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 !