# Engineering Acoustics/Piezoelectric Transducers

 Part 1: Lumped Acoustical Systems – 1.1 – 1.2 – 1.3 – 1.4 – 1.5 – 1.6 – 1.7 – 1.8 – 1.9 – 1.10 – 1.11 Part 2: One-Dimensional Wave Motion – 2.1 – 2.2 – 2.3 Part 3: Applications – 3.1 – 3.2 – 3.3 – 3.4 – 3.5 – 3.6 – 3.7 – 3.8 – 3.9 – 3.10 – 3.11 – 3.12 – 3.13 – 3.14 – 3.15 – 3.16 – 3.17 – 3.18 – 3.19 – 3.20 – 3.21 – 3.22 – 3.23 – 3.24

# 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 polerized 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 dymanic 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.

## Frequency Response

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

# 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 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:

${\displaystyle \eta \approx 1-{\frac {1}{1+k_{eff}^{2}Q_{E}Q_{L}}}-{\frac {1}{1+{\frac {Q_{m0}}{Q_{L}}}}}}$

             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:

${\displaystyle Q_{L}={\frac {1}{k_{eff}}}{\sqrt {\frac {Q_{m0}}{Q_{E}}}}=Q_{Lopt}}$

then:

${\displaystyle \eta _{\max }=1-{\frac {2}{k_{\mathrm {eff} }{\sqrt {Q_{E}Q_{m0}}}}}\qquad \left(k_{\mathrm {eff} }{\sqrt {Q_{E}Q_{m0}}}\ll 1\right)}$

The maximum ultrasonic efficiency is described by:

${\displaystyle I_{\mathrm {w} max}={\frac {1}{2}}(\omega _{5}u_{l})_{max}^{2}\ \rho _{m\mathrm {w} }\nu _{\mathrm {w} }(W/m^{2})}$

Applications of ultrasonic transducers include:

 Welding of plastics
Atomization of liquids
Ultrasonic drilling
Ultrasonic cleaning
Ultrasound
Non destructive testing
etc.