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International ARENA Workshop at DESY, Zeuthen
May 2005
Measurements and Simulation Studies of Piezoceramics for Acoustic Detection
Karsten Salomon
Universität Erlangen-Nürnberg
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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)
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K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005
Sources for Calibration for Acoustic Particle Detection
Electric bulbs
Heated wires
Laser
Piezos
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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
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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
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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
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K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005
Setup of the Interferometer
2cm
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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
)
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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
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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
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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
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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:
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K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005
Direction Characteristics:Simulation and Measurement
Simulation Measurement
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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
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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
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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
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K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005
Measurement: Displacement of a Commercial Hydrophone
• Measurement with Laser Doppler Vibrometer
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K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005
Measurement: Displacement of a Commercial Hydrophone
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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
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K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005
Thanks for your attention
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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
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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
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K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005
Measurement: displacement of the HTI
• Explanaition: Additional damping due to water not completely known.
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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
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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
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K. Salomon, Universität Erlangen-Nürnberg International ARENA Workshop, May 2005
Receiving the Bipolar Signal
Measured
Signal
Second deriv. of signal