A
crystal oscillator is an
electronic circuit that uses the
mechanical
resonance of a vibrating
crystal of
piezoelectric material to create
an electrical signal with a very precise
frequency. This frequency is commonly used to keep
track of time (as in
quartz
wristwatches), to provide a stable
clock signal for
digital
integrated circuits, and to
stabilize frequencies for
radio
transmitters and
receivers. The
most common type of piezoelectric resonator used is the
quartz crystal, so oscillator circuits
designed around them were called "crystal oscillators".
History
Piezoelectricity was discovered by
Jacques and
Pierre
Curie in 1880.
Paul Langevin first
investigated quartz resonators for use in
sonar during World War I. The first crystal controlled
oscillator, using a crystal of
Rochelle salt, was built in 1917 and
patented in 1918 by Alexander M.
Nicholson at Bell Telephone
Laboratories
, although his priority was disputed by Walter Guyton Cady. Cady built the
first quartz crystal oscillator in 1921.Other early innovators in
quartz crystal oscillators include
G.
W. Pierce
and
Louis Essen.
Quartz crystal oscillators were developed for high-stability
frequency references during the 1920s and 1930s. By 1926 quartz
crystals were used to control the frequency of radio broadcasting
stations and were popular with amateur radio operators. A number of
firms started producing quartz crystals for electronic use during
this time. Using what are now considered primitive methods, about
100,000 crystal units were produced in the United States during
1939. During WW2, demand for accurate frequency control of military
radio equipment spurred rapid development of the crystal
manufacturing industry. Suitable quartz became a critical war
material, with much of it imported from Brazil.
Although crystal oscillators still most commonly use quartz
crystals, devices using other materials are becoming more common,
such as
ceramic resonators.
Operation
A
crystal is a
solid in
which the constituent
atoms,
molecules, or
ions are packed in
a regularly ordered, repeating pattern extending in all three
spatial dimensions.
Almost any object made of an elastic material could be used like a
crystal, with appropriate transducers, since all objects have
natural
resonant frequencies of vibration.
For example,
steel is very elastic and has a
high speed of sound. It was often used in mechanical filters before
quartz. The resonant frequency depends on size, shape,
elasticity, and the speed of sound in
the material. High-frequency crystals are typically cut in the
shape of a simple, rectangular plate. Low-frequency crystals, such
as those used in digital watches, are typically cut in the shape of
a
tuning fork. For applications not
needing very precise timing, a low-cost
ceramic resonator is often used in place
of a quartz crystal.
When a crystal of
quartz is properly cut and
mounted, it can be made to distort in an electric field by applying
a
voltage to an
electrode near or on the crystal. This property is
known as
piezoelectricity. When the
field is removed, the quartz will generate an electric field as it
returns to its previous shape, and this can generate a voltage. The
result is that a quartz crystal behaves like a circuit composed of
an
inductor,
capacitor and
resistor,
with a precise resonant frequency. (See
RLC
circuit.)
Quartz has the further advantage that its elastic constants and its
size change in such a way that the frequency dependence on
temperature can be very low. The specific characteristics will
depend on the mode of vibration and the angle at which the quartz
is cut (relative to its crystallographic axes). 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 (2×10
9) crystals are manufactured
annually. Most are small devices for consumer devices such as
wristwatches,
clocks,
radios,
computers, and
cellphones.
Quartz crystals are also found inside test and measurement
equipment, such as counters,
signal
generators, and
oscilloscopes.
Modeling
Electrical model
Schematic symbol and equivalent circuit for a quartz crystal in an
oscillator
A quartz crystal can be modelled as an electrical network with a
low
impedance (series) and a
high
impedance (parallel)
resonance point spaced closely together. Mathematically (using the
Laplace transform) the impedance
of this network can be written as:
- Z(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\cdot
C_0)[s^2 + 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}} =
\omega_s \sqrt{1+\frac{C_1}{C_0}} \approx \omega_s \left(1 +
\frac{C_1}{2 C_0}\right) \quad (C_0 \gg C_1)
where s is the complex frequency (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 at which a crystal oscillator 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 6 pF 32 kHz crystal has a
parallel resonance frequency of 32,768 Hz when a 6.0 pF
capacitor is placed across the crystal. Without this capacitance,
the resonance frequency is higher than 32,768 Hz.
Resonance modes
A quartz crystal provides both series and parallel resonance. The
series resonance is a few kilohertz lower than the parallel one.
Crystals below 30 MHz are generally operated between series
and parallel resonance, which means that the crystal appears as an
inductive reactance in
operation. Any additional circuit capacitance will thus pull the
frequency down. For a parallel resonance crystal to operate at its
specified frequency, the electronic circuit has to provide a total
parallel capacitance as specified by the crystal
manufacturer.
Crystals above 30 MHz (up to >200 MHz) are generally
operated at series resonance where the impedance appears at its
minimum and equal to the series resistance. For 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="" its=""
overtone modes, which occur at multiples of the
fundamental resonant frequency. Only odd numbered overtones are
used. Such a crystal is referred to as a 3rd, 5th, or even 7th
overtone crystal. To accomplish this, the oscillator circuit
usually includes additional
LC circuits
to select the wanted overtone.
Temperature effects
A crystal's frequency characteristic depends on the shape or 'cut'
of the crystal. A tuning fork crystal is usually cut such that its
frequency over temperature is a parabolic curve centered around 25
°C. This means that a tuning fork crystal oscillator will resonate
close to its target frequency at room temperature, but will slow
down when the temperature either increases or decreases from room
temperature. A common parabolic coefficient for a 32 kHz
tuning fork crystal is −0.04 ppm/°C².
- f = f_0[1-0.04 \ \mbox{ppm}(T-T_0)^2]
In a real application, this means that a clock built using a
regular 32 kHz tuning fork crystal will keep good time at room
temperature, lose 2 minutes per year at 10 degrees Celsius above
(or below) room temperature and lose 8 minutes per year at 20
degrees Celsius above (or below) room temperature due to the quartz
crystal.
Electrical oscillators
The crystal oscillator circuit sustains oscillation by taking a
voltage signal from the quartz resonator, amplifying it, and
feeding it back to the resonator. The rate of expansion and
contraction of the quartz is the
resonant
frequency, and is determined by the cut and size of the crystal.
When the energy of the generated output frequencies matches the
losses in the circuit, an oscillation can be sustained.
A regular timing crystal contains two electrically conductive
plates, with a slice or tuning fork of quartz crystal sandwiched
between them. During startup, the circuit around the crystal
applies a random noise
AC signal
to it, and purely by chance, a tiny fraction of the noise will be
at the resonant frequency of the crystal. The crystal will
therefore start oscillating in synchrony with that signal. As the
oscillator amplifies the signals coming out of the crystal, the
signals in the crystal's frequency band will become stronger,
eventually dominating the output of the oscillator. Natural
resistance in the circuit and in the quartz crystal
filter out all the unwanted
frequencies.
The output frequency of a quartz oscillator can be either the
fundamental resonance or a
multiple of the
resonance, called an
overtone
frequency. High frequency crystals are often designed to operate at
third, fifth, or seventh overtones.
A major reason for the wide use of crystal oscillators is their
high
Q factor. A typical
Q value
for a quartz oscillator ranges from 10
4 to
10
6, compared to perhaps 10
2 for an
LC oscillator. The maximum
Q for a
high stability quartz oscillator can be estimated as
Q =
1.6 × 10
7/
f, where
f is the resonance
frequency in megahertz.
One of the most important traits of quartz crystal oscillators is
that they can exhibit very low
phase
noise.In many oscillators, any spectral energy at the resonant
frequency will be amplified by the oscillator, resulting in a
collection of tones at different phases.In a crystal oscillator,
the crystal mostly vibrates in one axis, therefore only one phase
is dominant.This property of low phase noise makes them
particularly useful in telecommunications where stable signals are
needed, and in scientific equipment where very precise time
references are needed.
Environmental changes of temperature, humidity, pressure, and
vibration can change the resonant frequency of a quartz crystal,
but there are several designs that reduce these environmental
effects. These include the TCXO, MCXO, and OCXO (defined below).
These designs (particularly the OCXO) often produce devices with
excellent short-term stability. The limitations in short-term
stability are due mainly to noise from electronic components in the
oscillator circuits. Long term stability is limited by aging of the
crystal.
Due to aging and environmental factors (such as temperature and
vibration), it is difficult to keep even the best quartz
oscillators within one part in 10
10 of their nominal
frequency without constant adjustment. For this reason,
atomic oscillators are used for
applications requiring better long-term stability and
accuracy.
Although crystals can be fabricated for any desired resonant
frequency, within technological limits, in actual practice today
engineers design crystal oscillator circuits around relatively few
standard frequencies, such as 3.58 MHz, 10 MHz,
14.318 MHz, 20 MHz, 33.33 MHz, and 40 MHz. The
vast popularity of the 3.58 MHz and 14.318 MHz crystals
is attributed initially to low cost resulting from
economies of scale resulting from the
popularity of television and the fact that this frequency is
involved in synchronizing to the
colorburst signal necessary to display color on
an
NTSC or
PAL based
television set. Using
frequency dividers,
frequency multipliers and
phase locked loop circuits, it is
practical to derive a wide range of frequencies from one reference
frequency.
Care must be taken to use only one crystal oscillator source when
designing circuits to avoid subtle failure modes of
metastability in electronics.
If this is not possible, the number of distinct crystal
oscillators,
PLLs, and their
associated clock domains should be rigorously minimized, through
techniques such as using a subdivision of an existing clock instead
of a new crystal source. Each new crystal source must be rigorously
justified, since each one introduces new, difficult-to-debug
probabilistic failure modes, due to multiple crystal
interactions.
Spurious frequencies
For crystals operated in series resonance, significant (and
temperature-dependent) spurious responses may be experienced. These
responses typically appear some tens of kilohertz above the wanted
series resonance. Even if the series resistances at the spurious
resonances appear higher than the one at wanted frequency, the
oscillator may lock at a spurious frequency (at some temperatures).
This is generally avoided by using low impedance oscillator
circuits to enhance the series resistance differences.
Commonly used crystal frequencies
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 certain
crystal frequencies are made in large quantities and stocked by
electronics distributors.
| Frequency (MHz) |
comm |
A/V |
RTC |
Primary uses |
| 0.032768 |
|
|
X |
Real-time clocks, quartz watches and clocks; allows binary
division to 1 Hz signal (215×1 Hz) |
| 1.8432 |
UART |
|
|
UART clock; allows integer division to
common baud rates.
(213×32×52; 16×115,200 baud or
96×16×1,200 baud) |
| 2.4576 |
UART |
|
|
UART clock; allows integer division to
common baud rates up to 38,400.
(215×31×52; 64×38,400 baud or
2048×1,200 baud) |
| 3.2768 |
|
|
|
Allows binary division to 100 Hz (32,768×100 Hz, or
215×100 Hz) |
| 3.575611 |
|
PAL |
|
PAL M
color subcarrier |
| 3.579545 |
|
NTSC |
|
NTSC M color subcarrier. Because these are
very common and inexpensive they are used in many other
applications, for example DTMF generators |
| 3.582056 |
|
PAL |
|
PAL N
color subcarrier |
| 3.686400 |
UART |
|
|
UART clock (2×1.8432 MHz); allows
integer division to common baud rates |
| 4.096000 |
|
|
|
Allows binary division to 1 kHz
(212×1 kHz) |
| 4.194304 |
|
|
X |
Real-time clocks, divides to
1 Hz signal (222×1 Hz) |
| 4.332 |
RDS |
|
|
The RDS signal bit rate is at
1.1875 kbit/s. While the frequency of 4.332 MHz is the
most commonly used crystal resonator, its multiples
(2×4.332 MHz = 8.664 MHz or 4×4.332 MHz =
17.328 MHz) have been used also. |
| 4.43361875 |
|
PAL/NTSC |
|
PAL B/D/G/H/I
and NTSC M4.43 color subcarrier |
| 4.9152 |
CDMA |
|
|
Used in CDMA systems; divided to
1.2288 MHz baseband frequency as specified by J-STD-008 |
| 6.144 |
UART |
audio |
|
Digital audio systems - DAT,
MiniDisc, sound
cards; 128×48 kHz (27×48 kHz). Also allows
integer division to common UART baud rates up to 38,400. |
| 6.5536 |
|
|
|
Allows binary division to 100 Hz (65,536×100 Hz, or
216×100 Hz); used also in red box |
| 7.15909 |
|
NTSC |
|
NTSC M color subcarrier (2×3.579545 MHz) |
| 7.3728 |
UART |
|
|
UART clock (4×1.8432 MHz); allows
integer division to common baud rates |
| 8.86724 |
|
PAL |
|
PAL B/G/H color subcarrier (2×4.433618 MHz) |
| 9.216 |
|
|
X |
Allows integer division to 1024 kHz and binary division to
lower frequencies that are whole multiples of 1 Hz. |
| 9.83040 |
CDMA |
|
|
Used in CDMA systems (2×4.9152 MHz);
divided to 1.2288 MHz baseband frequency |
| 10.245 |
FM radio |
|
|
Used in radio receivers; mixes with 10.7 MHz intermediate frequency (IF) yielding
455 kHz signal, a common second IF for FM
radio |
| 11.0592 |
UART |
|
|
UART clock (6×1.8432 MHz); allows
integer division to common baud rates |
| 11.2896 |
|
audio |
|
Used in compact disc digital audio
systems and CDROM drives; allows binary
division to 44.1 kHz (256×44.1 kHz), 22.05 kHz, and
11.025 kHz |
| 12.0000 |
USB |
|
|
Used in USB systems as the reference clock
for the full-speed PHY rate of 12 Mbit/s, or multiplied up using a
PLL to clock high speed PHYs at 480 Mbit/s |
| 12.288 |
UART |
audio |
|
Digital audio systems - DAT,
MiniDisc, sound
cards; 256×48 kHz (28×48 kHz). Also allows
integer division to common UART baud rates up to 38400. |
| 13.500 |
|
PAL/NTSC |
|
Master clock for PAL/NTSC DVD players, Digital TV receivers,
etc. (13.5 MHz is an exact multiple of the PAL and NTSC line frequencies) |
| 13.56 |
RFID |
|
|
Common contactless smartcard frequency (ISO/IEC 14443) |
| 13.875 |
teletext |
|
|
Used in some teletext circuits;
2×6.9375 MHz (clock frequency of PAL B teletext; SECAM uses
6.203125 MHz, NTSC M uses 5.727272 MHz, PAL G uses
6.2031 MHz, and PAL I uses 4.4375 MHz clock) |
| 14.31818 |
|
NTSC |
|
NTSC M color subcarrier (4×3.579545 MHz). Common seed
clock for modern PC motherboard clock generator chips, also common
on VGA cards. |
| 14.7456 |
UART |
|
|
UART clock (8×1.8432 MHz); allows
integer division to common baud rates |
| 16.368 |
GPS |
|
|
Commonly used for down-conversion and sampling in GPS-receivers. Generates intermediate frequency signal at
4.092 MHz. 16.3676 or 16.367667 MHz are sometimes used to
avoid perfect lineup between sampling frequency and GPS spreading code. |
| 16.9344 |
|
audio |
|
Used in compact disc digital audio
systems and CDROM drives; allows integer
division to 44.1 kHz (384×44.1 kHz), 22.05 kHz, and
11.025 kHz. Also allows integer division to common UART baud
rates. |
| 17.734475 |
|
PAL |
|
PAL B/G/H color subcarrier (4×4.433618 MHz) |
| 18.432 |
UART |
audio |
|
UART clock (10×1.8432 MHz); allows
integer division to common baud rates. Also allows integer division
to 48 kHz (384×48 kHz), 96 kHz, and 192 kHz
sample rates used in high-end digital audio. |
| 19.6608 |
CDMA |
|
|
Used in CDMA systems (4×4.9152); divided to
1.2288 MHz baseband frequency |
| 20.000 |
Ethernet |
|
|
10 Mbit/s ethernet |
| 22.1184 |
UART |
|
|
UART clock (12×1.8432 MHz); allows
integer division to common baud rates |
| 24 |
USB |
|
|
full-speed USB (24 MHz * 20 = 480Mbit/s); LCD monitor some
MCU |
| 24.576 |
Firewire |
audio |
|
Digital audio systems - DAT,
MiniDisc, AC'97,
sound cards; 512×48 kHz
(29×48 kHz); also used as bus reference clock in
Firewire systems |
| 25.000 |
Ethernet |
|
|
Fast Ethernet MII clock (100 Mbps/4-bit
nibble) |
| 25.175 |
|
VGA |
|
Common Video Graphics Array
pixel clock (i.e., 640x350@70 Hz,640x400@70 Hz,
640x480@60 Hz) |
| 26.000 |
GSM/UMTS |
|
|
Commonly used as a reference clock for GSM
and UMTS handsets. (26 MHz is exactly 96
times the GSM bit rate) |
| 26.2144 |
|
|
|
Popular for 102.4 kS/s, 204.8 kS/s or similar sampling systems,
when a power-of-two size FFT follows the
sampling. In this case the FFT frequency bins end up to be
at "nice" frequencies for humans. Also allows integer division to
25 Hz and multiples of 25 Hz (50 Hz, 100 Hz, 200 Hz);
26.2144 MHz = 100 x 218 = 25 x 220. |
| 27.000 |
|
PAL/NTSC |
|
Master clock for PAL/NTSC DVD players, Digital TV receivers,
some modems etc. (27 MHz is an exact
multiple of the PAL and NTSC
line frequencies) |
| 28.224 |
modems |
|
|
used in some modems |
| 28.375 |
|
PAL |
|
Master clock for some PAL CCD cameras; 2 periods per pixel,
1816 periods per scan line, 567500 periods per frame |
| 28.636 |
|
NTSC |
|
Master clock for some NTSC CCD cameras |
| 29.4912 |
UART |
|
|
UART clock (16×1.8432 MHz); allows
integer division to common baud rates |
| 30.0000 |
|
|
|
common CPU clock |
| 33.33 |
|
|
|
common CPU clock |
| 40.000 |
|
|
|
common CPU clock, WiFi, OFDM |
| 50.000 |
Ethernet |
|
|
Fast Ethernet (2×25 MHz) |
| 66.667 |
|
|
|
common CPU clock |
| 80.0000 |
|
|
|
common CPU clock |
Circuit notations and abbreviations
On electrical schematic diagrams,
crystals are designated
with the class letter
Y (Y1, Y2, etc.) Oscillators,
whether they are crystal
oscillators or other, are
designated with the class letter
G (G1, G2, etc.) (See
IEEE Std
315-1975, or
ANSI Y32.2-1975.) On
occasion, one may see a crystal designated on a schematic with
X or
XTAL, or a crystal oscillator with
XO, but these forms are deprecated.
Crystal oscillator types and their abbreviations:
See also
References
- , filed April 10, 1918, granted August 27, 1940
- http://www.ieee-uffc.org/fc_history/bottom.html A History of
the Quartz Crystal Industry in the USA, Virgil E. Bottom, from the
Proceedings of the 35th Annual Frequency Control Symposium 1981,
retrieved June 19, 2008
- [1]
- http://www.tinyvga.com/vga-timing VGA Signal Timing
7 * Ulrich L. Rohde "Microwave and Wireless Synthesizers: Theory
and Design ", John Wiley & Sons, August 1997, ISBN
0-471-52019-5
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