Piezoelectric transducers

Transcription

1 Piezoelectric transducers are beased on the property to accumulate charges if stressed (direct effect)and to strain in case of an electric signal is applied across their electrods(inverse effect) 1

2 basics.. Piezoelectricity is due to asymmetries in the crystallographic structure. Null polarization Polarization in the same direction as the stress Perpendicular polarization 2

3 An example.. BariumTitanate(BaTiO 3 ) 3

4 Rosettes of piezoelectrics exist to detect deformation in two or three direction Ref. Book G. Gautschi, Piezoelectric Sensorics, Springer Edt. 4

5 Advantages High stiffness, to measure force. High resonant frequency(up to 500 khz) Stability, reproducibility and linearity Large operating temperature range Low sensitivity to external magnetic field. Drawbacks CurieTemperature,T c Resonant behavior High output impedance Cannot be used to detect static quantities 5

6 Benchmark between sensors Low threshold!! High responsitivity!! High operating range!! 6

7 Modelling.. T S = F A = Y l l = YS = st; s = 1 Y Y=Young module In case an electric field is applied to a dielctric material D = εe = ε 0E + P Where D is the elctric displacement vector and P is the polarization 7

8 Modelling.. In case of a piezoelectric the mutual effects come to play: Polarization Stress Electric field Strain ε T D = S = s dt + ε E T + de dielectric constant for a constant stress s E softness for a constant E field d (C/N) Piezoelect ric constant T E 8

9 Modelling.. T D = dt + ε E S = s E T 1) Actuator working mode : + de T D = ε E S = de 2) Sensor working mode in short circuit (E=0) D S = dt = s 3) Sensor working mode in open circuit (D=0) : S = s E T T 0 = dt + ε E E T + de d E = T = gt g is the voltage piezoelectric constant ε T 9

10 A method for the estimation of thedparameter R s, C s sensor C c wires R a, C a voltage amplifier. D = d33t Q = d F I 33 dq = dt = d 33 df dt R scr I C = I = I R scr sc 1 1 scr R V = IC = I = I = sc sc 1+ scr 1+ scr R d33f src d33f τs = d33sf = = 1+ scr C 1+ scr C 1+ τs con τ = RC In the high frequency domain the relationship between V and F is frequency independent Forcing the device with a known force and measuring V it is possible to estimate d 33 In case of a unknown C a high value capacitor can be added in parallel. 10

11 A method for the estimation of thedparameter R s, C s del sensore C c del cavo R a, C a dell ampl. di tens. D = d33t Q = d F I 33 dq = dt = d 33 df dt V F d s = 33 τ = C 1+ τs con τ The circuit is a high pass filter. Ex. In case of C=0.1pF, R=1TΩ : f t,amp =1/(2πRC)=3Hz RC Moreover, the high output impedence of the piezoelectric can cause coupling problem with the amplifier 11

12 A method for the estimation of thedparameter I I eq V I 2 V A ' = V 10 5 A I sd V V F V F + 33 I eq F V 1 1+ A = + I 2 ' Ad C Ad C scr R f f = src R + sc src R 1+ scr f src + ( V V' ) ( 1+ A) ( + C ) sr C f + src f A sc A f f f sc f = = sd 33 0 F f 1 t,cha = πrc A << 2 f f t,amp 12

13 A method for the estimation of thedparameter The Drift problem!! I I 2 ' V = V A I eq V R 1+ scr f t, ChA 1 = 2 π R f C suitbale feedback f parameters can allow to obtain : f t, ChA < f t, Amp Ex: if C f =10pF, C=0.1pF, R=1TΩ, R f =1T Ω si ha: f t,amp =1/(2πRC)=3Hz f t, ChA =1/(2πR f C f )=0.03Hz 13

14 Piezoelectric Cristals Piezoelectric behavior in lithium niobate (LiNbO3) and lithium tantalate (LiTaO3) was first studied in the mid-1960s [2]. Both have ε values of approximately 40. If cut correctly, they have coupling coefficient (k) values of 0.65 and 0.4, respectively. In addition, the Curie points for both are extremely high (T0 ~ 1210 C for LiNbO3,and 620 C for LiTaO3). PbTiO3 shows to posses excellent piezoelectric properties when oriented along the [001] direction. The piezoelectric charge coefficient d33 of C N 1, coupling coefficient k of more than 0.9, and ultrahigh strain of 1.7% were achieved in Pb(Zn1/3Nb2/3)O3-PbTiO3 solid solution. These single-crystal relaxor materials are now being intensively investigated and show great promise for future generations of piezoelectric transducers and sensors. 14

15 Piezoelectric Ceramics Perovskites Perovskite is the name given to a group of materials with general formula ABO3 having the same structure as the mineral calcium titanate (CaTiO3), barium titanate (BaTiO3), lead titanate (PbTiO3), lead zirconate titanate (PbZrxTi1-xO3, or PZT), lead lanthanum zirconate titanate [Pb1- xlax(zryt1-y)1-x/4o3, or PLZT], and lead magnesium niobate [PbMg1/3Nb2/3O3, or PMN]. Es. The d15 and d33 coefficients of BaTiO3 are 270 and C N 1, respectively. The k for BaTiO3 is approximately 0.5. Calcium-doped PbTiO3 has a relative dielectric constant e33 of 200, a d33 of C/N, and a k of approximately 0.5. The addition of calcium results in a lowering of the Curie point to 225 C. 15

16 Piezoelectric Ceramics Originally piezoelectric ceramics shows a random orintation of dipoles leading to a null polarization In order to obtain a preferential axis (polar axis) a polling process Is required.. 1) heating the material close to the Curie temperature 2) applying an electric field (10kV/cm) parallel to the polar axis 3) cooling the material exposed to the electric field 16

17 Examples 17

18 Example 1: Lead titanate: d=-44pc/n; ε T =600ε o ; g=-8(mv/m)/(n/m 2 ); We are looking for the Voltage (open circuit)duetoaforceof 1000 Napplied toacubewitha1cmside. SOLUTION: E Open circuit operation: = V = d T ε T E h D = 0 ( 12 )( /(.01) ) = = 82.9 kv/m = * = V = 18

19 EXAMPLE 2: Requirements: The strain due to an applied voltage V=1kV(no mechanical load). SOLUTION S = de = h = T ( ) ( ) = = 4.4µε 0.01 = = 44nm = = = 19

20 In real devices 6 possible axis must be considered: 3 for stress due to compression/expansion 3 for torsional stress 20

21 The matrix form of equations are: [ S ] = [ s ][ T ] i i = 1, 2, 3 j = 1,..,6 [ D ] = [ ε ][ E ] i, j = 1, 2, 3 i ij ij j j [ S ] = [ s ][ T ] + [ d ][ E ] i ij j ik k i, j, [ D ] = [ ε ][ E ] + [ d ][ T ] i n = 1,...,6 im k, m = 1, 2, 3 ε m im d = 0 in ij n = d for ji i m 21

22 Ex. In case of a torsional stress of 1N/m 2 applied to axis 2 (direction 5) will produceachargedensityof 515 pc/m 2 along direction 1. 22

23 23

24 PZT characterization Target: a new low cost strategy to characterize the behaviour of piezoelectric bimorphs in a cantilever configuration, envisaged for research and educational activities. Methodology: a contact-less measurement system based on coupled Infra-Red (IR) sensors and a CCD based calibration facility. IR Transmitter IR Receiver EL-23G/ST-23G Reference point Piezoelectric bimorph IR sensors DAQ Card PCI-6052E Infrared Diode Waveform generator Piezoelectric bimorphs Plexiglas Piezoelectric bimorph Conditioning circuit Physik Instrument Amplifier

25 PZT characterization The calibration strategy for the IR system. The system is composed of: a CCD sensor an image processing tool estimating the position of a marker deposited on the top of the piezoelectric actuator (LabVIEW, IMAQ Vision). To this aim the actuator is activated by a low frequency stimulus (lower than 200 mhz) (compatible with the 30 frames/s rate of the video acquisition system). Deflection Conversion factor [mm/pixel] Environment developed to process frames recorded by the CCD device. The virtual instrument for calibration of the IR tool.

26 PZT characterization The calibration strategy for the IR system. δ = u δ =6 µm V out CCD conversion factor: 13.7 µm/pixel

27 PZT characterization S Hysteresis Inverse piezoelectric effect. Rate-dependent memory dominates at high frequencies due to a phase-lag effect. Rate-independent memory prevails at low frequencies.

28 Pyroelectric materials Among Piezoelectric, some materials exist which show a spontaneous polarization: these materials are called Piroelectrics and shows a relationship between the polarization and the temperature. DP = A DT 28

29 Ferroelectric materials Ferroelectric materials are a special class of non linear Piroelectric materials where the spontaneous polarization can be reversed by an external electric field. Domain wall and dipoles inertia! V(P) DV P - P +

30 Sumarizing Perovskite: (BaTiO 3 ); (PbTiO3); (CaTiO3); PZT; PLZT; ceramics 30

31 Ceramics Ex. Barium Titanate: (a) Cubic lattice (above Curie temperature). (b) Tetragonal lattice (below Curie temperature). The Curie point is about 130 C. Above 130 C, a nonpiezoelectric cubic phase is stable, where the center of positive charge (Ba2+ and Ti4+) coincides with the center of the negative charge (O2 ) (Figure a). When cooled below the Curie point, a tetragonal structure (shown in Figure b) develops where the center of positive charge is displaced relative to the O2 ions, leading to the formation of electric dipoles. 31

32 Ultrasound sensors They are based on emission and reflection of sound waves. Elettrostatici Types: Piezoelettrici 1. Mechanics 2. Elettromagnetics: low frequency 3. Piezoelectrics: for high frequency; they can be used both as Transmitter and Receiver. 4. Electrostatics: a capacitor with a free central plate; they can be used both as Transmitter and Receiver. 5. Magnetostrictive: ferromagnetic materials which can be strained in the presence of a magnetic field; they can be used both as Transmitter and Receiver. 32

33 Ultrasound sensors Distance measurement are based on the time of flight (TOF). Reflected beam S A O Transmitted beam z TOF = 2d v s S A Receiver d Target y 33

34 Ultrasound sensors Notes: Working temperature below the Curie temperature. The same device can be operated as transmitter and receiver (transceiver). They are typically operated at their resonance frequency 40kHz. Low cost Strongly influenced by the temperature Resolution is limited to the wavelength 34

35 Ultrasound sensors Principles of Time-of-Flight Systems Pulse echo method: is the simplest one; Low signal to-noise ratio (SNR) because of the low transmitted energy due to the short duration of the pulse. Multireflections are detectable. Phase angle method: the phase angle is measured between the continuous transmitted signal and the continuous received signal and is used as a measure of the distance. Relatively insensitive to disturbances. Multireflections are not detectable in a meaningful way. No usable when the distance is longer than one wavelength. Frequency modulation method: uses transmitted signals that are linearly frequency modulated. Thus, detected signals are a delayed replica of the transmitted signal at an earlier frequency. The frequency shift is proportional to the time-of-flight. Robust against disturbing signals; Multireflections are detectable. Correlation method: determines the cross-correlation function between transmitted and received signals. Robust against disturbances; Multireflections are detectable. 35

36 Ultrasound sensors Electronics for the correlation method Comparison between different strategy 36

37 Encoders They provide a digital output and can be used for translational or rotational displacement Main types: Incremental Absolute. Examples of optical encoders 37

38 Encoders Binary Absolute Encoder Ambiguity of the binary code: Ex: the switching between 7 and 8 will produce double inversions of bit (1 to 0 and 0 to 1). Loss of synchronization can cause ambiguity. 38

39 Encoders The Gray code will avoid ambiguity because the transition between two consecutive states will produce variation of 1 bit 39

40 Incremental encoder Encoders The use of two independent output signals will allow to detect the magnitude and the versus of the displacement. 40