International ARENA Workshop at DESY, Zeuthen

1
Measurements and Simulation Studies of
Piezoceramics for Acoustic Detection

• Karsten Salomon
• Universität Erlangen-Nürnberg

2
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)

3
Sources for Calibration for Acoustic Particle
Detection
Electric bulbs
Heated wires
Laser
Piezos
4
Piezoelectric Effect

• Equation of motion of piezos is complicated -
  coupled Partial Differential
  Equations (PDE) of an anisotropic material
• Hookes law electrical coupling
• Gauss law mechanical coupling
• Finite Element Method chosen to solve these PDE

5
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

6
Schematic of the Interferometer

• Measurement Direct measurement of the
  displacement with a self built fibre coupled
  interferometer
• Multiple reflections between piezo and fibre
  ending

7
Setup of the Interferometer
8
Optical Path of the Interferometer

• Displacement measurement with interference
• Interference of the rays
• Calculation using geometric series
• Amplitude squared proportional to photodiode
  voltage

9
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

10
Displacement - Results

• Measurement white noise applied to Piezos
• Simulation Finite Element Method
• Eigenfrequencies --gtno flat frequency
  response

11
Sending Signals with the Piezo

• Frequency response -gt 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

12
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 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

13
Direction CharacteristicsSimulation and
Measurement

• Simulation of a piezo disc R7.5mm H5mm
• Coupling of the piezo displacement to water
• Acoustic field after 20 µs when applying a 20kHz
  sine

14
Direction CharacteristicsSimulation and
Measurement
Simulation
Measurement
15
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

16
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

17
Impedance of the Piezo Simulation and
Measurement

• Far from resonances, the piezo acts like a
  capacitor Z1/f

18
Measurement Displacement of a Commercial
Hydrophone

• Measurement with Laser Doppler Vibrometer

19
Measurement Displacement of a Commercial
Hydrophone
20
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

21
Thanks for your attention
22
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

23
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

24
Measurement displacement of the HTI

• Explanaition Additional damping due to water not
  completely known.

25
Emulating a Neutrino Signal

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

26
Displacement using this Signal

• But Amplifiing the frequencies at the resonances
  
• Send
• Simpler Use a piezo with relatively flat
  frequency response

Measurement
Simulation
27
Receiving the Bipolar Signal
Signal
Measured
Second deriv. of signal