International ARENA Workshop at DESY, Zeuthen

May 2005

Measurements and Simulation Studies of Piezoceramics for Acoustic Detection

Karsten Salomon

Universität Erlangen-Nürnberg

K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005

Motivation

• Development and simulation of calibration sources for acoustic detection

• Simulation of detector devices

• Understanding of the whole system emitter to receiver (finding the transfer functions)

K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005

Sources for Calibration for Acoustic Particle Detection

Electric bulbs

Heated wires

Laser

Piezos

K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005

Piezoelectric Effect

• Equation of motion of piezos is complicated - coupled Partial Differential Equations (PDE) of an anisotropic material:– Hooke’s law + electrical coupling– Gauss law + mechanical coupling

• Finite Element Method chosen to solve these PDE

K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005

Displacement

• Motivation: Calibration of sound source to measure the sensitivity of the hydrophone

• Simulation: Displacement of a piezo disc due to electrical voltage is simulated for different frequencies using CAPA

K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005

Schematic of the Interferometer

• Measurement: Direct measurement of the displacement with a self built fibre coupled interferometer

– Multiple reflections between piezo and fibre ending

K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005

Setup of the Interferometer

2cm

K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005

• Description possible with geometric series

• dU proportional dx

• Calibration before each measurement

• Photodiode voltage proportional to intensity

• Precision of ~0.1nm

Calibration of the Interferometer

0

0,5

1

1,5

2

2,5

3

3,5

4

0 5 10 15Aktuator Spannung (V)

Ph

oto

dio

de

n S

pa

nn

un

g (

V)

MeasurementCos^2 ApproxGeometric series

0 /8-/8

dUPhoto

dx

Actuator Voltage (V)

Pho

todi

ode

Vol

tage

(V

)

K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005

Displacement - Results

• Measurement: white noise applied to Piezos

• Simulation: Finite Element Method

• Eigenfrequencies -->no flat frequency response

K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005

Sending Signals with the Piezo

• Frequency response -> response to arbitrary signal

• As a source for calibration a pressure signal is needed

• How does the movement of the piezo result in a defined pressure signal?

• Small excursion: signal production in water

K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005

Signal Production in Water

• Signal propagation in water is described with a wave equation

• If the sent wavelength is larger than the dimension of the transmitter, then:

• Change in volume dVA dx

• Equation for pressure:

• Displacement of piezo is proportional to the applied voltage

• Outside resonances, the second derivative of the applied voltage will be sent

r

crtVt

tp

4

)/(2

2

00

r

crtVt

4

)/(

01

2

2

2

tc

K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005

Direction Characteristics:Simulation and Measurement

• Simulation of a piezo disc R=7.5mm H=5mm

• Coupling of the piezo displacement to water

• Acoustic field after 20 µs when applying a 20kHz sine:

K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005

Direction Characteristics:Simulation and Measurement

Simulation Measurement

K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005

Impedance of the Piezo: Simulation and Measurement

• Motivation: – Understand electrical properties of the piezo – Calculate parameters for equivalent circuit diagram

• Simulation– Apply charge pulse to the piezo.– Calculate voltage response. – Impedance is given in the frequency domain as:

)(Q

)(

)(

)()(

i

U

I

UZ

K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005

Impedance of the Piezo: Equivalent Circuit Diagram

• First resonance and antiresonance of a piezo can be described with an equivalent circuit diagram:

• L,C and R are equivalent to mass, stiffness and damping

• With these parameters one gets a simplified piezo model

K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005

Impedance of the Piezo: Simulation and Measurement

• Far from resonances, the piezo acts like a capacitor Z~1/f

K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005

Measurement: Displacement of a Commercial Hydrophone

• Measurement with Laser Doppler Vibrometer

K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005

Measurement: Displacement of a Commercial Hydrophone

K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005

Summary

• Summary:

– Simulation in good agreement with measurement of piezos

– Signal propagation in water described by simulation

– Ideas how to calibrate hydrophones with impedance measurements

– First steps how to calibrate hydrophones with displacement measurements

K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005

Thanks for your attention

K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005

The Finite Element Method

• Numerical method to solve PDE with boundary value problems

• Areas are discretisized into cells (finite elements)

• Within a finite element characteristic functions are defined

• Linear combinations of these functions then give possible solutions within an element

K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005

Measurement: displacement of the HTI

• Measurement with a Laser Doppler Velocimeter

• Clearly seen a Peak at 57kHz but

• Measurement: send different gaussians with HTI and receive with same type of HTI. Calculate Transferfunction:

22

1

)()2(_

))((

))(_(

1

1_

fdispfdispncTransferfu

gaussianFFT

iSignalreceivedFFT

NgaussncTransferfu

N

i i

K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005

Measurement: displacement of the HTI

• Explanaition: Additional damping due to water not completely known.

K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005

Emulating a Neutrino Signal

• Calculated neutrino signal in 400m distance following the thermoacoustic model for a 1PeV shower.

• Send two times integrated neutrino signal

K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005

• But: Amplifiing the frequencies at the resonances

• Send:

• Simpler: Use a piezo with relatively flat frequency response

Displacement using this Signal

MeasurementSimulation

Signal in frequency space

Frequency response of the piezo

K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005

Receiving the Bipolar Signal

Measured

Signal

Second deriv. of signal