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Understanding Piezo based Understanding Piezo based Sensors for an acoustic Sensors for an acoustic
neutrino detectorneutrino detector
Christopher Naumann,Christopher Naumann, Universität Erlangen-NürnbergUniversität Erlangen-Nürnberg
ARENA-06, Newcastle, UKARENA-06, Newcastle, UK
Christopher NaumannARENA Workshop 2006, Newcastle
Acoustic Detection with the ANTARES Telescope
re-fit several ANTARES storeys with acoustics hardware (sensors and DAQ)
Aims:
-design studies for an acoustic neutrino detector in the deep sea
-thorough studies of the acoustic environment in the deep sea: Correlations of the acoustic background over several length scales (<1m up to > 100m)
replace optical sensors with acoustic sensors
(schematic)
Christopher NaumannARENA Workshop 2006, Newcastle
Aim: Acoustic Sensors
• Basic Design of Sensors for the ANTARES acoustics
– Sensor = piezo element (disc and/or tube) + pre-amplifier– either encapsulated in polyurethane = > "hydrophone" – or coupled to ANTARES glass sphere = > "acoustic module"
piezo sensors + pre-amplifiers
17"
(42c
m)
piezo tube
internalpre-amplifier
PU coating
cable ANTARES glass sphere
Signal response and noise characteristics of sensors depend on piezo element try to build model
Christopher NaumannARENA Workshop 2006, Newcastle
Electro-Mechanical Equivalent Circuit
• Piezo couples mechanical and electrical properties• analogy between forced mechanical and electrical oscillation mechanical properties of piezo expressible by equivalent electrical
properties:
force F U=F/ voltage U
elongation x Q=·x charge Q
stiffness S C=²/S capacity C
damping W R=W/² resistance R
inertia m L=m/² inductance L
SxxWxmFext QCQRQLU ext1
LRC
(Cp = electrical capacity between electrodes)
knowledge of equivalent circuit simple model of piezo
= electromechanical coupling constant
(depends on material)
F
h
A
mechanical oscillator electrical oscillator
p
Christopher NaumannARENA Workshop 2006, Newcastle
Equivalent Properties (1): Measurement
• get all properties from single impedance measurement on piezo element:
1
1
1,
n
iiLRCpPiezo ZCiZ
i
iiiLRC CiRLiZ 1,
Fit with Li, Ri and Ci as parameters
apply gaussian signal on voltage divider made of piezo and suitable capacitor
1. measure signal over capacitor
2. calculate fourier transforms of signals
3. from these calculate impedance spectrum of piezo element
equiv. circuit with n parallel LRC branches
possible for free and coated or attached piezos
10kHz 100kHz 1MHz
Impe
danc
e (k
)
0.1
1
1
0
100
Resonance(Z minimal)
Anti-Resonance(Z maximal)
Christopher NaumannARENA Workshop 2006, Newcastle
Equivalent Properties (2): Coupling
Properties of piezo elements depend on coupling to environment:
coupling limits movement
damping R increases resonances are weakened
- other properties unchanged -
significant increase of equivalent ohmic resistance damping
sensitivity of piezo element can now be
modelled...
free piezo: strong resonances
coupled: resonances suppressed
10kHz 100kHz 1MHzFrequency
Impe
danc
e (k
)
0.1
1
10
10
0
free piezo piezo in sphere
74mH 666 25pF 74mH 3043 23pF
Christopher NaumannARENA Workshop 2006, Newcastle
Sensitivity (1): Derivation
• piezoelectric effect: pressure voltage
generalised n > 1
1kHz 10kHz 100kHz 1MHz
1
10
0.1
0.01 6 LRC branches
FU 0
LRC
CpUa
a) ideal piezo converter: U / p independent of frequency
b) real piezo converter: LRC branches and Cp as voltage divider Ua / p frequency dependent
(for 0 constant static case) real piezo converter, n=1
electrodes
"pressure signal"
1kHz 10kHz 100kHz 1MHz
1
10
0.1
0.01
rela
t. s
ensi
tivity
static sensitivity
sensitivity resonance
Christopher NaumannARENA Workshop 2006, Newcastle
Sensitivity (2): Comparison
• From Impedance get equiv. parameters sensitivity prediction
• Measurement of Sensitivity directly on complete sensor in water tank
good agreement between prediction and measurement !
calibrated transducer
sensor signal generator+ oscilloscope
Points: MeasurementLine: Prediction
10 20 30 40 50 60 70 80 90kHzsens
itivi
ty d
B r
e 1V
/µP
a -180
-190
-200
data sheet: -192dB=.25mV/Pa
example: piezo coupled to tank wall
Christopher NaumannARENA Workshop 2006, Newcastle
Sensitivity Measurement - Principles
Calibration Chain:
1. Cross-calibrate transducers using identical pair
2. calibrate receivers against transducer
can get complete spectrum from onlyone measurement per sensor device !
voltage pulse sent
pulse received
time(µs)
ampl
itude
(V
)
frequency domain
transfer spectrum (raw)
corrected sensitivity
fourier transform and divide correct for
distance and sender
log frequency (kHz)
dBre
1V
/µP
adB
(V
/V)
Christopher NaumannARENA Workshop 2006, Newcastle
Device Calibration – Examples
• done for commercial hydrophones (cross-check!) and self-made sensors
can also invert this process to predict signal shapes...
Acoustic Module (Piezo in Sphere)
10kHz 100kHz
amplifier cut-off
“plateau” at -120dBre(V/µPa)
piezo resonances
~ -120dBre(V/µPa)(=1 V/Pa) between 10
and 50kHz
commercial hydrophone with pre-amp (HTI)
measurement: -156.7dBre(V/µPa)
(=14.6mV/Pa)
data sheet: -156dBre(V/µPa)
piezo resonance
Christopher NaumannARENA Workshop 2006, Newcastle
100 200 300 400 500kHzlo
g P
SD
[a.
u.]
0 100 200 300 400 500 µs
ampl
itude
[a.
u.]
raw signal
2-res. piezo
raw signal
signal response
Prediction of Signal Response
Knowledge of system transfer function allows calculation of signal response:• signal response R(t) = raw signal S(t) convoluted with impulse response I(t)
• Thus, calculate signal response by multiplication in fourier domain and subsequent re-transformation into the time domain
dtIStR
)()()( ISR~~
)(~ fourier transform
FT
FT-1
Christopher NaumannARENA Workshop 2006, Newcastle
predictedmeasured sensitivity
Application: Response of Complex System
•measure system sensitivity (absolute value only ?)
•model piezo response + amplifier characteristics
•fit model to measurement:
get full (i.e. complex) transfer function
•predict signal shapes => simulate signals and noise !
predicted
measured
model fit (3 resonances)
measured sensitivity
impulse response(calc.)
400µs
a.u.
example:
BIP signal as seen by commercial hydrophone
?
apply this knowledge of piezo response also to complex sensor systems:
FT
Christopher NaumannARENA Workshop 2006, Newcastle
Model Predictions (2) – Piezo Elongation
• inverse piezoelectric effect: applied voltage U = > elongation x (important e.g. for acoustic senders)
LRCLRC Z
UIv
11
t
LRC
tdtUZ
tx0
1
)(~
)(~1~
U
ZA
gdU
Zix
LRCLRC
LRCLRC ZiZAi
gh
U
x
1
~~
s
F
s
UCU
A
ghx
CiZ stat
statstatLRC ...
1
coupling: current <-> velocity:
for sine signal, frequency :
applicable to arbitrary signals by fourier analysis
behaviour for 0:
static case x=U/s
=displacement averaged over face of piezo
displacement proportional to integral over voltage
see Karsten's talk tomorrow
Christopher NaumannARENA Workshop 2006, Newcastle
Noise
• Important in addition to sensitivity: intrinsic noise of sensors = noise of piezo element + amplifier
– intrinsic noise of piezo: thermal movement equivalent to thermal (Nyquist) noise of real part of piezo impedance
– amplifier noise from OP amps (active) and resistors (passive)
piezon ZkTe Re42
close to resonances, piezo dominates, below amplifier
noise spectral density (PSD)
example:
acoustic module
sensitivity ca.-115 dB re 1V / µPa=1.8 V / Pa
•guidelines for amplifier design
•S/N prediction50kHz 100kHz 150kHz
-80
-100
-110
PS
D [
dB r
e 1V
/H
z]
op amp
piezo element
Piezo+Amp (measured)-90
acoustic back-ground in lab
Christopher NaumannARENA Workshop 2006, Newcastle
Conclusions and Outlook
• Achievements:– easy description of piezo sensors by electromechanical equivalent
properties possible– Acquisition of equivalent parameters by impedance measurement (also
for coupled or coated piezo elements) – very good agreement between model predictions and measurements for
sensitivity, displacement and noise– possibility to model signal response
• Outlook:– use this knowledge to design and build acoustic storeys for ANTARES
for operation in the deep sea !– do extensive simulation / reconstruction studies using realistic system
response
Thank you for your attention !
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