Transcript ARENA06 Naumann

Understanding Piezo based
Sensors for an acoustic
neutrino detector
ARENA-06, Newcastle, UK
Christopher Naumann, Universität Erlangen-Nürnberg
Acoustic Detection with the ANTARES Telescope
re-fit several ANTARES
storeys with acoustics
hardware (sensors and DAQ)
Aims:
replace optical sensors
with acoustic sensors
(schematic)
-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)
ARENA Workshop 2006, Newcastle
Christopher Naumann
Aim: Acoustic Sensors
• Basic Design of Sensors for the ANTARES acoustics
cable
internal
pre-amplifier
ANTARES
glass sphere
17" (42cm)
– Sensor = piezo element (disc and/or tube) + pre-amplifier
– either encapsulated in polyurethane = > "hydrophone"
– or coupled to ANTARES glass sphere = > "acoustic module"
piezo tube
PU coating
piezo sensors + pre-amplifiers
Signal response and noise characteristics of sensors depend on
piezo element  try to build model
ARENA Workshop 2006, Newcastle
Christopher Naumann
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:
A
F
h
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
mechanical oscillator
p
inductance L
 = electromechanical
coupling constant
(depends on material)
Fext  mx  Wx  Sx
LRC
(Cp = electrical capacity
between electrodes)
electrical oscillator
  RQ  1 Q
U ext  LQ
C
knowledge of equivalent circuit  simple model of piezo
ARENA Workshop 2006, Newcastle
Christopher Naumann
Equivalent Properties (1): Measurement
• get all properties from single impedance measurement on piezo element:
apply gaussian signal on voltage divider
made of piezo and suitable capacitor
measure signal over capacitor
2.
calculate fourier transforms of signals
3.
from these calculate impedance
spectrum of piezo element
Impedance (k)
100
10
1
0.1
1.
AntiResonance
(Z maximal)


1


Z Piezo     iC p   Z LRC


,i
i 1


100kHz
n
Z LRC ,i    iLi  Ri  1
Resonance
(Z minimal)
10kHz
equiv. circuit
with n parallel
LRC branches
1MHz
1
iC i
Fit with Li, Ri and Ci as parameters
possible for free and coated or attached piezos
ARENA Workshop 2006, Newcastle
Christopher Naumann
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 free piezo
74mH 666 25pF
Impedance (k)
100
10
0.1 1
free piezo: strong resonances
coupled:
resonances
suppressed
10kHz
piezo in sphere
74mH 3043 23pF
100kHz
1MHz
Frequency
sensitivity of piezo
element can now be
modelled...
significant increase of equivalent ohmic resistance  damping
ARENA Workshop 2006, Newcastle
Christopher Naumann
Sensitivity (1): Derivation
• piezoelectric effect: pressure  voltage
a) ideal piezo converter: U / p
independent of frequency 
"pressure signal"
U0     F
b) real piezo converter: LRC branches
and Cp as voltage divider
 Ua / p frequency dependent
Cp
(for 0 constant  static case)
relat. sensitivity
LRC
Ua
electrodes
real piezo converter, n=1
sensitivity resonance
10
10
1
1
generalised n > 1
0.1
0.01
0.1
static sensitivity
1kHz 10kHz 100kHz 1MHz
ARENA Workshop 2006, Newcastle
0.01 6 LRC branches
1kHz 10kHz 100kHz 1MHz
Christopher Naumann
Sensitivity (2): Comparison
• From Impedance get equiv. parameters  sensitivity prediction
• Measurement of Sensitivity directly on complete sensor in water tank
sensitivity dB re 1V/µPa
example: piezo coupled to tank wall
sensor
calibrated
transducer
signal generator+
oscilloscope
ARENA Workshop 2006, Newcastle
-180
Points: Measurement
Line: Prediction
-190
data sheet:
-192dB=.25mV/Pa
-200
10 20 30 40 50 60 70 80 90kHz
good agreement between
prediction and measurement !
Christopher Naumann
Sensitivity Measurement - Principles
frequency domain
amplitude (V)
dB (V/V)
voltage pulse
sent
transfer spectrum (raw)
time(µs)
fourier transform
and divide
Calibration Chain:
1. Cross-calibrate transducers using
identical pair
2. calibrate receivers against transducer

can get complete spectrum from only
one measurement per sensor device !
ARENA Workshop 2006, Newcastle
dBre 1V/µPa
pulse received
correct for
distance and
sender
corrected sensitivity
log frequency (kHz)
Christopher Naumann
Device Calibration – Examples
•
done for commercial hydrophones (cross-check!) and self-made sensors
commercial hydrophone
with pre-amp (HTI)
piezo resonance
measurement:
-156.7dBre(V/µPa)
(=14.6mV/Pa)
data sheet:
-156dBre(V/µPa)
Acoustic Module
(Piezo in Sphere)
“plateau” at
-120dBre(V/µPa)
piezo resonances
amplifier cut-off
~ -120dBre(V/µPa)
(=1 V/Pa) between 10
and 50kHz
10kHz
100kHz
can also invert this process to predict signal shapes...
ARENA Workshop 2006, Newcastle
Christopher Naumann
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)

R(t ) 
 S ( )  I (t   ) d
fourier transform
~
~
~
R ( )  S    I  

raw signal
FT
signal
response
log PSD [a.u.]
amplitude [a.u.]
• Thus, calculate signal response by multiplication in fourier domain and
subsequent re-transformation into the time domain
raw signal
2-res. piezo
FT-1
0
100
200
300
400
500 µs
ARENA Workshop 2006, Newcastle
100
200 300 400 500kHz
Christopher Naumann
Application: Response of Complex System
apply this knowledge of piezo response also to
complex sensor systems:
example:
•measure system sensitivity (absolute value only ?)
•model piezo response + amplifier characteristics
•fit model to measurement:
 get full (i.e. complex) transfer function
BIP signal as
seen by
commercial
hydrophone
?
a.u.
•predict signal shapes => simulate signals and noise !
measured
sensitivity
predicted
measured
impulse
response
(calc.)
FT

model fit
(3 resonances)
400µs
ARENA Workshop 2006, Newcastle
Christopher Naumann
Model Predictions (2) – Piezo Elongation
• inverse piezoelectric effect: applied voltage U = > elongation x
(important e.g. for acoustic senders)
coupling: current <-> velocity:
v
1

I LRC
1 U

 Z LRC
1
xt  
  Z LRC
 U t dt 
t
0
displacement proportional
to integral over voltage
for sine signal, frequency :
~
x   
1
gd
~
~
U ( ) 
U ( )
iZ LRC  
AZ LRC
~
x
gh
1


~
U AiZ LRC iZ LRC
behaviour for 0:
Z LRC 
U stat. F
1
gh
 xstat. 
CU stat. 

iC
A
s
s
ARENA Workshop 2006, Newcastle
=displacement averaged
over face of piezo
applicable to arbitrary signals
by fourier analysis
see Karsten's talk tomorrow
static case x=U/s
Christopher Naumann
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
en2  4kT Re Z piezo 
noise spectral density (PSD)
example:
acoustic module
sensitivity ca.
-115 dB re 1V / µPa
=1.8 V / Pa
PSD [dB re 1V/Hz]
– amplifier noise from OP amps (active) and resistors (passive)
-80
acoustic background in lab
Piezo+Amp
(measured)
-90
-100
-110
close to resonances,
piezo dominates,
below amplifier
•guidelines for
amplifier design
op amp
piezo element
50kHz 100kHz 150kHz
ARENA Workshop 2006, Newcastle
•S/N prediction
Christopher Naumann
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 !
ARENA Workshop 2006, Newcastle
Christopher Naumann