Acoustic Response of Piezoelectric

Thanks to Bruce Chang for getting me started on the bulge testingequipment and to everyone in the MEMS lab who were there to bounceideas off of.

This work was supported by the National Science Foundation’s REUprogram under grant number DMR-0755055.

INTRODUCTION

The acoustic response of piezoelectric membranes has beenshown to improve when bulged by a differential pressure.Research to this point has been focused on transducersusing lead zirconate titanate (PZT) as the piezoelectriclayer.

MembranesA.S. Wixom, D.F. Bahr, M.J. Anderson

WSU REU 2010 – Materials Science and Engineering

OBJECTIVES

•Develop transducers using the piezoelectric polymerpolyvinylidene flouride (PVDF)

•Investigate the effect of pre-stress in the membrane onacoustic response

•Compare PZT and PVDF transducers

TRANSDUCER CONSTRUCTION

•Sheets of 28 μm think PVDF film are cut into transducerblanks

•Silver ink painted onto the film is patterned to formelectrodes and leads

•Transducers are stretched to stress the membrane

•A two part puck is used to mount and clamp the active areaof the transducer

•Testing is completed using the bulge testing apparatus topressurize the transducers

PRE-STRESS EFFECT

•Pressure-deflection Curve is regressed to the equation

where

•Results for several PVDF membranes and a PZT membranefor comparison

•Response to a harmonic input was measured at differingpressurization levels

Trans. ID γo (kPa/μm) δ (mPa/μm^3) σ (Mpa) E (Gpa)

2A 0.0062 0.484 3.85 5.29

2B 0.0116 0.473 7.24 5.18

2C 0.0215 0.447 13.4 4.89

PZT 0.2968 64.6 90.0 102

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

-10 -5 0 5 10

Dis

pla

cem

en

t (μ

m/V

)

Pressure (kPa)

Pre-Stress Peak - 500 Hz

2A

2B

2C

• Total Harmonic Distortion (THD)

21a

tdo

3wwP o

42)1( a

tEd

P = Applied pressurew = Center displacement of membrane

γo = Initial edge tensionδ = Sheet stiffness

a = Membrane span (radius)

t = Membrane thicknessd1, d2 = Geometry constants

E = Young’s Modulusν = Poisson’s Ratio

σ = Initial stress in membrane

Reduced pre-stressresults in anincreasing peak inresponse due to asmaller levels ofpressure differential

PVDF vs. PZT

•Frequency Response

PZT

Pressure (kPa)

Dis

pla

cem

ent

(μm

/V)

Pre

ssu

re (

kPa)

Frequency (Hz)

Frequency (Hz)

PVDF – 2C

Pressure (kPa) Frequency (Hz)

Frequency (Hz)

Dis

pla

cem

ent

(μm

/V)

Pre

ssu

re (

kPa)

PVDF has a lower resonant frequency as well as a lower overall response whencompared to PZT. The symmetry of layers in PVDF results in zero bending actuationcausing the dead spot to occur at zero pressure differential where the PZT occurs ata slight negative pressure due to non-symmetrical layers.

Cut and patternedtransducer beingstretched to produceuniform biaxial stressin the active area.

Mounted transducerbeing tested on bulgetesting set-up.

THD has a strong dependence on resonance, so in order to comparedifferent transducers, a normalized frequency was defined.

B

R

f

fff

f_bar = Normalized frequencyf = Frequency of interestfR = Resonant frequencyfB = Lower half-bandwidth of resonance

An example of these values is shown below for both PVDF and PZTtransducers.

fB

fR

PVDF – 2C

Dis

pla

cem

ent

(μm

/V)

Frequency (Hz)

fB

fR

PZT

Dis

pla

cem

ent

(μm

/V)

Frequency (Hz)

Restricting measurements to negative normalized frequencies,those between -1 and 0 are within the resonance band with fullresonance occurring at 0. THD measurements for both PZT andPVDF transducers at different normalized frequencies and pressureswere gathered.

0.1

1

10

100

-2.5 -2 -1.5 -1 -0.5 0

THD

(%

)

Normalized Frequency

THD Comparison - 1 kPa

PVDF-2C

PZT

0.1

1

10

100

-2.5 -2 -1.5 -1 -0.5 0

THD

(%

)

Normalized Frequency

THD Comparison - 3 kPa

PVDF-2C

PZT

1

10

100

1000

-2.5 -2 -1.5 -1 -0.5 0

THD

(%

)Normalized Frequency

THD Comparison - 5 kPa

PVDF-2C

PZT

The PVDF transducer tends tohave slightly lower levels of THD.The peak in the PZT THD is due tothe smaller resonance regionbelow the main resonantfrequency.

CONCLUSION

Reduction of pre-stress in piezoelectric membranesproduces a peak in acoustic response for low levels ofdifferential pressure. When comparing PVDF and PZTtransducers, we see that PVDF has a smaller response but italso has less THD and therefore produces a cleaner signal.

Future work can be done examining the power required tooperate piezoelectric acoustic transducers. Also, thesensitivity of piezoelectric membranes acting as free fieldmicrophones should be investigated.