1. Understanding Piezo based Sensors for an acoustic neutrino detector Christopher Naumann, Universität Erlangen-Nürnberg ARENA-06, Newcastle, UK

2. 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 ( 100m) replace optical sensors with acoustic sensors (schematic)

3. 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" (42cm) piezo tube internal pre-amplifier PU coating cable ANTARES glass sphere Signal response and noise characteristics of sensors depend on piezo element  try to build model

4. 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/U=F/ voltage U elongation x Q=·xQ=·x charge Q stiffness S C=  ²/S capacity C damping W R=W/²R=W/² resistance R inertia m L=m/²L=m/² inductance L LRC (C p = electrical capacity between electrodes) knowledge of equivalent circuit  simple model of piezo  = electromechanical coupling constant (depends on material) F h A mechanical oscillatorelectrical oscillator p

5. Christopher NaumannARENA Workshop 2006, Newcastle Equivalent Properties (1): Measurement get all properties from single impedance measurement on piezo element: Fit with L i, R i and C i 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 Impedance (k  ) 0.1 1 10 100 Resonance (Z minimal) Anti- Resonance (Z maximal)

6. 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 1MHz Frequency Impedance (k  ) 0.1 1 10 100 free piezopiezo in sphere 74mH 666  25pF74mH 3043  23pF

7. 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 LRC CpCp UaUa a) ideal piezo converter: U / p independent of frequency  b) real piezo converter: LRC branches and C p as voltage divider  U a / 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 relat. sensitivity static sensitivity sensitivity resonance

8. 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: Measurement Line: Prediction 10 20 30 40 50 60 70 80 90kHz sensitivity dB re 1V/µPa -180 -190 -200 data sheet: -192dB=.25mV/Pa example: piezo coupled to tank wall

9. 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 only one measurement per sensor device ! voltage pulse sent pulse received time(µs) amplitude (V) frequency domain transfer spectrum (raw) corrected sensitivity fourier transform and divide correct for distance and sender log frequency (kHz) dBre 1V/µPa dB (V/V)

10. 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) 10kHz100kHz 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

11. Christopher NaumannARENA Workshop 2006, Newcastle 100 200 300 400 500kHz log PSD [a.u.] 0 100 200 300 400 500 µs amplitude [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 fourier transform FT FT -1

12. Christopher NaumannARENA Workshop 2006, Newcastle predicted measured 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 

13. Christopher NaumannARENA Workshop 2006, Newcastle Model Predictions (2) – Piezo Elongation inverse piezoelectric effect: applied voltage U = > elongation x (important e.g. for acoustic senders) 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

14. 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) 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 prediction 50kHz 100kHz 150kHz -80 -100 -110 PSD [dB re 1V/  Hz] op amp piezo element Piezo+Amp (measured) -90 acoustic back- ground in lab

15. 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 !