Download Measurement

International ARENA Workshop
at DESY, Zeuthen
May 2005
Measurements and Simulation Studies of
Piezoceramics for Acoustic Detection
Karsten Salomon
Universität Erlangen-Nürnberg
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
Calibration of the Interferometer
•
•
•
•
Description possible
with geometric series
dU proportional dx
Calibration before each
measurement
Photodiode voltage
proportional to intensity
Precision of ~0.1nm
PhotodiodenVoltage
Spannung
(V)(V)
Photodiode
•
dx
4
Measurement
Cos^2 Approx
Geometric series
3,5
3
2,5
dUPhoto
2
1,5
1
0,5
-/8
0
0
/8
0
5
10
Aktuator Spannung (V)
Actuator
Voltage (V)
K. Salomon, Universität Erlangen-Nürnberg
International ARENA Workshop, May 2005
15
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
1  2
  2 2  0
c t
•
If the sent wavelength is larger than the dimension of the transmitter,
then:

V (t  r / c)

t

4r
•
Change in volume dVA 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
2
V (t  r / c)
2

p   0
   0 t
t
4r
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
K. Salomon, Universität Erlangen-Nürnberg
International ARENA Workshop, May 2005
Measurement
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:
U ( )
U ( )
Z ( ) 

I ( ) iQ( )
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:
1 N FFT (received _ Signal (i ))
Transferfunc _ gauss 
 FFT ( gaussian ( ))
N  1 i 1
i
Transferfunc _ disp  (2f ) 2 disp ( f ) 2
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
Displacement using this Signal
• But: Amplifiing the frequencies at the resonances
Simulation
• Send:
Measurement
Signal in frequency space
Frequency response of the piezo
• Simpler: Use a piezo with relatively flat frequency response
K. Salomon, Universität Erlangen-Nürnberg
International ARENA Workshop, May 2005
Receiving the Bipolar Signal
Signal
Measured
Second deriv. of
signal
K. Salomon, Universität Erlangen-Nürnberg
International ARENA Workshop, May 2005