Piezoelectric Transducer
`
`Certain material are characterized that they generate electric voltage when they
`are deformed by subjecting to mechanical force or stress.
`
`The best known material is quartz crystal (SiO2), Barium titanate, lead zirconium
`titanate (PZT) or poly vinylidene fluoride (PVDF)
`
`Piezoelectric materials are characterized by their ability to output a proportional
`electrical signal to the stress applied to the material.
`This property makes piezoelectric materials useful as a primary sensors.
`
`Piezoelectric materials (piezo = pressure) possess the property that a
`voltage applied to them will produce a pressure field on the atoms in
`their lattice (a stress) with an accompanying overall contraction or
`expansion in one or more dimensions of the material (a strain).
`
`1
`
`APPLE 1041
`
`1
`
`
`
`Certain material are characterized that they generate electric voltage when they
`are deformed by subjecting to mechanical force or stress.
`
`The best known material is quartz crystal (SiO2), Barium titanate, lead zirconium
`titanate (PZT) or poly vinylidene fluoride (PVDF)
`
`Piezoelectric materials are characterized by their ability to output a proportional
`electrical signal to the stress applied to the material.
`This property makes piezoelectric materials useful as a primary sensors.
`
`Piezoelectric materials (piezo = pressure) possess the property that a
`voltage applied to them will produce a pressure field on the atoms in
`their lattice (a stress) with an accompanying overall contraction or
`expansion in one or more dimensions of the material (a strain).
`
`1
`
`APPLE 1041
`
`1
`
`
`
`These material can be cut along its axes in x, y and z directions.
`
`Pairs of atoms
`
`View along the Z-axis
`
`An asymmetric atomic structure will distort in an applied electric field. By
`the piezoelectric property of the material, electrical excitation is changed
`into motion and pressure, the necessary elements for acoustic waves.
`
`2
`
`2
`
`
`
`The sensor is governed by Newton’s law of motion F = ma.
`
`- The force experienced by the piezoelectric crystal is proportional to the seismic
`mass times the input acceleration.
`
`- The more mass or acceleration, the higher the applied force and the more
`electrical output from the crystal.
`
`3
`
`3
`
`
`
`Voltage Generation
`- In a single crystal cell there are three atoms of silicon and six atoms of oxygen.
`
`- Each silicon atoms caries four positive charges, and oxygen atom carry two
`negative charges.
`
`- A pair of oxygen atom carries 4 negative charges , when there is no force applied
`on the quartz crystal, the quartz cell is electrically neutral.
`
`- When compressive forces are applied along the x- axis, the hexagonal lattices
`become deformed. The forces shift the atoms in the crystal in such a manner the
`
`positive charges are accumulated at the silicon atom side the negative charges at positive charges are accumulated at the silicon atom side the negative charges at
`the oxygen pair side.
`
`4
`
`4
`
`
`
`- The crystal tends to exhibit electric charges along the y-axis .
`
`- If the crystal is subjected to a tension along the x-axis, a charge of opposite
`polarity is produced along the y-axis.
`
`- To transmit the charge that has been develop, conductive electrodes are applied
`to the crystal at the opposite side of the cut.
`
`- The piezoelectric material acts as a capacitor, with the piezoelectric crystal
`acting as the dielectric medium. The charge is stored because of the inherent
`capacitance of the piezoelectric material.
`
`Two opposite Two opposite
`
`faces of the
`transducer are
`plated with
`conductive metal
`films; a voltage
`generator V is
`attached to the
`electrodes to
`produce an
`electric field
`
`5
`
`5
`
`
`
`6
`
`Transverse effect
`
`ba
`
`⋅=
`FdQ
`
`longitudinal effect
`
`⋅=
`FdQ
`
`6
`
`
`
`The piezoelectric is reversible. If a varying potential is applied to the proper axis of
`the crystal, it changes the dimension of the crystal, thereby deforming it.
`
`A piezoelectric element used for converting motion to electrical signal, thus though
`as both charge generator and a capacitor.
`
`The charge appears as a voltage across the electrodes. The magnitude
`and polarity of the induced surface charges are proportional to the
`magnitude and direction of the applied force
`
`
`The charge generated is defined as
`
`(longitudinal effect)……………………………………………1
`
`(Transverse effect)……………………………………………2
`
`⋅=
`FdQ
`
`ba
`
`⋅=
`FdQ
`
`d is the piezoelectric coefficient of the material, it is also known as the
`charge sensitivity of the crystal d=2.3X10-12 F/N, F = applied force.
`
`7
`
`7
`
`
`
`If the ratio of a / b is greater than 1, the transverse effect produces more charge
`than the longitudinal effect. The force F, results in a change in thickness of the
`crystal
`
`t∆
`If the original thickness of the crystal is t, and is the change in thickness
`due to the applied force, then Young’s modulus E can be expressed as the ratio
`of stress to strain.
`
`=
`
`⋅
`tF
`∆⋅
`tA
`
`tAF
`
`∆
`
`
`
`tt
`
`E
`
`=
`
`stress
`
`strain
`
`=
`
`F
`
`=
`
`⋅
`EA
`
`t
`
`∆
`t
`
`……………………………………………3
`
`A = area of the crystal, m2
`
`t = thickness of the crystal, m
`
`8
`
`8
`
`
`
`9
`
`From equation 1 and 3
`
`Q
`
`=
`
`⋅
`⋅
`∆⋅
`tEAd
`
`t
`
`coulombs
`
`……………………………………………4
`
`The charge at the electrodes produces the voltage
`
`…………………………………………….………………5
`
`CQ
`
`V =
`
`9
`
`
`
`The capacitance of the piezoelectric material between the two electrodes is
`
`………………………………………………………6
`
`A
`
`rεεε
`0=
`t
`
`tA
`
`C
`
`=
`
`rεrε
`
`0ε
`
`
`
`= the dielectric constant (permittivity) of the material= the dielectric constant (permittivity) of the material
`
`= for free space
`
`10
`
`⋅
`Fd
`
`tA
`
`r 0εε
`
`=
`
`CQ
`
`V
`
`=
`
`10
`
`
`
`dtF
`εε
`r
`
`0
`
`A
`
`=
`
`⋅
`Fd
`
`tA
`
`εε
`r
`
`0
`
`=
`
`CQ
`
`V
`
`=
`
`By expressing
`
`g
`
`as the crystal voltage sensitivity factor
`
`
`
`g =g =
`
`V
`
`=
`
`d
`0εεr
`
`gtF
`
`A
`
`g =
`
`V
`
`tP
`
`also
`
`
`
`Vm/NVm/N
`
`..=
`Ptg
`
`Where
`V
`
`t
`
`is the electric field strength, P is the pressure or stress
`
`11
`
`11
`
`
`
`Piezoelectric Excitation Circuit
`
`Pulsed Excitation
`
`12
`
`12
`
`
`
`• The electrical circuit generates a sharp voltage pulse to a transducer.
`
`• During the off-time of the transistor, the capacitor charges to the high supply
`voltage.
`
`• When the transistor is turned ON by the trigger pulse, its low on resistance
`takes the left side of the capacitor to the near ground voltage.
`
`• Thus the left side of the capacitor is applied to the ground voltage, applying
`a large negative pulse to the upper transducer terminal .
`
`13
`
`13
`
`
`
`Exponential decay
`
`Pressure
`
`Time
`
`The pressure wave radiated by
`the transducer takes the form of
`an exponentially decaying
`sinusoid
`
`14
`
`14
`
`
`
`Sensitivity
`
`The sensitivity of a piezoelectric crystal may be represented either by
`
`A -Charge sensitivity
`
`B -Voltage sensitivity
`
`15
`
`15
`
`
`
`A - Charge sensitivity
`
`Fq
`∂∂
`
`S q
`
`=
`
`q = the generated charge
`
`F = the applied force
`
`For a crystal with surface area A
`
`pq
`∂∂
`
`1
`
`A
`
`S q
`
`=
`
`16
`
`AF
`
`p = the stress or pressure applied to the crystal surface
`
`P =
`
`16
`
`
`
`B - Voltage Sensitivity
`
`Voltage sensitivity is given by the change in voltage due to a unit increment in
`pressure per unit thickness of the crystal.
`
`pv
`∂∂
`
`1
`
`d
`
`Sv
`
`=
`
`d = the crystal thickness
`
`CQ
`
`V =
`
`Since
`
`17
`
`ε
`
`dA
`
`C
`
`=
`
`δ =
`δ
`vCq
`
`As
`
`17
`
`
`
`18
`
`_ lov
`1
`=
` d op
`d
`
`pv
`∂∂
`
`S v
`"
`
`Ad
`
`A
`
`
`
` C=ε C=ε
`
`pq
`∂∂
`
`1
`
`A
`
`Sq
`
`=
`
`vq
`∂∂
`Ad
`
`=
`
`vq
`SS
`
`C
`C
`
`Ad
`
`A
`
`SS
`
`q =
`=
`Sv
`
`S q ε=
`Sv
`
`18
`
`
`
`The relation ship between charge sensitivity and voltage sensitivity
`
`S
`
`q
`
`ε=
`S
`
`v
`
`ε Is the dielectric constant (permittivity) of the crystal capacitor
`
`19
`
`19
`
`
`
`Equivalent Circuit of a piezoelectric Transducer
`
`The equivalent circuit can be derived from the electrical and mechanical parameters
`of the transducer.
`
`Q
`The charge generated is across the capacitance Cc and its leakage
`resistance is Rc
`
`The charge source can be replaced by a voltage source
`
`20
`
`⋅
`Fd
`cC
`
`=
`
`CQ
`
`V
`
`=
`
`20
`
`
`
`When the piezoelectric crystal is coupled with leads and cables as well as a
`readout device, the voltage depends not only on the element but also on the
`capacitance of cables, charge amplifier and oscilloscope display.
`
`The total capacitance is
`
`C
`T
`
`=
`
`+
`CC
`C
`amplifier
`
`+
`
`C
`display
`
`21
`
`21
`
`
`
`The feedback resistance of the charge amplifier is kept high so that this circuit
`draws very low current and produces a voltage output that is proportional to the
`charge
`
`22
`
`22
`
`
`
`The typical arrangement is shown
`
`Typical arrangement when sensing element and charge amplifiers are present
`
`23
`
`23
`
`
`
`
`
`Combined equivalent circuit
`Combined equivalent circuit
`
`24
`24
`
`24
`
`24
`
`
`
`Piezoelectric Applications
`
`Piezoelectric Accelerometer (Theory of Operation)
`
`The construction is as follows:-
`
`A piezoelectric element in the form of a cylinder is bonded to a central pillar.
`
`A cylinder mass is bonded to the outside piezoelectric element.
`
`Acceleration in the direction of the cylinder axis causes a shear force on the
`.=
`FdQ
`element , which provides its own spring force
`As the housing of the accelerometer is subjected to vibrations, the force
`exerted on the piezoelectric element by the mass is altered .
`
`The charge generated on the crystal is sensed using a charge amplifier.
`
`A force F applied to the crystal develops a charge .
`
`25
`
`25
`
`
`
`When a varying acceleration is applied to the mass crystal assembly, the crystal
`experiences a varying force described by
`
`=
`⋅
`aMF
`
`⋅=
`⋅=
`⋅
`aMdFdQ
`
`CQ
`
`V =
`
`
`
`VV
`
`
`
`==
`
`
`⋅⋅
`
` Fd Fd
`
`C
`
`
`
`==
`
`
`⋅⋅
`
`⋅⋅
`
` aMd aMd
`
`C
`
`a = acceleration
`
`V = the voltage produced
`
`26
`
`26
`
`
`
`Piezoelectric Accelerometer
`
`- Accelerometers are sensing transducers that provide an output proportional
`to acceleration, vibration and shock.
`
`- These sensors have found a wide variety of applications such as package
`testing, accelerometers, airbag sensors and automotive security alarms.
`
`- It is possible to measure velocity by first converting the velocity into force
`
`- By using a viscous damping element and then measuring the resulting force
`with piezo-electric transducer.
`
`Motion
`
`Accelerometer
`(piezoelectric)
`
`Amplification
`& Integration
`
`Velocity
`
`As for its high output impedance,
`amplifiers are used to condition the
`output signal and to reduce the
`loading error
`
`27
`
`27
`
`
`
`- The piezoelectric accelerometer is an acceleration sensor.
`
`- Used to measure the inertia force caused by acceleration
`
`28
`
`28
`
`
`
`The base of the device is attached to the object whose motion is to be measured.
`
`Inside the piezoelectric acceleration transducer, mass m is supported on a spring
`of stiffness K and a viscous damper with damping coefficient c
`
`X, Y , Z = the three possible axis of motion (generally represented by d)
`
`29
`
`29
`
`
`
`Charge Amplifier
`
`The piezoelectric signals cannot be read using low impedance devices as for
`
`1- High output impedance in the sensor, results in small output signal levels
`and large loading errors.
`
`2- The charge can quickly leak out through the load.
`
`3- by using charge amplifier circuit with relatively large time constant, speed of
`charge leakage can be decreased
`
`30
`
`30
`
`
`
`Piezoelectric accelerometer
`
`31
`
`31
`
`
`
`Analogy Equations
`
`- The base of the device is attached to the object whose motion is to be measured.
`
`- The piezoelectric acceleration transducer, mass m is supported on a spring of
`stiffness k and damper with damping coefficient c.
`
`- The motion of the object results in the motion of the mass relative to the frame.
`
`32
`
`32
`
`
`
`- The transducer equation is obtained by considering the inertial forces of the
`mass and the restoring force of the spring and the damper
`
`33
`
`(
`(cid:1) −
`yc
`
`)x
`(cid:1)
`
`(
`yk
`
`−
`
`)x
`
`x
`
`2
`
`yd
`
`2
`
`dt
`
`+
`
`c
`
`(
`yd
`
`−
`
`)
`
`x
`
`dt
`
`+
`
`(
`yk
`
`−
`
`) 0
`=
`
`x
`
`m W
`
`here y = absolute motion of the mass
`
`33
`
`
`
`The relative motion z = y - x is expressed as
`
`)
`
`x
`
`2
`
`(
`zd
`dt
`
`+
`
`2
`
`+
`
`c
`
`dz
`
`dt
`
`+
`
`kz
`
`=
`
`0
`
`m (
`
`mD
`
`2
`
`+
`
`cD
`
`+
`
`)
`zk
`
`−=
`
`2
`
`xmD
`
`where
`
`D =
`
`d
`
`dt
`
`The equation is of the second order and relates the input and output of the
`transducer
`
`34
`
`34
`
`
`
`We can discuss the analogy approach, by using the mechanical elements
`(inertial elements , spring and damper.
`
`The mechanical system can be analyzed C, L, and R
`
`=
`mF
`
`2
`
`xd
`
`2
`
`dt
`
`+
`
`c
`
`dx
`
`dt
`
`+
`
`kx
`
`
`
`v =v =
`
`dx
`
`
`
`dtdt
`
`=
`mF
`
`dv
`
`dt
`
`+
`
`cv
`
`(cid:1)+
`dtvk
`
`e
`
`=
`
`Ri
`
`+
`
`L
`
`di
`
`dt
`
`1
`
`(cid:1)+
`c
`
`dti
`
`35
`
`35
`
`
`
`Magnitude frequency of the relative displacement for a transducer used to
`measure acceleration
`
`36
`
`36
`
`
`
`
`
`Vibration and longitudinal response gain
`
`37
`37
`
`37
`
`37
`
`
`
`Structures for Piezoelectric Accelerometers
`
`A variety of mechanical configurations are available to perform the transduction
`principles of a piezoelectric accelerometer. These configurations are defined by
`the nature in which the inertial force of an accelerated mass acts upon the
`piezoelectric material.
`
`38
`
`38
`
`
`
`Shear Mode
`
`-Shear mode accelerometer designs bond, or “sandwich,” the sensing material
`between a center post and seismic mass.
`
`-A compression ring or stud applies a preload force required to create a rigid linear
`structure.
`
`-Under acceleration, the mass causes a shear stress to be applied
`to the sensing material.
`
`-This stress results in a proportional electrical output by the piezoelectric material.
`
`-The output is then collected by the electrodes and transmitted by lightweight lead
`wires to either the built-in signal conditioning circuitry, or directly to the electrical
`connector for a charge mode type.
`
`39
`
`39
`
`
`
`Shear mode accelerometer.
`
`40
`
`40
`
`
`
`Flexural Mode
`
`-Flexural mode designs utilize beam-shaped sensing crystals, which are supported to
`create strain on the crystal when accelerated.
`
`-The crystal may be bonded to a carrier beam that increases the amount of strain when
`accelerated.
`
`-Flexural beam designs are well suited for low frequency, low gravitational (g)
`
`acceleration applications such as those that may be encountered during structural acceleration applications such as those that may be encountered during structural
`testing.
`
`41
`
`41
`
`
`
`Piazoelectric Elament
`
`Seismic Wass
`
`
`
`
`». Accelerometer Base
`
`42
`42
`
`42
`
`42
`
`
`
`Compression Mode
`-Compression mode accelerometers are simple structures which provide high
`rigidity.
`
`-Upright compression designs sandwich the piezoelectric crystal between a seismic
`mass and rigid mounting base.
`
`-A pre-load stud or screw secures the sensing element to the mounting base.
`
`-When the sensor is accelerated, the seismic mass increases or decreases the
`
`amount of compression force acting upon the crystal, and a proportional electrical amount of compression force acting upon the crystal, and a proportional electrical
`output results.
`
`The larger the seismic mass, the greater the stress and, hence,
`the greater the output.
`
`43
`
`43
`
`
`
`This design is generally very rugged and can withstand high-g shock levels.
`However, due to the intimate contact of the sensing crystals with the external
`mounting base, upright compression designs tend to be more sensitive to base
`bending (strain).
`
`Compression mode accelerometer.
`
`44
`
`44
`
`
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