# Acoustics/Piezoelectric Transducers

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# Introduction

Piezoelectricity from the Greek word \"piezo\" means pressure
electricity. Certain crystalline substances generate electric charges
under mechanical stress and conversely experience a mechanical strain in
the presence of an electric field. The piezoelectric effect describes a
situation where the transducing material senses input mechanical
vibrations and produces a charge at the frequency of the vibration. An
AC voltage causes the piezoelectric material to vibrate in an
oscillatory fashion at the same frequency as the input current.

Quartz is the best known single crystal material with piezoelectric
properties. Strong piezoelectric effects can be induced in materials
with an ABO3, Perovskite crystalline structure. \'A\' denotes a large
divalent metal ion such as lead and \'B\' denotes a smaller tetravalent
ion such as titanium or zirconium.

For any crystal to exhibit the piezoelectric effect, its structure must
have no center of symmetry. Either a tensile or compressive stress
applied to the crystal alters the separation between positive and
negative charge sights in the cell causing a net polarization at the
surface of the crystal. The polarization varies directly with the
applied stress and is direction dependent so that compressive and
tensile stresses will result in electric fields of opposite voltages.

# Vibrations & Displacements

Piezoelectric ceramics have non-centrosymmetric unit cells below the
Curie temperature and centrosymmetric unit cells above the Curie
temperature. Non-centrosymmetric structures provide a net electric
dipole moment. The dipoles are randomly oriented until a strong DC
electric field is applied causing permanent polarization and thus
piezoelectric properties.

A polarized ceramic may be subjected to stress causing the crystal
lattice to distort changing the total dipole moment of the ceramic. The
change in dipole moment due to an applied stress causes a net electric
field which varies linearly with stress.

# Dynamic Performance

The dynamic performance of a piezoelectric material relates to how it
behaves under alternating stresses near the mechanical resonance. The
parallel combination of C2 with L1, C1, and R1 in the equivalent circuit
below control the transducers reactance which is a function of
frequency.

## Equivalent Electric Circuit

## Frequency Response

The graph below shows the impedance of a piezoelectric transducer as a
function of frequency. The minimum value at fn corresponds to the
resonance while the maximum value at fm corresponds to anti-resonance.
^Superscript\ text*Italic\ text*^

# Resonant Devices

Non resonant devices may be modeled by a capacitor representing the
capacitance of the piezoelectric with an impedance modeling the
mechanically vibrating system as a shunt in the circuit. The impedance
may be modeled as a capacitor in the non resonant case which allows the
circuit to reduce to a single capacitor replacing the parallel
combination.

For resonant devices the impedance becomes a resistance or static
capacitance at resonance. This is an undesirable effect. In mechanically
driven systems this effect acts as a load on the transducer and
decreases the electrical output. In electrically driven systems this
effect shunts the driver requiring a larger input current. The adverse
effect of the static capacitance experienced at resonant operation may
be counteracted by using a shunt or series inductor resonating with the
static capacitance at the operating frequency.

# Applications

## Mechanical Measurement

Because of the dielectric leakage current of piezoelectrics they are
poorly suited for applications where force or pressure have a slow rate
of change. They are, however, very well suited for highly dynamic
measurements that might be needed in blast gauges and accelerometers.

## Ultrasonic

High intensity ultrasound applications utilize half wavelength
transducers with resonant frequencies between 18 kHz and 45 kHz. Large
blocks of transducer material is needed to generate high intensities
which is makes manufacturing difficult and is economically impractical.
Also, since half wavelength transducers have the highest stress
amplitude in the center the end sections act as inert masses. The end
sections are often replaced with metal plates possessing a much higher
mechanical quality factor giving the composite transducer a higher
mechanical quality factor than a single-piece transducer.

The overall electro-acoustic efficiency is:

`             Qm0 = unloaded mechanical quality factor`\
`             QE  = electric quality factor`\
`             QL  = quality factor due to the acoustic load alone`

The second term on the right hand side is the dielectric loss and the
third term is the mechanical loss.

Efficiency is maximized when:

then: 

The maximum ultrasonic efficiency is described by:


Applications of ultrasonic transducers include:

` Welding of plastics`\
` Atomization of liquids`\
` Ultrasonic drilling`\
` Ultrasonic cleaning`\
` Ultrasonic foils in the paper machine wet end for more uniform fibre distribution`\
` Ultrasound`\
` Non-destructive testing`\
` etc.`

# More Information and Source of Information

MorganElectroCeramics

Ultra Technology

