Piezoelectric Resonators
ME 2082
Department of Mechanical Engineering
Introduction
KT: relative dielectric constant of the material
εo: relative permittivity of free space (8.854*1012F/m)
h: distance between electrodes (m - material
thickness)
A: area of the electrodes (m2)
C0: measured capacitance at 1kHz (F)
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Topics of Discussion
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Equivalent Circuit of a Ceramic Element
(Non-resonant operation)
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Mechanical Q
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Mechanical Q Equation
Fr: resonance frequency (Hz)
Fa: anti-resonance frequency (Hz)
Zm: resistance at Fr (ohm)
C0 :static capacitance (Farad)
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Alternatively, QM can also be determined using
the equation:
where F1, F2 are -3dB points on the
frequency/impendance curve from the
resonance frequency Fr.
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Piezoelectric Modes
of Vibration
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The frequency constant, N, is
the product of the resonance
frequency and the linear
dimension governing the
resonance. The various modes
of resonance are shown
schematically for:
N1=FrD (Hz.m) Radial Mode
Disc
N2=Frl (Hz.m) Length Mode
Plate
N3=Frl (Hz.m) Length Mode
Cylinder
N4=Frh (Hz.m) Thickness
Mode Disc, Plate
N5=Frh (Hz.m) Shear Mode
Plate
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Variation of Coupling Coefficients as a
Function of Relative Frequency Interval
between Series and Parallel Resonant Frequencies
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Equivalent Circuit of a
Piezoelectric Resonator
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Measurement of Resonant
Frequencies - Circuits
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Constant Voltage Circuit:
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Constant Current Circuit:
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Measurement of Resonant
Frequencies - Variations
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Variation of Impedance
with Frequency:
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Variation of Admittance
with Frequency:
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Measurement of Resonant
Frequencies - Variations
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Variation of Phase Angle with
Frequency:
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Piezoelectric Composite
Transducers
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1-3 Composites
Property
Dielectric Constant K33T
Dissipation factor
Frequency Constant N3
Kε
Q (unloaded)
Ceramic Volume
Frequency
1-3 Composites
Monolithic Ceramic
890 ± 20%
3250
0.03
0.025
1475 ± 5%
1850
0.62
5
70
25-30%
100
150 KHz-1.5MHz
150 KHz-5 MHz
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Piezoelectric Flexure Elements
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Bimorph: Flexure elements have two layers of PZT material
bonded together, with electrodes in series or parallel
configuration. These elements offer large displacements for
positioning devices or actuators.
Series configuration:
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Piezoelectric Flexure Elements
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Parallel configuration:
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Piezoelectric Actuators
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An actuator is a device that produces a displacement (movement)
when voltage is applied. Actuators are used for many functions,
including canceling vibration, tool adjustment and control, micropumps, mirror positioning, wave generation, structural deformation,
inspection systems and scanning microscopes. When a voltage is
applied to the assembly, it produces small displacements with a high
force capability. These actuators can be built from wide ranging
piezoelectric materials offered by Sensor, depending on the various
end uses.
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Piezoelectric Actuators
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Bending mode actuators
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Piezoelectric Actuators
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Multilayer piezoelectric actuator is a device consisting of a
number of piezoelectric elements in a stack. The elements are
generally connected in parallel either through the electrode
structure or the insertion of brass electrodes between the
elements
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Piezoelectric Actuators
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Diaphragm actuators:Diaphragm actuators consist of a piezoelectric washer
bonded to a metal diaphragm. This configuration provide a low cost but good
displacement actuator. In applications, the diaphragm must be clamped on its
edges to produce the deflection.
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Piezoelectric Actuators
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Tube actuators: A piezoelectric tube element with electrodes on its curved
surfaces can be used as an actuator element. The elements offer good
structural rigidity, but are more difficult to manufacture. They are often
used in such applications as scanning tunnelling microscopes (STMs).
A tube actuator is generally poled through the wall, but other
configurations involving split electrodes and segments are also used as
actuator elements.
The extension of the piezoelectric tube element under a DC voltage V
applied in the direction of polarization is given by the formula:
Displacement = [L/W]d31V
Where:
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L is the length of the tube
W is the thickness of the wall
d31 is the piezoelectric coefficient
V is the applied voltage
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Piezoelectric Actuators
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Electrode Configurations for Tube Elements:
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Igniter Elements
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Operating Principle:
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High voltages are generated when piezoelectric
materials are impacted. When this voltage is
applied across an air gap, an arc is generated
whenever the voltage exceeds the breakdown
voltage of the air gap.
The voltage V generated during the impact can
be expressed as:
V=L x g33 x S
Where L is the length of the element, g33 is the
piezoelectric voltage coefficient and S is the
mechanical load in the axial direction.
A spring-loaded mechanism is generally used to
produce the mechanical load on the ceramic
element. The energy E is then determined by
the equation:
E= 1/2 CV2
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