Modelo Electrico en Ingles
description
Transcript of Modelo Electrico en Ingles
7/18/2019 Modelo Electrico en Ingles
http://slidepdf.com/reader/full/modelo-electrico-en-ingles 1/10
Modeling[edit]
Electrical model[edit]
Electronic symbol for a piezoelectric crystal resonator
A quartz crystal can be modelled as an electrical network with a low impedance (series)
and a high impedance (parallel) resonance point spaced closely together. athematically
(using the !aplace transform) the impedance of this network can be written as"
or#
where s is the comple$ frequency ( )# is the series resonant angular
frequency and is the parallel resonant angular frequency.
%chematic symbol and equi&alent 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. 'his can be used to adust the frequency
at which a crystal oscillates. rystal manufacturers normally cut and trim their
crystals to ha&e a specified resonance frequency with a known *load*
capacitance added to the crystal. +or e$ample# a crystal intended for a , p+
load has its specified parallel resonance frequency when a ,.- p+ capacitor is
placed across it. ithout this capacitance# the resonance frequency is higher.
Resonance modes[edit]
7/18/2019 Modelo Electrico en Ingles
http://slidepdf.com/reader/full/modelo-electrico-en-ingles 2/10
Temperature effects[edit]
A crystal*s frequency characteristic depends on the shape or *cut* of the crystal.
A tuning fork crystal is usually cut such that its frequency o&er temperature is a
parabolic cur&e centered around /0 1. 'his means that a tuning fork crystal
oscillator will resonate close to its target frequency at room temperature# but
will slow down when the temperature either increases or decreases from room
temperature. A common parabolic coefficient for a 2/ k3z tuning fork crystal is
4-.-5 ppm617.
8n a real application# this means that a clock built using a regular 2/ k3z
tuning fork crystal will keep good time at room temperature# lose / minutes
per year at 9- degrees elsius abo&e (or below) room temperature and
lose : minutes per year at /- degrees elsius abo&e (or below) room
temperature due to the quartz crystal.
Electrical oscillators[edit]
A crystal used in hobby radio controlequipment to select frequency.
'he crystal oscillator circuit sustains oscillation by taking a &oltage signal
from the quartz resonator # amplifying it# and feeding it back to the
resonator. 'he rate of e$pansion and contraction of the quartz is
the resonant frequency# and is determined by the cut and size of the
crystal. hen the energy of the generated output frequencies matches thelosses in the circuit# an oscillation can be sustained.
An oscillator crystal has two electrically conducti&e plates# with a slice or
tuning fork of quartz crystal sandwiched between them. ;uring startup# the
controlling circuit places the crystal into an unstable equilibrium# and due
to the positi&e feedback in the system# any tiny fraction of noise will start to
get amplified# ramping up the oscillation. 'he crystal resonator can also be
seen as a highly frequency<selecti&e filter in this system" it will only pass a
&ery narrow subband of frequencies around the resonant one# attenuating
e&erything else. E&entually# only the resonant frequency will be acti&e. As
7/18/2019 Modelo Electrico en Ingles
http://slidepdf.com/reader/full/modelo-electrico-en-ingles 3/10
the oscillator amplifies the signals coming out of the crystal# the signals in
the crystal*s frequency band will become stronger# e&entually dominating
the output of the oscillator. 'he narrow resonance band of the quartz
crystal filters out all the unwanted frequencies.
'he output frequency of a quartz oscillator can be either that of the
fundamental resonance or of a multiple of that resonance# called
aharmonic frequency. 3armonics are an e$act integer multiple of the
fundamental frequency. =ut# like many other mechanical resonators#
crystals e$hibit se&eral modes of oscillation# usually at appro$imately odd
integer multiples of the fundamental frequency. 'hese are termed
>o&ertone modes># and oscillator circuits can be designed to e$cite them.
'he o&ertone modes are at frequencies which are appro$imate# but not
e$act odd integer multiples of that of the fundamental mode# and o&ertone
frequencies are therefore not e$act harmonics of the fundamental.
A maor reason for the wide use of crystal oscillators is their high ? factor .
A typical Q &alue for a quartz oscillator ranges from 9-5 to 9-,# compared
to perhaps 9-/ for an ! oscillator . 'he ma$imum Q for a high stability
quartz oscillator can be estimated as Q @ 9., 9-B6f # where f is the
resonance frequency in megahertz.
Cne of the most important traits of quartz crystal oscillators is that they can
e$hibit &ery low phase noise. 8n many oscillators# any spectral energy at
the resonant frequency will be amplified by the oscillator# resulting in a
collection of tones at different phases. 8n a crystal oscillator# the crystal
mostly &ibrates in one a$is# therefore only one phase is dominant. 'his
property of low phase noise makes them particularly useful in
telecommunications where stable signals are needed# and in scientific
equipment where &ery precise time references are needed.
3igh frequency crystals are often designed to operate at third# fifth# or
se&enth o&ertones. anufacturers ha&e difficulty producing crystals thin
enough to produce fundamental frequencies o&er 2- 3z. 'o produce
higher frequencies# manufacturers make o&ertone crystals tuned to put the
2rd# 0th# or Bth o&ertone at the desired frequency# because they are thicker
and therefore easier to manufacture than a fundamental crystal that would
produce the same frequencyDalthough e$citing the desired o&ertone
frequency requires a slightly more complicated oscillator circuit. [9/][92][95][90]
[9,] A fundamental crystal oscillator circuit is simpler and more efficient and
has more pullability than a third o&ertone circuit. ;epending on the
7/18/2019 Modelo Electrico en Ingles
http://slidepdf.com/reader/full/modelo-electrico-en-ingles 4/10
manufacturer# the highest a&ailable fundamental frequency may be
/0 3z to ,, 3z.[9B][9:]
En&ironmental changes of temperature# humidity# pressure# and &ibrationcan change the resonant frequency of a quartz crystal# but there are
se&eral designs that reduce these en&ironmental effects. 'hese include the
'C# C# and CC (defined below). 'hese designs (particularly the
CC) often produce de&ices with e$cellent short<term stability. 'he
limitations in short<term stability are due mainly to noise from electronic
components in the oscillator circuits. !ong term stability is limited by aging
of the crystal.
;ue to aging and en&ironmental factors (such as temperature and
&ibration)# it is difficult to keep e&en the best quartz oscillators within one
part in 9-9- of their nominal frequency without constant adustment. +or this
reason# atomic oscillators are used for applications requiring better long<
term stability and accuracy.
Spurious frequencies[edit]
/0<3z crystal e$hibiting spurious response
+or crystals operated at series resonance or pulled away from the main
mode by the inclusion of a series inductor or capacitor# significant (and
temperature<dependent) spurious responses may be e$perienced. 'hough
most spurious modes are typically some tens of kilohertz abo&e the
wanted series resonance their temperature coefficient will be different from
the main mode and the spurious response may mo&e through the mainmode at certain temperatures. E&en if the series resistances at the
spurious resonances appear higher than the one at wanted frequency a
rapid change in the main mode series resistance can occur at specific
temperatures when the two frequencies are coincidental. A consequence
of these acti&ity dips is that the oscillator may lock at a spurious frequency
(at specific temperatures). 'his is generally minimized by ensuring that the
maintaining circuit has insufficient gain to acti&ate unwanted modes.
%purious frequencies are also generated by subecting the crystal to
&ibration. 'his modulates the resonance frequency to a small degree by
the frequency of the &ibrations. %<cut crystals are designed to minimize
7/18/2019 Modelo Electrico en Ingles
http://slidepdf.com/reader/full/modelo-electrico-en-ingles 5/10
the frequency effect of mounting stress and they are therefore less
sensiti&e to &ibration. Acceleration effects including gra&ity are also
reduced with % cut crystals as is frequency change with time due to long
term mounting stress &ariation. 'here are disad&antages with % 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 subect to a full ambient
range. % cut crystals are most ad&antageous where temperature control
at their temperature of zero temperature coefficient (turno&er) is possible#
under these circumstances an o&erall stability performance from premium
units can approach the stability of Fubidium frequency standards.
Commonly used crystal frequencies[edit]
Main article: Crystal oscillator frequencies
rystals can be manufactured for oscillation o&er a wide range of
frequencies# from a few kilohertz up to se&eral hundred megahertz. any
applications call for a crystal oscillator frequency con&eniently related to
some other desired frequency# so hundreds of standard crystal frequencies
are made in large quantities and stocked by electronics distributors. +or
e$ample# many (non<tele&ision) applications use 2.0BG050 3z crystals
since they are made in large quantities for H'% color tele&ision recei&ers.
Ising frequency di&iders#frequency multipliers and phase lockedloop circuits# it is practical to deri&e a wide range of frequencies from one
reference frequency.
Crystal structures and materials[edit]
ommon package types for quartz crystal products
7/18/2019 Modelo Electrico en Ingles
http://slidepdf.com/reader/full/modelo-electrico-en-ingles 6/10
luster of natural quartz crystals
A synthetic quartz crystal grown by the hydrothermal synthesis# about9G cm long
and weighing about9/B grams
'uning fork crystal used in a modern quartz watch.
7/18/2019 Modelo Electrico en Ingles
http://slidepdf.com/reader/full/modelo-electrico-en-ingles 7/10
%imple quartz crystal
8nside construction of a modern high performance 3<5G packagequartz crystal
+le$ural and thickness shear crystals
'he most common material for oscillator crystals is quartz. At the
beginning of the technology# natural quartz crystals were usedJ now
synthetic crystalline quartz grown by hydrothermal synthesis ispredominant due to higher purity# lower cost# and more con&enient
7/18/2019 Modelo Electrico en Ingles
http://slidepdf.com/reader/full/modelo-electrico-en-ingles 8/10
handling. Cne of the few remaining uses of natural crystals is for pressure
transducers in deep wells. ;uring orld ar 88 and for some time
afterwards# natural quartz was considered a strategic material by the I%A.
!arge crystals were imported from =razil. Faw >lascas># the source
material quartz for hydrothermal synthesis# are imported to I%A or mined
locally by oleman ?uartz. 'he a&erage &alue of as<grown synthetic
quartz in 9GG5 was ,- I%;6kg.[9G]
'wo types of quartz crystals e$ist" left<handed and right<handed# differing
in the optical rotation but identical in other physical properties. =oth left
and right<handed crystals can be used for oscillators# if the cut angle is
correct. 8n manufacture# right<handed quartz is generally used.[/-] 'he
%iC5 tetrahedrons form parallel helicesJ the direction of twist of the heli$
determines the left< or right<hand orientation. 'he heli$es are aligned along
the z<a$is and merged# sharing atoms. 'he mass of the heli$es forms a
mesh of small and large channels parallel to the z<a$isJ the large ones are
large enough to allow some mobility of smaller ions and molecules through
the crystal.[/9]
?uartz e$ists in se&eral phases. At 0B2 1 at 9 atmosphere (and at higher
temperatures and higher pressures) the K<quartz undergoesquartz
in&ersion# transforms re&ersibly to L<quartz. 'he re&erse process howe&er
is not entirely homogeneous and crystal twinning occurs. are has to be
taken during manufacture and processing to a&oid the phase
transformation. Cther phases# e.g. the higher<temperature
phases tridymite and cristobalite# are not significant for oscillators. All
quartz oscillator crystals are the K<quartz type.
8nfrared spectrophotometry is used as one of the methods for measuring
the quality of the grown crystals. 'he wa&enumbers 20:0# 20--# and
259- cm49 are commonly used. 'he measured &alue is based on
the absorption bands of the C3 radical and the infrared ? &alue is
calculated. 'he electronic grade crystals# grade # ha&e ? of 9.: million or
abo&eJ the premium grade = crystals ha&e ? of /./ million# and special
premium grade A crystals ha&e ? of 2.- million. 'he ? &alue is calculated
only for the z regionJ crystals containing other regions can be ad&ersely
affected. Another quality indicator is the etch channel densityJ when the
crystal is etched# tubular channels are created along linear defects. +or
processing in&ol&ing etching# e.g. the wristwatch tuning fork crystals# low
etch channel density is desirable. 'he etch channel density for swept
quartz is about 9-M9-- and significantly more for unswept quartz.
Nresence of etch channels and etch pits degrades the resonator*s ? andintroduces nonlinearities.[//]
7/18/2019 Modelo Electrico en Ingles
http://slidepdf.com/reader/full/modelo-electrico-en-ingles 9/10
?uartz crystals can be grown for specific purposes.
rystals for A'<cut are the most common in mass production of oscillator
materialsJ the shape and dimensions are optimized for high yield of the
required wafers. 3igh<purity quartz crystals are grown with especially low
content of aluminium# alkali metal and other impurities and minimal
defectsJ the low amount of alkali metals pro&ides increased resistance to
ionizing radiation. rystals for wrist watches# for cutting the tuning fork
2/B,: 3z crystals# are grown with &ery low etch channel density.
rystals grow anisotropicallyJ the growth along the O a$is is up to 2 times
faster than along the a$is. 'he growth direction and rate also influences
the rate of uptake of impurities.[/2] P<bar crystals# or O<plate crystals with
long P a$is# ha&e four growth regions usually called Q# <# O# and %.
[/5] 'he distribution of impurities during growth is une&enJ different growth
areas contain different le&els of contaminants. 'he z regions are the
purest# the small occasionally present s regions are less pure# the Q$
region is yet less pure# and the <$ region has the highest le&el of impurities.
'he impurities ha&e a negati&e impact on radiation hardness# susceptibility
to twinning# filter loss# and long and short term stability of the crystals.
[/0] ;ifferent<cut seeds in different orientations may pro&ide other kinds of
growth regions.[/,] 'he growth speed of the <$ direction is slowest due to
the effect of adsorption of water molecules on the crystal surfaceJ
aluminium impurities suppress growth in two other directions. 'he content
of aluminium is lowest in z region# higher in Q$# yet higher in <$# and
highest in sJ the size of s regions also grows with increased amount of
aluminium present. 'he content of hydrogen is lowest in z region# higher in
Q$ region# yet higher in s region# and highest in <$.[/B] Aluminium inclusions
transform into color centers with gamma ray irradiation# causing a
darkening of the crystal proportional to the dose and le&el of impuritiesJ the
presence of regions with different darkness re&eals the different growth
regions.
rystals for %A de&ices are grown as flat# with large <size seed with low
etch channel density.
%pecial high<? crystals# for use in highly stable oscillators# are grown at
constant slow speed and ha&e constant low infrared absorption along the
entire O a$is. rystals can be grown as P<bar# with a seed crystal in bar
shape and elongated along the P a$is# or as O<plate# grown from a plateseed with P<a$is direction length and <a$is width. [/-] 'he region around
7/18/2019 Modelo Electrico en Ingles
http://slidepdf.com/reader/full/modelo-electrico-en-ingles 10/10
the seed crystal contains a large number of crystal defects and should not
be used for the wafers.