capacitance added to the crystal. For example, a 6 pF 32 kHz crystal has a parallel resonance frequency of 32,768 Hz when a 6.0 pF capacitor is placed across the crystal. Without this capacitance, the resonance frequency is higher than 32,768 Hz.
Temperature effects
A crystal's frequency characteristic depends on the shape or 'cut' of the crystal. A tuning fork crystal is usually cut such that its frequency over temperature is a parabolic curve centered around 25 °C. This means that a tuning fork crystal oscillator will resonate close to its target frequency at room temperature, but will slow down when the temperature either increases or decreases from room temperature. A common parabolic coefficient for a 32 kHz tuning fork crystal is −0.04 ppm/°C².
f = f_0 \ \mbox{ppm}(T-T_0)^2
In a real application, this means that a clock built using a regular 32 kHz tuning fork crystal will keep good time at room temperature, lose 2 minutes per year at 10 degrees Celsius above (or below) room temperature and lose 8 minutes per year at 20 degrees Celsius above (or below) room temperature.
Crystals and frequency
equipment to select frequency.
The crystal oscillator circuit sustains oscillation by taking a voltage signal from the quartz resonator, amplifying it, and feeding it back to the resonator. The rate of expansion and contraction of the quartz is the resonance frequency, and is determined by the cut and size of the crystal.
A regular timing crystal contains two electrically conductive plates, with a slice or tuning fork of quartz crystal sandwiched between them. During startup, the circuit around the crystal applies a random noise Alternating current signal to it, and purely by chance, a tiny fraction of the noise will be at the resonant frequency of the crystal. The crystal will therefore start oscillating in synchrony with that signal. As the oscillator amplifies the signals coming out of the crystal, the crystal's frequency will become stronger, eventually dominating the output of the oscillator. Natural resistance in the circuit and in the quartz crystal electronic filter out all the unwanted frequencies.
One of the most important traits of quartz crystal oscillators is that they can exhibit very low phase noise. In other words, the signal they produce is a pure tone. This makes them particularly useful in telecommunications where stable signals are needed, and in scientific equipment where very precise time references are needed.
The output frequency of a quartz oscillator is either the fundamental resonance or harmonic, called an overtone frequency.
A typical Q factor for a quartz oscillator ranges from 104 to 106. The maximum
Q for a high stability quartz oscillator can be estimated as
Q = 1.6 × 107/
f, where
f is the resonance frequency in megahertz.
Environmental changes of temperature, humidity, pressure, and vibration can change the resonant frequency of a quartz crystal, but there are several designs that reduce these environmental effects. These include the TCXO, MCXO, and OCXO (defined below). These designs (particularly the OCXO) often produce devices with excellent short-term stability. The limitations in short-term stability are due mainly to noise from electronic components in the oscillator circuits. Long term stability is limited by aging of the crystal.
Due to aging and environmental factors such as temperature and vibration, it is hard to keep even the best quartz oscillators within one part in 10−10 of their nominal frequency without constant adjustment. For this reason,
atomic oscillators are used for applications that require better long-term stability and accuracy.
Although crystals can be fabricated for any desired resonant frequency, within technological limits, in actual practice today engineers design crystal oscillator circuits around relatively few standard frequencies, such as 3.58 MHz, 10 MHz, 14.318 MHz, 20 MHz, 33.33 MHz, and 40 MHz. The vast popularity of the 3.58MHz and 14.318MHz crystals is attributed initially to low cost resulting from mass production resulting from the popularity of television and the fact that this frequency is involved in synchronizing to the colorburst signal necessary to display color on an NTSC or
PAL based
television set. Using
frequency dividers, frequency multipliers and phase locked loop circuits, it is possible to synthesize any desired frequency from the reference frequency.
Care must be taken to use only one crystal oscillator source when designing circuits to avoid subtle failure modes of
metastability in electronics. If this is not possible, the number of distinct crystal oscillators, PLLs, and their associated clock domains should be rigorously minimized, through techniques such as using a subdivision of an existing clock instead of a new crystal source. Each new distinct crystal source needs to be rigorously justified, since each one introduces new, difficult to debug probabilistic failure modes, due to multiple crystal interactions, into equipment.
Commonly used crystal frequencies
{| class="wikitable sortable"! Frequency (MHz)! Primary uses|-| 32.768 kHz|
Real-time clocks, allows binary division to 1 Hz signal (215 x 1 Hz); also often used in low-speed low-power circuits] clock; allows integer division to common
baud rates] clock; allows integer division to common baud rates up to 38400|-| 3.2768| allows binary division to 100 Hz (32768x 100 Hz, or 215 x 100 Hz)|-| 3.575611| PAL Broadcast television systems#ITU identification scheme color subcarrier M color subcarrier; very common and inexpensive, used in many other applications, eg. [DTMF generators] Broadcast television systems#ITU identification scheme color subcarrier|-|
3.686400| UART clock (2x 1.8432 MHz); allows integer division to common baud rates]s, clearly divides to 1 Hz signal (222 x 1 Hz)|-| 4.433618|
PAL Broadcast television systems#ITU identification scheme and NTSC M4.43 color subcarrier|-| 4.9152| Used in CDMA systems; divided to 1.2288 MHz baseband frequency as specified by J-STD-008] source|-| 6.144| digital audio systems - digital audio tape,
MiniDisc, sound cards; 128x 48 kHz (27 x 48 kHz). Also allows integer division to common UART baud rates up to 38400.]es|-|
7.15909| NTSC M color subcarrier (2x 3.579545 MHz)|-|
7.3728|
UART clock (4x 1.8432 MHz); allows integer division to common baud rates] systems (2x 4.9152); divided to 1.2288 MHz baseband frequency|-| 10.245| used in radio transceivers; mixes with 10.7 MHz subcarrier yielding 455 kHz signal, a common second
intermediate frequency for
FM radio and first IF for AM radio source|-|
11.0592| [UART clock (6x 1.8432 MHz); allows integer division to common baud rates] digital audio systems and
CDROM drives; allows binary division to 44.1 kHz (256x 44.1 kHz), 22.05 kHz, and 11.025 kHz],
MiniDisc,
sound cards; 256x 48 kHz (28 x 48 kHz). Also allows integer division to common UART baud rates up to 38400.] circuits; 2x 6.9375 MHz (clock frequency of PAL B teletext; SECAM uses 6.203125 MHz, NTSC M uses 5.727272 MHz, PAL G uses 6.2031 MHz, and PAL I uses 4.4375 MHz clock)|-|
14.3182| NTSC M color subcarrier (4x 3.579545 MHz). Also common on VGA cards.] clock (8x 1.8432 MHz); allows integer division to common baud rates|-| 16.368| Commonly used for down-conversion and sampling in
GPS-receivers. Generates
Intermediate_frequency signal at +4.092 MHz. 16.3676 or 16.367667 MHz are sometimes used to avoid perfect lineup between sampling frequency and GPS
CDMA.|-| 16.9344| Used in
compact disc digital audio systems and CDROM drives; allows integer division to 44.1 kHz (384x 44.1 kHz), 22.05 kHz, and 11.025 kHz. Also allows integer division to common UART baud rates.] clock (10x 1.8432 MHz); allows integer division to common baud rates. Also allows integer division to 48 kHz (384x 48 kHz), 96 kHz, and 192 kHz samplerates used in high-end digital audio.|-|
19.6608| Used in CDMA systems (4x 4.9152); divided to 1.2288 MHz baseband frequency],
MiniDisc,
sound cards; 512x 48 kHz (29 x 48 kHz)] clock (16x 1.8432 MHz); allows integer division to common baud rates|}
Series or parallel resonance
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 at parallel resonance, which means that the crystal impedance appears infinite. Any additional circuit capacitance will thus pull the frequency down. For a parallel resonance crystal to operate at its specified frequency, the electronic circuit has to provide a total parallel capacitance as specified by the crystal manufacturer.
Crystals above 30 MHz (up to >200 MHz) are generally operated at series resonance where the impedance appears at its minimum and equal to the series resistance. For this reason the series resistance is specified (
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