Piezo film: Form and function

129

Sensors and Actuators, A21bA23 (1990) 729-733

Piezo Film: Form and Function RICHARD

H BROWN

Pennwalt Pzezo Film Ltd. 22 Ruigeway, lidlend Industnal Park, Dunfermlme, FtJie KY1 1 5JN (V K)

Abstract Many excellent mathematical models exist for predlctmg the h&-frequency response of plezoelectnc transducers Most of these, however, are designed to descnbe the behavlour of thickness-mode devices With the advent of plezoelectnc polymer matenal and, m paticular, large-scale produclon of the plezo form of polyvmyhdene fluonde (PVDF), a new class of very useful transducers has amen These are more closely allied to stram gauges, but demonstrate very high voltage sensmvtty to strain In many circumstances low-frequency response is of more concern than the upper hrmts and a sample resistor/capacitor model sufEces But the umque properties of ‘piezo film’ allow operation into frequency ranges far beyond those possible usmg foil resistance gauges The object of this paper IS to demonstrate how the hgh-frequency response of planar plezoelectnc strain sensors may be denved qmte sunply from mspectlon of the surface geometry of the elements themselves The standard tools of signal theory are applied m an abstract manner, and the general form of the results allows prediction and construction of complex signal-processing elements usmg standard film pattermng techmques The author has worked wtth the applications engmeermg group of Pennwalt Corporation’s plezo Film Department since 1984, and has seen the development of PVDF from a laboratory cunoslty into its current poslhon of major unportance as an electromechamcal and pyroelectnc transducer component 1. Introduction The effects which govern the frequency response of plezoelectnc transducers are, generally speakmg, well defined and understood At the low-frequency end of the spectrum a simple R-C model adequately describes device behavlour (see Fig 1) For higher frequencies more complex models have been developed and refined [l] Such models were ongmally deslgned for highly resonant matenals 0924-4247/90/$3 50

such as quartz and PZT Polymer matenals such as polyvmyhdene fluonde (PVDF) show much higher damping factors, but the mathematical models can be modified to reflect thus With the current expansion m the scope of plezoelectnc polymer transducer applications, however, a werent set of conslderatlons may anse In perhaps the= simplest mode, plezo-film transducers (m the ‘receiver’ mode) act as dstnbuted ‘dynanuc stram gauges’, where the sensing area can be virtually unhnuted Here the transducer consists simply of an mve area of fihn defined by a repon of overlapping metalhzed electrodes on upper and lower surfaces, and a connection arrangement The device IS then bonded, hke a strain gauge, to the substrate under test In ths case the effective damping factor for the polymer ISmtmtlvely h@er than for an unsup ported element operatmg m the ‘thckness’ mode The extremely thm cross section would not be expected to support resonant modes between its ends (assummg that the lateral dunenslons are orders of magmtude greater than the thickness) In fact, the properties of the substrate are assumed to govern all aspects of resultant signals The object of this paper is to investigate the relahonshlp between the geometry of such transducers and thar function as signal-processing elements in an abstract manner, by considermg thar response to a hypothetical mechamcal impulse A techmque, rather than a model, 1s proposed to descnbe the high-frequency behavlour of piezoelectnc polymer stram transducers using the standard tools of signal theory To avoid duphcation, the plezo-iilm devices are assumed to be mechamcal-to-electrical energy convertors, although the governing pnnclples apply equally well in reverse 2. Discussion of MechamicdUnit Impulse In electromc circuit analysis, the frequency response of a system can be described equally well by a graph m the frequency domain or by the amphtude/tlme plot of the impulse response By the duahty property of the Founer transform, the 0 Elsevler &quola/Pnnted m The Netherlands

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mformatlon dlsplayed m either form 1s equivalent An analog clrcult IS excited by a high amphtude pulse of extremely short duration whose ‘area’ (product of amphtude and duration) 1s umty This input signal contams equal energy over a very wide bandwdth and can thus ehclt all of the clrcuzt behavzour The resultmg output or impulse response can then be processed by the Founer transform to reveal the arcmt frequency response In the mechamcal world, severe practical problems underlie the generatlon of anythmg resembling a umt impulse, and so the normal procedure 1s to apply an input of known Founer transform, obtain the transform of the output signal and, by dzvzslon, extract the system frequency response For plezo-film stram transducers the problem is to apply an input of sufliclently high bandwdth, since the frequency response may extend to many megahertz It 1s proposed that an entirely conceptual analysis can, m tlus case, be performed by consldermg a hypothetical planar impulse which artrves from a gzven dire&on as a parallel wavefront onented perpendicular to the direction of propagation This slgnal 1s carned by the substrate, not by the film itself, and zts ueloczty rejects fhls At any instant, the film output IS then determmed by the ‘area’ of mtersectlon of the wavefront with the transducer area By the ‘szftmg’ property of the Dzrac functlon, this overlap 1s simply the width of the plezoelement at that instant (Fig 2) Thus there is a

Fig 2 Unit sample method

very direct relation&p between the active area and the system impulse response and the response can, m fact, be wntten down by mspection By changmg the angle of mcldence of the planar Impulse It 1s possible to bmld up a polar response pattern Symmetry m the geometry of the transducer 1s obvzously camed through to the polar frequency response 3. Piem Film as a Signal processOr The effect of Merent transducer shapes can now be considered By &rect consequence of the properties of the Founer transform, a rectangular element &splays a frequency response curve of the form smx/x Hrlth the mam lobe centered on zero frequency and a setles of nulls spaced equally m frequency (Fig 3) (It 1s worth noting that tlus response would be predicted for film operatmg m the thickness mode if the level of damping was cntical The nulls would represent the frequencies at which the wavelength of mcldent energy corresponded to the thickness of the sensmg element If the Q of the thickness-mode device was lugher, then there would also exist a senes of peaks at the multiples of 1212 It 1s assumed that the effective level of damping will not support resonances m the planar mode) A circular element shows snmlar form, but wrth a wder mam lobe and faster roll-off of mmor lobes Care must be taken when comparmg circular and square elements, since for umt areas the diameter of the circle IS longer than the width of the square Hence the wdth of the main lobe in the frequency response 1s reduced to Just fractzonally wader than the square The upper frequency roll-off 1s perhaps the most mterestmg area of difference If a tangent 1s drawn to the peaks of the mmor lobes, It 1s found that the rectangle shows - 20 dB/decade slope, while the czrcle gives - 32 db/decade Another shape of interest, although perhaps zmpracfical from symmetry conslderatlons, 1s a bilateral exponential (hke a htghly styhzed Chrrstmas star) This shape, when either axls is perpen-

731

roll-off of the longer element’s response was then clearly seen Before consldermg the derived polar frequency responses of vatlous shapes, it is important to take mto account the Merence between the two commencally avadable forms of PVDF, namely um- and blaxlally one&d film Umaxutl film vvlll show higher plezo output for stress mduced parallel to the machme direction of the 6hn and reduced output m a drrectlon perpendicular to the machme axis Blaxlal fihn shows more! umform actiwty at a ‘compronuse’ output level Both types can be programmed usmg we@mg factors varymg wth Incidence angle for polar response plots Circular elements are the snnplest case by virtue of their symmetry For blaxlal film, the result becomes tnvlal wth the polar response relktmg the symmetry of the element With umaxial fihn, only the mam lobe 1s affected s~gmficantly A dipole-hke pattern 1s introduced near the ongm, wth the zero and 90” values showmg the difference between the machme and transverse axes plezo coelkents (Fig 5) Square elements show that the mam lobe de scribes an almost circular polar response unbl the amphtude has fallen considerably Upper frequencles then tend towards a square polar pattern Thrs IS mterestmg because the dagonal or 45” response shows the wtdest mam-lobe bandmdth, although this angle presents the longest time-duration response from the element The reason hes m the form the impulse response m this case becomes tnangular An mtultive explanation IS that the mangle more closely approximates an impulse by focusmg more signal around the mrd-

Fig 3 Typical frequency response of element of piezo 6lm

dlcular to the nnpulse wavefront, should show no nulls m the frequency response but snnply an exponential decay w$h mcreasmg frequency Agam, thus results from the mtegratlon properties of the exponenual function A simple expenment was designed to demonstrate the higher bandwdth of short elements versus long Two narrow (6 mm) sttlps of fihn were prepared, one of length 50 mm, the other 350 mm Both were bonded to the surface of a circular bar of brass Impulses were applied to one face of the bar, and the resulting signals for each transducer were averaged and compared Obvlously, the bar did not transnut all frequencies equally well, and the narrow-band spectra only show a trend (Fig 4) The spectra were reprocessed to obtam the band energes as a fixed bandwrdth lilter was stepped through the full spectra The SPAN

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point, whereas the square has evenly dtstnbuted output over ttme Rectangular shapes m general have rectangular polar responses, but the long axes of the shape results m a narrower bandwtdth of frequency response, and vtce versa Thus a rot&on of shape 1s tmphed m the transformatton between surface geometry and polar response

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Electrode patterns may be formed on ptezo film by sputtermg or deposrtmg through a mask, or by screen-pnntmg wrth conducttve mk It 1s therefore very easy to form many discrete sensing elements on one contmuous sheet, and also to mterhnk these elements As an example of how the very abstract methods descrtbed above can be harnessed m a useful way, a device was constructed whtch resembled m many ways a convenwave tional mterdrgrtal surface acoustic transducer Two interlaced sets of ‘fingers’ were patterned on the upper surface of a sheet of film The lower electrode was contmuous and covered only the overlapping regton of the fingers Imtmlly thts rear electrode was made rectangnlar, later versions used one or several lobes of the smx/x function The two mterdtgttal electrodes only were electrtcally connected to measunng equipment The device was bonded to sheets of glass, for reasons which wtll become apparent later With a rectangular rear electrode, the theorettcal impulse response should consist of a series of

Fig 6 lnterdlgltal and circular elements, response to Impulse on glass

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alternating polanty umt impulses, with the spacmg of the impulses determmed by the speed of sound m glass This velocity 1s rather hard to define preasely, since the propagation of different types of wave under different condltlons leads to a wide vanety of numbers At any rate, the Founer transform of such an impulse response predicts a band-pass charactenstlc, wth the wdth of the pass band being determmed by the number of separate impulses m the complete response The centre frequency 1s simply the mverse of the transit time between two posltlve (or negative) ‘fingers’ Expenmental venficatlon of this deuce proved prehctably difficult, due to the tmpossibthty of launching a unit mechamcal impulse However, the output resulting from breakmg the glass sheet showed that frequencies around the predicted pass band were gven preferential amphficahon The glass-break event, m fact, offered a nearly random input signal for htgh frequencies when checked with a single broad-bandwidth transducer (Fig 6) Eventually, another similar mterdlgtal transducer was used to launch a low-amphtude signal onto the glass, and the resulting output showed very clearly the charactenshc of the combined transmit/receive system The centre of the pass band was found to be affected by different thickness (or possibly composition) of glass The intended use for the devices was as glassbreak detectors The benefit of the pass-band limitation was to allow only certain frequencies that result exclusively from breakage to be detected and thus ehmmate false alarms In fact, it was found that minor breakage (as found Hrlth the impact of gravel) could generate almost as much lngh-frequency signal as total fracture One significant advantage of the transducer was then that one side of the mterdi@tal pattern could be momtored with reference to the rear plane, gvmg a low-pass charactenstic Thus the low frequencles resulting from the ‘push’ exerted on the glass could also be measured Combmmg the low- and high-frequency signals Hrlth simple AND logs gave an extremely reliable decision on the event A possible development IS the production of an mterdlgtal device showmg circular symmetry (a senes of rmgs or arcs alternately Hrlred) Such a device has been tned, with good prehmmary results Off-axis response was found to be better than for hnear arrays These mterdlgtal devices effectively supply gain at certain frequencies with very simple control over pass-band charactenstlcs The major differences over existing SAW filters are that the operating frequency 1s determined by the sub-

strate matenal and not by the transducer alone, and that much lower frequencies can be achieved easdy since very large area devices are possible and thus vvlder spacmg of the ‘fingers’ Fmger Hrldth actually controls the amphtude of the upper harmomcs of the filter response Very narrow fingers, wluch themselves would show high bandwdth, allow multiple pass bands repeating through the frequency domam Wide fingers supempose a smx/x characterrstlc on the upper harmonics It is interesting to note that this type of filter cannot be exactly represented by any analogue electronic network, but that it closely resembles a class of d@al filter described by a simple polynormal expression m the z domam The degree of the polynormal ts determmed by the number of fingers m the device, and the repeating property m the frequency domain 1s precisely analogous to any d@al filter If no ‘spaces’ are included m the impulse response, then the d@al equivalent filter IS actually a high-pass one, but the repetlhon m frequency of d@al filters makes the class&cation of band-pass or high-pass m this comparison irrelevant When one or more zero samples are included between the unit samples, then the d@al filter 1s indeed a band-pass

5. Conclusions

It has been shown that the h&-frequency response of planar piezoiihn elements can be denved very simply from analysis of their physlcal shape Their propeties are also affected by the substrate to which they are attached In general, large planar dlmenslons imply low bandwidth, and vice versa Frequency response can be altered by selection of shape to enhance or rmmnuze hrgh-frequency attenuation More complex patterning can offer controlled band-pass and other charactenstrcs

Reference 1 W P Mason, Ekctromechanrcal Transabcers and Wave AIrem, Van Nostrand, New York, 2nd edn, 1948, pp 185% 224

Bibliography General mfornuhon about Reu, Fdm may be found m I Techwul hfunrwl, Rem Fdm Department, Pennwalt Corporat1on, 1987 2 M G WC, Ultrasonrc Transducers for Nondestructrw Testmg, Adam Hdger, Bnstol, 1984