Mechanical Filters-A Review of Progress

IEEE TRANSACTIONS ON SONICS AXD ULTRASONICS, VOL. SU-18, NO. 3, JULY 1971 155 Mechanical Filters-A Review of Progress

ROBERTA. JOHNSON, MEMBER, IEEE, MANFRED BORNER, AKD MASASIII KONKO, MEMBER, IEEE

- Abstract-This paper isareview of electromechanicalbandpass 0 filter, resonator, and transducer development. Filter typesdiscussed include intermediate and low-frequency configurations composed of rod, disk,and flexure-barresonators and magnetostrictive ferrite g and piezoelectricceramic transducers. The resonators and transducers areanalyzed in terms of theirdynamic and material char- 2 2o acteristics. The paper also includes methods of realizing attenuation 2 poles at real and complex frequencies. The last section is a look at future developments. future 30

1 I II l I I 1 IXTRODUCTIOX 100 2W 300 500 1 OW 2000 30W 5ooo FREGUENCY (Hz1 ORE THAN 20 years haw passed since the first Fig. 1. Improvementin phonograph design through the use of practical mechanical filters were introduced by filter design metl~ods[61. Adler [l],Roberts [2], andDoelz [3]. These fibers met an existing need for greater selectivity in the IF stages of AM and SSB receiversdesigned for voice n m / FLEXURE (F" communication. Rlodern receivers and telephone communication equipments carry not only voice but data mes- sages as well, thus requiring lower passband ripple and well-definedand stable passband limits. In addition, greaterselectivity and lon.er loss areoften required. Mcchanic:~l filter development has kept pace with the demands of communicationengineers. For instance, filtershaving passband-~,ipple requirements of 0.5 dB or less or 60/3-dB bandwidthratios of 1.3/1 arenot unusual. Package size has also heen reduced; a 10-pole filter can be designed into a l-c1n3 package. In addition, the lower frequency limits of mechanical filters are now in the audio rangr; the upper limit is that of an AT-cut crystal. Although the mechanical filter was conceived in the US, a great' amount of cleyelopmental work is now being conductet1in Europe and .Japan. Early interestin the use of 111cchanical elementsto providepasshand cllaracteristics resulted from the de- velopnlent, of the electrical bandpass filter by Campbell and Wagner in 1917 [4].A number of patents relating tospring-mass systcms [5] were filed soonafter, but FREOUENCY - the most significant work in terms of practicaldeyices Fig. 2. Distributedelemrmt mecllanicnl filtcr (Mnson, 1941). wasdone by Maxfield and Harrison on phonograph

filter shown in Fig. 2 [TI.Pome of the significant, features M:~nuscripl rrceivetl .J:ln11:ly F, 1971. of this design includedthe use of piezoelectrictrans- R. A. Jnhnson is with the CollinsRadio Company, Newport ducers,distributed-Flement llalf-wavelength resonators, Bcnch, Calif. M. F3iirner iswith AEG-Telefunken Rescarcl1 Institute, Ulm; and an attenuation-pole-producing coupling element. Crrmnny. Just a fev7 years later, the first practical IF mechan- M. Iconno is with theDcpartmcnt, of ElectricalEngineering, Pnm:lgataUniversity, Yonemws, Japan. icalfilter, shownFig. in 3(a)! wasdeveloped by Adler. 156 IEEE TR.INSACTIONS ON SOSICS AND ULTRASONICS, JULY 1971

STATIC CAPACITY COUPLING TRANSDUCER COUPLING REGION COIL Wi RE

ELECTRODE PAIR

This fi1tc.r Inrltle we of ldf-mrclcngth platw coupled hy short small-tli:unctrr wires. The plate resonators can be representcc1 bp p:~raIlel tuned circuits, the coupling wires by seriw inclurtors, as shon-n in the electrical equivalent circuit of Fig.3 (b). The nickel end platesact’ a.: magnet.o- strictive input and output transducers. The frcqucncp response cllaracteristics are monotonic, that is there arc no finite attenuation poles. Adler’s filter is typic:ll of most modernmcchanical filters in that distrihutetlparameter resonators arc coupledthrough nonrcsorlnnt lincs. ‘I‘here is a striking similarity betmeen theplnte-\\-irc filter ant! the latest t;vi)c of mech:anical filter, thc n~onolithicor quartz mechanic:zl filter shown in Fig. 4(:~’l. uset1 modes are theone-nodal circle (-50-200 The quartz nlcclmlical filter cleveloped by Beaver and kHz) and the two-circle mode (200-600 kIIzl. The Sykcs [S1 and K:‘:lkaza~:l [91 makesuse of the cnergy- resonators are coupled h>- small-diameter wire tht :11’(’ t,rapping concept; whcre standing wa~ware set 11p under ?pot n.cltlcrl around the circumftwnce of the disks. As a eacheloctrode pair. 111 the regionshetn.ecn the elec- rwult of the yery complex displacement at the ctlgc of trodes, tllc, acoustic, xivc clcc‘ays oxponcntinlly,the the tlisk, the coupling mode is a con1hinat)ion of extension electro(]ctl rc,gions actlike r(~sonntOrs, andthe non- and flexure and is,therefore, very difficult to analyze. clcmcnts. clcctrodcd regions actlike coupling The elec- The earliest designs made uw of small-diameter odd- t,ric:il cyuivnlcnt circnit of tI1v platc-n-i1,c and the quartz nun1l)er quarter-wawlengtll iron-nickel alloy transducers. mechanirnl filtcxr sllonn in Fig. 4(b) are itlentical except Latclr dcsigns, such 5s tllat shown in Fig. 5(a),use onc- t,llat in the plate-wire case the input and output capac- half and full-wawlcngth ferrite transducers. itors are replaced coils. The monolithic filter also has by Ferrite transducers are also used on the rod-wire filt,er monotonic frequency responsecharacteristics. A con- shown inFig. 5(h’l. Thetorsional rod-wire filter was structionsimilar to that of themonolithic filters rle- developedindepcndcntly hy Biirnerin Gerrnnny [lZ], scribed abore 11as been used byBorner and Schussler [ 131, and Tanaka in .Japan [l41 ; the Tanaka design uses Langeyin metal alloy/ceramic transducers in place BASICFILTER STRCCTURES of the ferrite.. Thecylindrical rod resonators are designed to vihratein R half-marclengthtorsional mode Monotortic Designs at frequencies up to 250 kHz and in a half-wavelength Adler’s tlevclopn~cntof the plate-wire mechanical filter longitudinal mode whenthe filters are designed to was soon followed by Doelz’s disk-wire filter [ 111, shown operate at 4.55 kHz. Use of the torsional mode results in in Fig. 5 (a). The disk-wire filter makes use of flexural longitudinal coupling between resonators, whereas at 455 modes of vibration of the disk resonators. The two most kHz the coupling involves bending or flexure. JOHKSON et d.: REVIEW' OF MECHANICAL FILTERS 157 Use of a wireto connect the transducer to the end 14@ r resonator, as shown in Fig. 5 (h), results in a reduction of 12c t -- - spurious or unwanted responses, particularly if it is nttacl~td at :I 11od:d point of thestrongest, unwanted 1'- -l------modes. This technique, which is often used on disk-wire 2 GC filters, rcsults in r1)urious modes being suppressod more U t 4@ than 60 dB, as shown in Fig. 6(a). Incontrast to the excellcntspurious response rc>jection of thetorsional rod-wirefilter is the response [Fig. Gcb)] of therod- 2:o--.- 200 400 G@@ 8W l0U0 neckfilter of Fig. 7(a), which is drivenin a similar FREOUENCY :kHz, manner, but, i.4 subject) to bro:ld banclwidthhn(1ing (:L) modes. The rocl-ncrk fi1tc.r was tlcwloped hy Roberts [2] at the same time the disk-wire filter was being developed. The basic clcl-ign concept is that of couplinghalf- wavelengthtol,sionnl or lorrgituclinal resonatorswith c~u:~rter-w:~rcl(~~l~tl~nc~ks:.Tllc, two mjor probltwls of the early designs were the easily excited spurious bending modes [l 51, :~nd thedifficulty in construct,ion and tuning due to hing turned out of a single rod. In adtli- t,ion, at lon.er frcquencicu like 100 kHz, the filtersbecome extremelylong. In oulcrto reduce the length,Tanakn. developed tllc folrlccl line filter show1 in Fig. 7(h). Thc resonatorsvihrntt: in n I~alf-n-:~wlengthlongitudinal mode and are coupled hy relatively large-diamctcr short wires. The usc of 1ongitutlin:ll-mode Langevintrans- ducers plus the rcduced ovcrall length rcsults in :L greater rejection of unwanted moden. Like the rod-wireand foldeddesigns, the disk-wire filter has a relatively low spurious response levc.1. All four filters discussed so far operate at' frequcncies above 50 kHz. With the exception of some work reported hy MaPon and Konno, tllcre was littleactivit,y at frequencies hclow 50 kHz hefore 1960.. One of thefirst practical tlesigns was that of Mason and Thurston [ 161, who used antisymmetric mode flexural resonators coupled in t,orsion as sllon-11 inFig. 8(a). Theantisymmetric mode makes this clesign less susceptible to rnicrophonic excitation. A more widrly used design is the symmetrical mode filtershown in Fig. 8h).Work by Iconno [ 171, [IS], Y,zkuwa [19], andAlhsmeier [20], hwe made this a wry practical tleyice in thefrequency range of 300 Hz to 30 kHz. The symmetric-mode filter is driven hy pictzoelectric-ceramic transducers. The coupling wires :m attached to tlx resonators at the nodal points, which resuks in torsional coupling. This type of filter is wry sensitive to chngcs in t,he position of the coupling wires so conderahle care is taken in manufacturing to ensure that bending modes are not propagated. The microphonic problenl has been solved, in part, by supporting the filter with high-damping silicon-ruhher supports. Inaddition to the flexural-har/wire lorn-frequency mechanicalfilters, a considerableamount of work has been done in ,Japan on the development of tuning-fork I mechanical filters [21], such as those shown in Fig. 9(a) (h) and (b). The three-prong filter is interesting in that it Pig. 8. Low-frcqrlrnrymeehnnicnl filters. (a) Antisymmet.ric acts like a coupled two-resonator filter, thus providing a mode [161. (b) Fundamental mode [181. 158 IEEE TRANSACTIONS ox SONICS ASD ULTRASONICS, JULY 1971

(b) Fig. 9. Tuning fork mechanical filters. (a) U-shapedcoupling type. (b) Two-pole three-prong type. ATTENUATION greateramount of selectivit'ythan a simpletwo-prong device. The tuning fork and flexural-bar filters are widely used in Japan for remote and automatic control, selective v callingand paging, telemetry, measuring instruments. and pilot and carrier signal pickup.

Finite Attenuation Poles. By usingas many as 15 rcsonntors,highly selective resonators as iuclc~penclcntlyconsidered by B6rner [25] mechanical filters of the bar-wire, disk-wire, and folded- and .Johneon [26]. Bijmer'sfilter shown in Fig. ll(a) resonatortypes are realizable.Although the resultant makes use of l~nlf-~~:~velengtll torsional-mode resonators passband amplitude and delay responses are sat'isfactory ant1 extensionalmode-coupling elements. Thedisk-wire for voice communication, the ripple amplitude and clif- filter of Fig. 11 (1)) is compos(d of flexuralmode disks ferentialdelay variations may beexcessive whendata and basicnlly extensional mode-coupling elements. When are to he transmitted. By making use of finite-frequency thespacing between the resonators is suchthat the attenuationpoles, fen-er resonatorsare needed, thereby hridging wire is less than one-half of an acoustic wave- reducingthe differential delay, size, cost,and, most length long, theideal transformer of Fig. ll(c)acts often, the pwsband ripple. like a simple one-to-one transformer and an attenuation One of thefirst practical del-ices to realizefinite pole is realized on the high-frequency side of the filter attenuation poles was the crystal-plate filter with cnpac- passband.This can be understood by converting the T itive hridging [X!], [23], shown in Fig. lO(a). Although network, composccl of thetwo adjacent resonator cou- t,he platcconfiguration was described in hdler's basic plingwires (inductors) and thebridging wire, to its T patent [24], the itlea of usingquartz and capacitive equivalent circuit,. The inductor in series with the center bridgingwas new. Connectingthe capacitor from the resonatorproduces an ilnpedance zero, which results in top electrode of the input plate to the bottom electrode an attenuation pole above the filter passhand, as shown of the output plate is the sameas adding a phase inverter in Fig. ll(d). across the out,put terminals of the equivalent circuit of When the bridging n-ire is hctwecn one-half and a full- Fig. lO(h) and results in a pair of attenuation poles as wa~elcngthlong, the transformer in the electrical equiv- shown in Fig. lO(c) . The phase inverter adjacent to the alent circuit acts like a phase inverter and an attenuation coupling clement represents the 180-dcg phase shift' be- polc is realized below the filter passband. An alternate tween resonators at the lowest nntural nlotle of the me- method of realizing the phase inversion in the rod-wire chanicalsystem. The resonators vihrate in alength- filter is ehoxm in Fig. l1 (a) by the dashed lines. In this extensionmodc (3'' - S or -18.5' - S)or face shear case,out-of-phase regions of thealternate resonators mode (CT) andare coupled throughso-called Poisson arecoupled. A similar mcthod is usedwith disk-wire coupling. Although thex filters have been designed and filterswhere one of thealternate disks vibrates in a builtwith more than two resonators, most currently diametermode (rather tllan a nodal-circlemode), the manufacturedfilters are de.4gnecl as 455-kHz 2 poles t,hreeadjacent diPk wiresbeing connected to in-phase in cascade for use in SS13 and FM receivers. sectors, and the bridging mire to an out-of-phase portion Theuse of wires to couplemechanically alternate of the resonator [27]. JOHNSON et al.: REVIEW OF MECHAXICAL FILTERS 159 TABLE I ATTENUATIONPOLE LOCATIOXS FOR VARIOUS BRIDQINGCONFIGURATIONS

~ ____-...... - m Direct (1 : 1) Inverted (- 1 : 1) One resonator Vpper stopband pole Lower stopband pole Two resonatorsDelay correction Upperand lower stopband poles

- l 50 ATTENUATION

Im 0 I z 40 - 0 3 FREQUENCY - 30 - (d) U

Fig. 11. Singlr-rrsonntoraconstir bridging. (a) Rod-wire, 1251. - (h) Disk-wire (Johnson, 19664). (c) Electrical erlnivalcnt circuit. 20 (cl) Frrqurncy response.

10 - If a high degree of selectivityis needed both above andbelow the filter passband, a coupling wire can be used to bridgetwo resonators producing a ,symmetrical 454456 455 457 458 459 460 pair of attenuation poles. This type of design is subject FREOUENCY (kHz) to beingahle to realize aphase inverter with each Fig. 12. Frequency responsc of :L double-diskbridging mechani- bridging wirc. When no phase inversion takes place, the cal filter. resultantfrequency response is less selectivethan the monotonic case but delay compensation due to right-half planeattenuation polcs is possible(see Table I). The moat common method used to realize the phase inverter, in the ease of therod-wire filter, is tospace adjacent rcvonators a quar.ter-wavelengtl1 apart, which results in thehridging wire being three-quarters of awavelength long. The advantages of the quartcr-wavelength coupling are that thc resonators are all tuned to the center fre- Fig. 13. hlrvhanical filter with wire bridging across two rrsona- quency of thefilter and, in addition, the coupling is tors (Collins Radio). relatively insensitive to variations in mire length. In order to maint,ain a small package size, the coupling convertedto a X network conlposed of twonegative wire length between disk resonators is usually less than inductors and one positive inductor, all having the same one-eighth of awavelength. At 455 kHz,due to the absolute value [29]. As an example, thelorn-pass network thickness of each disk being on the order of a quarter- of Fig. 14(h), whichmay be a Cauer-typefilter [30], wavelength,simple tm-0-disk bridgingresults in sym- can be convertedtothe bandpass double-resonator metricalfinite-nttrnuatiol1 poles. Fig. 12 showsthe fre- bridging topology al1on.n in Fig. 14(c). Theuse of tloublc quencyresponse of the12-disk filter shown in Fig. 13. (coincident) polcs rcsults in a physicallysgnmetrical Note that the passband ripple is quite low. This is in mechanicalconfiguration, ~hichis helpful in reducing part due to the fact that the disk-wire wellas as the rod- nmnufacturing costs. Thc short coupling wire length be- wire finite-pole filters are designed with modern insertion- tween resonators, a,s shown in Fig. 13, not only decreases loss techniques. Included in the design method are trans- the package size but, increases t'he strength of the filter. formationssuch as that shown in Fig. 14(a) where a The ahilit,y of the structure to withstand high ehork and low-pass or bandpass ladder network is converted to an vibration levels is also due to the coupling wires being equivalentbridged form [28]. Because of thenarrow- located away from the centroid of t'he st'ructure. 160 lEEE TR4NSACTIONS ON SONICS AND ULTRASONICS, JULY 1971

(b)

F2 iqy7j- 1

(C) Fig. 15. Multiple-modefinite pol? configuration. (a) Disk-wire. (p) Simplified electrical cquirn,lcnt circuit.(c) Platc-typr dc- slpn.

(c) Fig. 14. Doublebridging trnnsformntions. (n,) Gcnmnl trnns- formation. (h) Lorv-pass prototypr. (c) Fmal hridging-wire bandpass electrical equivalent circllit, have beendesigned to makeuse of spuriousmodes of vibrationto control stophand selectivity. Although the theory was notunderstood until recently [31], it was foundthat by varying the coupling-wire orientation around the circumference of the disks the slope of one side of the responsecould be increased at the expense of the other side. For inst'ance, in Fig. 15(a) each disk has a natural resonance near-frequency PI in the passband. Each disk also has a natural resonance (actually F2 x F1 two as well as many others at different frequencies) near F, abovethe filter passband. Making use of thesim- (1)) plifiedequivalent circuit shown in Fig. 15(b), me see Fig. 16. Multiple resonant8 modc filters. (a) Disk-wire design. (b) that an attenuation pole is produced at F, between F1 Lom-frcquency flexural hnr. and F,. Thisresults ina steeper response above the filter passband, which can be controlled by varying the quencyrwponse equivalent to a four-resonator design. couplingwire orientat,ion, which in turn controls the The soIidnodal lines correspond to tJhe highcst natural effect of resonator Fa.The same technique has been used mode. in the design of plate filters [32] D-here the length and In thecase of low-frequency filters, a similar kchnique widthdimensions control the frequencies Fl and F2 as can beused where the corner of aflexural bar can be shown in Fig. 15 (c). removed to producetwo natural modes by destroying By removingasegment from the edge of a disk Fymmetry of the nloments of inertia. An example of this rrsonator, two controllablediameter modes correspond- type of resonator is shown in Fig. 16(b) where the arrows ing to each pair of degeneratemodes can be produced show the displacement directions of the two modes [37]. [33]. This technique has beenused to design a variety Fig. 17 shows anearly filter that makes use of this of multiplemode filters 1341-[36], most of whichare technique to obtain a total of six natural resonances as still only laboratory models. An example of this type of well as additional attenuation poles [38]. -4large variety designis shownin Fig. 16(a). Thisparticular filter of devices haw been designed using this method, includ- employsone-circle one-diameter modes of vibration, as ing a t,hrce-resonancetwo-attenuation pole filter con- well as piezoelectric ceramic transducers and has a fre- structed from a single bar [39]. JOHNSON et al.: REVIEW+(-----l OF >IECIIA~-IC.ILFILTEHS 161

D 0 I 2 4 3 5 6

ATTEYUATION I l1 -%,,.l- -%,,.l- 1 Q21 '

(C) - UFREOUEVCY - Fig. 18. Two-port two-mode disk rcsonntor. (a) Driving point imprdancc modc.1. (h) Disk nodal patterns. (c) Single-mode bo- port cquivnlrnt circuit.

11010gy) i = 1. Tllc resonator could be :I rod or bar vibratingin a flexural anda longitudinal mode or, as s1~on.n in Fig. 18(b),a disk vibrating in x two-diameter flexure Inode and a single-circle flcsurc motlc. If ordy one of themotles, but tn.0 point:: on the disk are con- sidered, theforce-vclocity relationsllips can IK found from the schenlatic diagram of Fig. 18(c). In gcneral, n resonator having 31 ports and S nat11ral rno(1es ran be descrihctl by the matrix equation

.v 211 = [ZI I1 211 = cdJkhj2i. (2) , -1

In (2j, v] and f] arc column n~nt~,icci.:of ortlcr 111 ancl zl,l is nn element in the X X A1 Z matrix. A gcncmlized equiralentcircuit Imed on (21 is shown in Fig. 19.

a 162 IEEE TRANSACTIOSS ON SONICS AND ULTRASONICS, JULY 1971 bymaking use of alinear combination of independent f M waves thatsatisfy the differential equations of motion I andboundary conditions on the major surfaces of the disk as well as approximately satisfying boundary conditions on thelateral surfaces [43]. Cnlike the exact solutions that are expected when analyzing an electrical network, solutions for frequency and equivalent mass of a mechanical resonator are only as good as the number of higllcr ordcr ~vaves that' are taken into account. The greaterthe number of '17'aves, the more accuratelythe boundaryconditions can he satisfied. The earliest work on finding the equivalent mass of a thick disk resonator was pcrformed by Sharma for the l case of axisymmetric mode3 [44].This analysis was "1 based on the nlethod of finding the cquivalent mass by 1 dividingthe tot>xl kinetic energy in the system (disk) I by one-half of the square of the velocity in a specified directionatj a point on thedisk [45]. This sametech- nique couplcd with that of Onoe's 1431 has been used to calculate the equivalmt mass of disks vihrating in both synmctricand nonsymmetric modes [46]. Examples of equivalent mass versusposition on thesurface of the diskare shown in Fig. 20 for twoadjacent vibration motlcs. Note that the equivalent mass at the disk edge (T = 1.0)is lomcr inthe case of theadjacent two- diameterone-circle mode than the two-circle mode. As a rule, the loner the impedance of a mode, the broader H, = s.s H, = S.c + C.s S = sinh CY is its coupledresponse andthe more difficult it is to suppress. I€, = c.c H7 = S + S S = sin CY Within the frequency range of interest (50-600 kHz) in the case of disk-wirefilters, there are various other H, = C%- 1 H, =s-S C = cosh a unwantedmodes present such asradial and concentric H, = C.C -4- 1 B, = c + c c =cos CY shear modes. These can often be troublesome in the case of widebandfilter designs where the modessometimes H, S.C - C.S H,, = C - C fall in the range of the paszband.These particular modes, CY* = (pA/K)w214 I(Cy2/(jW1*) = (p-4K)1'z/j. called contour modes because they involve no tran- -verse (flexural)vibration but only a changein the shape or In (3), wllich relates to Fig. 21 (a), I< reprcxntsthe contour of a disk,have studied by Onoe [47]. product of Young's modulus times the moment of inertia of the crosssection of thebar, and A, and l are,re- Bar Resonators and CouplingElements spectively, the density, cross sectional area, and length of Flexural-moderesonators are also used at low fre- the bar. quencies. In thc 500-Hz-to-50-kHz frequency range, the Using (3), we can represent :I flexural-mode resonator resonators are in the form of bars such as those shown by the equivalent circuit, shown in Fig. 21. This equiva- in Fig. 8. Analysis of the resonantfrequencies of thick lentcircuit represents a one-resonatortwo-port system flexural-barresonators has been performed by Mason similar to that shown inFig. 18(c). Note that in this [45] andNiiser [48]. If theresonator is treatedas a case therepresentation (where force is an across vari- thin bar, equations similar to those describing a trans- able) is used resulting in a dual formulation where the mission line can 1)c writtcn :LT;[ 1.51, [49] resonator is represented by a series-tuned circuit. Inacldi-

- II,(cu/l) IZ, Hlo(jwlz/Kaz) Hi(jwl/Ka) 163 JOHNSON et d.: REVIEW OF 41ECHASIC.4L FILTERS

G-

C-

I I I 0- 1 l a 7 4 6 8 10 RADIAL POSITION ir. (a)

(a)

-E;yjq"1 tion, the two ports or points on the resonator are actually represented in the equivalent, circuit by four ports, two for linear motion and two for rotation. As in the earlier (b) disk case, a general equivalent circuit canbe drawn with- Fig. 22. (a) Longitudinal bar-rcsonntor wire-coupling element out difficultyby parallel connecting networks of the (case of zcro rotation). (b) r equivalent circuit. form shown in Fig. 21(b) [49]. Konno'snormalized function E is similar to the 4 function of (2) when the The ABCD matrix of (4) canbe transformed to a impressedbending moments are equal to zero. y matrix,which, in turn, can be used to calculate Theequivalent circuits of Fig. 21(b) and (3) are and yb of thea-equiwtlent circuit of Fig. 22 (h). We veryuseful in the case of arod-wire filter where the find that rod resona.tor vibrates in anextensional mode [50]. Fig. 22(a) shows a couplingwire attached to the ends Y, = ~(Iww[(H~ + m/&] (5) of two rcsonators. The coupling wire is driven in flexure, Y, = - j(Ka3/uZ3)(I17/H3) . butthere is norotation of the wire atthe pointas of contact with the resonator, i.e., O1 = e2 = 0. After some The couplingwire actsas a quarter-wavelengthline minipulation of 131 me canwrite when 116 = 0. In this caw, we we from (5) that ga = -yb

~~ ~~~ ~ ~~ . __ 164 IEEE TRANSACTIONS ON SONICS AND ULTRASONICS, JULY 1971 andfrom (4) after somemanipulation that [50]

An analysis of an extensional-mode resonator or coupling wire is somewhatless difficult, than thatof a flexural element. A rod or wire vibrating in an extensional mode acts as asimple transmission line and, t.hus, can be describedby the ABCD matrix

1- 1,' i- cos (Dl) i~,sin (p/): rJ!r2 I=; 1 (7) NI .-SPAN C LF,.~ L j(sin (PO/Z,,) cos (PI) A FREOUtNCY = 455 LHI

COLD WORK ~ 33'. where = W dzj antl Zo = (9da). I!: is Young's modulus.Exteltsional-motle resonators and coupling yo 40 +An 1 R0 elements hve beendescribed inconsitlernble detail in [l41 :Lnd [30]. Resonator Xaterials Bccause of transduccr bandwidth limitations, the pres- ence of unwantedmodes of vibration and competition with 7,C' andceramic filters, the rntio of 1)andn-irlth to centerfrequency in the case of nxxllarlicalfilters is Be or Ti also improves the Q of the resonators,which usually less than 10 percent but more commonly about mayvary from 10 000 to 25 000, dependingon the I percent. This small fractional bandwidth requires the amount of cold working and precipitation hardening. A resonators to have a temperature coefficient of frequency value of 20 000 is typicalfor most applications and of 1-10 ppm/"C, a corresponding low aging rate, and a cawesonly a smallamount of loss atthe pasband Q value of at least10 000. edgcs of a 1 percent, f1xctional hndwidth filter. For in- The major contribution to the variation of frequency stance, the response of a 3-kHz bandwidth filter at 200 kHz is practically that of a lossless network. in :L metallic alloy with temperature is the change in the stiffllcss or Young's nlodult1s of the material. Iron-nickcl TT'hen adjustedfor the best temperature coefficient, thc resonatorfrequency Fhifts havelittle effecton the alloys that contain either27 or 44 percent Xi harea low- passband ripple. The pni;s~)antl-ripple variation mill, for temperature coefficient. of stiffness Imt are relntively 1111- the most part, bedetermined by thecharacteristics of stn1)le withregard to changes of thepercentage of Ki. Byadding cl~romium, the stahilitycan heimprovccl the transducer. consider:lbly, but the aging charactctristics and Q values TRASFI)T:CERSASD TR.4iXSI)CCER RI.ATEIZIAIS of ttme so-callecl Elinvnr materials are not acceptable. The addition of titanium or beryllium to the Fe-Ni-Cr Transducer Configurations improves hth agingand (2 antl, inaddition, nlakes it The most. n-itlely used transducers ham been the sirn- possible to vary the tcmpcrature coefficient of resonant' plcmngnctostrictive ferrite rod transducer (Fig. 5) :m1 frequency material by cohl work and lleat treating [51]. the 1,anger-in ceralnic-nlc4nl alloy transtlllcer [Fig. 7 (b)] In order to obtain a low tcnlpcrature coefficient, thc forfrcqucncies above 60 kHz andthe compositr or Fe-hTi-Cr and BC or Ti nmterial is firzt solutionan- sanclnic.l~-typc~of ccr:~mic-rnetnlt~ranstiuca~r :It lorn frc- ne:ilc[l, thcw qncrrcllc~(1,and tllen cold worked 15-50 per- quenciw (Fig 8). Altllough thcnc are the most popular, cent. Kext,the rnatcri:d isprecipitation hartlcncd (A? filt'ers arcIx3ing manufacturetl that use longitadinal mode is precipitated from a supcwaturated solution by the BC ceramic rock;, iron-nickel alloy wires, and various qu:~rte or Ti) by heat treatment at 40Oo-675"C for at least two crystal cuts. hours. The amount of roltl ~orkand temperature time An electron~ecl~a~~icnltranatlucer, regarcllcss of the determinesthe temperature coefficient. of thematerial. type,can be char:lcterizccl by its resonantfrequency, Fig. 23(a) and(b) showtemperature curves of Ther- coupling coefficient, and static rcnctancc. As an example, malast 5409 (Be) and Xi-Span C (Ti) after having lxen thc nlagnetostrictivc ferrite tr:mducer shown in Fig. 24 acljudcd for best temperature coefficiont. Both materials can be defined by the mechanical reuonant frequency fl S~OWfl,ccluency shifts of 1~sthan 50 Hz Over a tempera- (actuallythe mechanical resonancewith the electrical ture range of 100°C at 500 kHz. terminals open circuited)! the electromechnnical coupling The addition of Be or Ti has the cffcct of reducing coefficient, whichrelates the electrical and mechanical the aging rateto leas than 1 X lo-' ppnl/week or approsi- parameters. and the inductnnce of the transducer coil L1. matcly 25 IIz :It 500 kHz over a period of 10 years. The If thet,ransducer is directlyatt'achcd to the end reso- 165

.1530.106 40 - 2c 20 40 60 80 TtMPERATU9E lDCl

(a)

nafor, it affects the repon:ult frequency of the comhina- tion in direct proportion to its relative equivalent mass. In the case of the electronwchanical coupling coefficient, it is importantthat it be constantbecause itdircctly determines the transformation of the electrical terminat'- ing rePistance into a mechanical termination that must be matchedto the nwchanicalimpetlance of the filter. In most applications, the elcctricd inductallre is resonated with a c:lpncitor, which is udfor temperature compensation in critical c:lscs. Tl~ctfilter designer has tlle task of finding the most stnhle transducer that will, in addition, propc!rly match the clcctrical and n1cchanic:tl network.<. Thisinvolves cl10041lg :L ~natc~inlwith :l st:~l)lccoupling coefficient firstand then :I configurntioll that retluco~the transducer cquiv:~lcnt111:is to a minimum so as to recluce thc frcqu(~ncy shift n.it11 tcw~pcwture.Thib cm hc clone 1)y decreasing thr tliamctcr of tho frrritv roc1 or the tlliclmcsb of tho ctbramic in n 1,angevin tlxnsclucer. The sim reduction is,in turn, limited by tlwsensitivity of the coil orstatic capacity, or inthc c:\sc of ~~ide-bnnrl~~irlth filtersby the fact that, in the limit, the electrical inductol.-c:1pacitor corn1)inations actually become the end resonators. Mngnetostrirtive Ferrite Transducers Thc most widely used filter transducer material is a cobalt-ruhstit~~tc.tliroll-nic1;c.l ferrite,which w:~.? spe- cially tlevclopotf for use in elect,romerhanical filters [fi2]. Addition of 0.6 percent cobalt results in a highly stable coupling coefficient, whereas 1.0 percent cobalt results in n very small variation of frequency fl with temperature. Fig.25 shows thevariation of coupling coefficient ant1 frcqucmcy f. with change in tclnperat,ure for B practical drsipn at 200 kHz [53]. In order to be able to reduce the effect of thetransducer on the end resonator frequency, optin~um vnluc~of pcrmancnt magnet bias and coil dimensionsmust be chosen so as to maximize t'he coupling coc.fficicnt. The coupling coefficicnt of 10 percent shown inFig. 2.5, whichis typical for R n-ell- designed trnnsduccr,is also thr limitingralue of the filter fractional bandwidtll. The coupling coefficientyaria- 166 IEEE TR4NS.4CTIONS OX SONICS AND ULTR.%SONICS: JULY 1971 transducers. The barium-titanate material used in early 3000X10~6r designs suffered from large changes in coupling coefficient and frequency with temperature, which, in turn, resulted inlarge passband-ripple variations with temperature. The development of lcad-zirconate-titanate (PZT) materials [55], which show vastlyimproved temperature charact,eristics, has madeit possible for piezoelectric ceramicmaterials not only to compete with, but in a number of cases to replace:magnetostrictive ferrite 3CCOX transducers. -40 + 40 Theprincipal advantage of thepiezoelectric ceramic TEMPERATURE l°Cl is itsexcellent electromechanical coupling coefficient. (a) Whereas a bar-typeferrite transducer has a coupling coefficient of 10 percent, a side-plated barof temperature- 232,- stablepiezoelectric ceramic has a coupling coefficient between l5 and 25 percent.The higher coupling coeffi- c I cienttherefore makes it possible touse a lninimum amount of ceramicmaterial as compared to a highly temperature-stablemetal disk alloy in the design of composite end resonator/transducer assemblies. In addi- t'ion, the higher electrical Q of the piezoelectric material resultsin lower filterinsertion loss andits greater 1 I I inherentlinearity results in lower intermodulationdis- - 40 0 *40 +EO tortion.Fig. 26 shows thevariation of frequencyand TEhlPERATURE 1%) coupling with temperature for the case of a PZT ceramic (b) thathas a coupling coefficient kIz3of approximately 23 Fig. 26. Characteristirs of PZT-type piezoelectric transducers perccnt. (Murata). (a) Frequcncyvariation. (b) Coupling Coefficient The mostwidely used of theceramic transducers is variation with rhsnge of trmprrxture. the Langcrin type, which is in the form of a rod composed of a ceramic disk sandwiched between two metal are excited by composite ceramic/metal alloy transducers. alloy rods, Fig. 7 (b). The high planar coupling coefficient In addition,the high electromechanicalcoupling coeffi- of a thindisk, which is on the order of 25-40 percent cient of theceramic makes it possible to designvery (forstable materials), and the Langevin configuration stablewide-bandwidth (10-20 perc,ent)low-frequency make it possible to design resonator/transducer assem- filters of this t>ype. blies that have high mechanical Q and good temperature A great deal of analytical work has been accomplished characteristics with onlya small reduction in the coupling in ,Japan in the area of describing the electromechanical coefficient [54]. Development' of this type of transducer characteristics of conlpositebending transducer reso- for filter applicationswa.s started approximately 15 years nators. Konno's and Kusakabe's published work on this ago by Tanaka [l41 and Tagawa 1561 in .Japan. Because particular subject alone totals more than 200 pages and of the instability and low Q of most bontling materials includestwisted bars, mass loadedbars, and bars that such as epoxy, coupled with the fact that the bond has vibrate in nondcgenerate modes, as well as simple bars a.n appreciable thickness, the ceramic/metal alloy attnch- driven with ceramic plates that only partially cover the ment prohlcm is one of importance and haas required a upper and lower surfaces [59]. 9 very detailed analysis great deal of effort in its solution. of afully covered bar has been achieved by Okamoto Inthe past few years,there has hem a consider- et al. [GO], and is summarized in [ 191. ableamount of analyticalwork clone inGermany on LOOKIXGTO THE FUTURE Langevin-typetransducers [54], [57] ~ and [as]. This workincludes equations that describe the variation of We will look at the nest few years based on the direc- coupling, frequency, Q, and temperature coefficient with tion of ourpresent technology. There will be break- changesin the relative thickness and position of the throughs of course such as the monolithic filter of some ceramicdisk and has been appliedto some ncw filter years ago, hut these are difficult to predict, even if one is types at' 45.5 kHz. playing an active part in the development. Some of the One of the mod importantCharacteristics of piezo- moreprctlictahle areas are size reduction, an expanded electric. transtluccrs is thecapability of operatingin use of lan--frequencyfilters, animprovement of delay variousmodes of vihration,as m11 asuse in a large andripple characteristics, the realization of multireso- nunlhcr of mechanical configur 1011s.a t' nator monolithic filters with finite attenuation poles, as A good examplc i3 shon-11in Fig. 8 where flexure modes well as variousin~proverncnt,~ in the discrete element JOHNSON et al.: REVIEW OF MECKINICAL FILTERS 167 mechanical filter as a result of the large amount of effort being expended on monolithic filters. Size Reduction In terms of mcch:mical filters, size reduction is still a relatively uncsplorcd technology. In the case of disk-wire mechanical filtcm a size reduction from 5.0-1.3 cm3 was made with relatively little effort and no breakthroughs in t,ecImology othclr than thc use of a lower order mode of vibrat'ion. By making use of ceramictransducers and small diameter disks the volume can be reduced by 2:l without a great deal of difficulty. ilt the present time, the longitudinal-mode bar, flexural-coupling rod design inde- pendentlydeveloped by Biirner [54] andIionno [IS], (seeFig. 27) is packagedin less than 1 cm".Although it may be somewhat more difficult (in comparison with thc tlisk-wirefilter) to reduce the size of thisdesign because of the fixed length of the resonators, it is pos- Fig. 27. I\ilininture 155-kHz rod-wire met.hnnicnl filter (lcn?). sible to do so by decreasingthe diamctcr of the rods, butonly to the point where flexuralmodes bcconle a problem. Discrete element filters such as the disk or rod types actually have an advantage over monolithic struc- tures(Fig. 28) in that relativelylarge plating surfaces are not needed to reduce both the filter impedance level and the effects of straycapacity. Disk and rod- type filters are low-impctlancedevices because of the high dicllectric constant of PZT transducer materials, or in the case magnetostrictive fcrrites, the of of ure IOTY- Fig. 25. Eight-pole monolithic clunrtz mec,hnnic:Il filtcr turn coils. In addition, only t,wo transducers are needed. resonator?pacing is conmlonly 0.025 cm rcgnrdless of filter hnndwiclth! and none of the volume is usecl for. the p1lrpow of rr(1ucing rrbflections from a boul1cl:iry ant1 very littlc is uw(1 for support. It n111rt l)e Fait1tl1:lt tllcre arc :1ls0 some basic limitations :IS to hen, nn:~llTW ran hilt1 a discrete component mechnnic~:~lfilter. One: of co~~rr;c',is that of fnhricating theparts antl nw~tnhlingthen1 withoutcwessivc fre- rlucncy shiftantl Ini>coupling. A wcond limit:ltion, as we' tli.srusscc1 earlicr,is that of spurious no dos due to having to fix one of the tlimcnsions thus tlrcrcasing the frequency spacing of nearbyhcnding modes 1541. &h- athcv size-retlllction linlitntion relates to the nonlinearity of the transtluccr and resonator nlaterinls a. a function of size. Y:lkuma has matlc a very interc,sting comparison of ferrite co~'einductors, piezoclcctric ceramics, nickel alloys,antl quartz, showing the relationshipbetween various loss factors and minimumsize for a specific son~eof the wi(1e variety of filters king manufactured handwiclth filter [61]. A final consideration is the three- byFujitsu 1,td. IIostapplications of low-frequency dimensional shape of most discrete element mechanical mechanicalfilters involve selecting single tones, which filters, which not only prevents the use of planar manu- inturn means that onlyone or two resonators at'e facturing proccsscs butultimately may be themost needed. Therefore, the selectivity is dependent solely on seriousvolume-rccluction limitation. resonatorsthat are coupled tothe external mounting structure. This results in lower resonator Q and micro- Low Frequencies phonic responses due to external vibrations. The large amount of developmentwork onlow- The microphonicsproblem has been solved to some frequency filters in Japan will most probably be felt in degree by the use of highly damped supports. This has ot8herparts of theworld. Fig. 29 shows, for example, made it, possible to use funclamental modes of vibration, 168 IEEE TIL\NS.KTIORTS ON BONICS AND ULTRASONICS, JULY 1971 Arf-l0.9538

l98 200 202 204

FREOUENCY !kHz)

uuuuuuuuuuu

12 11L I

I 0 \I 200 207 W 204 cL a ,,,7/,;<<<;~,7L;,’.:,,’; 3 z -Oo2i r’ U FREOUENCY (kHz1 c (l>1 Fig. 30. Mcasurcd (a) stopbnndamplitude and (h) passband response of a high-performancerod-wire mechanirnl filter that emplavs douhlo rcsonatorbridging of thetype shown in Fig. l8~199 200 14 (Tclrfunkcn). FREUUZNCY ikHr) which redurc both the complexity of thefilter and its physical size. The problem of minimizing unwanted out- puts due to impulse noise may be solved to some degree hy the use of H-shaped resonators [G2]. Thistypc of filter consists of two idcnticnl vertical masses connected by a flexible web (the horizontal elcment of the H). -4 piezoelectricceramic transducercauses the web to flex computer-niclctl tuning tt~chniques, which have also been and the masses to rotate. Each mass is supported near rcportc(1 1)s Ynno [68]. In ortlcr to further improve the its centroid, thus preventing the ~rchfrom flexing when excellentresponse of voice chmnel filters, it will be subjected to n shock impulse through the support.. A advantageous in some casc~ to ~nakeuse of on-line com- detailed analysis of the frequencyresponse chnracterist’ics putersin the factory. The tlevelop~nent of practical of this device hns hccn macle by Konno [631. computcr-a..,~isted tuning methodsmay result from work presently hing done on quartz monolithicmechanical Inp-oven~entoj Delny and Passband Ripple filters. It ispossihlc to intornally delay equnlize a ~nechan- Quartz Jlonolithic Allechanirnl Filters icnl Incider filter by making use of bridgingu-ires C2.51. This 1x1s pmwl to hc a ~orypractical nwthotl [G$], Inmuch the s:tnlc n’ay 11s the tlimttc elenltwt me- [65). This ticsign ia haw1 on the mc of very exact chanicalfiltw may benefit from monolithicmechanic:d clllar.tcr-~~avelengthlong coll1)ling nircs. No frequency filter tccllnology, R number of concepts ,such :Mac!onstic acljustnlcnts arc ncctlctl nftcrassembling the pretuned hridging will he applied to the monolithic filter. At the ro.mn:ltor.q:, in the case of chnnnclfilters with pairs of present timc,attenuation poles arerealized in t,wo- attt~n~lntionpoles (Fig. 30 :~nd [M]) andin the case resonator str11ctarcs throughcapacitive bridging. The of rllanncl filtcrs n-it11 tlrl:zy equalization (Fig. 31). tn-o-resonatorsections :ire capacjt,ively coupled to form Anothcr practical method is to we mechanical resonators n multiwronnntfiltcr having a somewhat equal-ripple ancl couplingclomrnts in an electricallattice structure response [SS]. It is pmhnhle that exact, designs with four in much the same way :E quartz resonators are usetl [67]. or more re.sonators 1wr plate ant1 electricalbridging The work onlattice filter,? has resultedin some new will soon hccome availal~le. JOHNSON et al.: REVIEW OF MECHAXICALFILTERS It has alrezttly been shown thatthickness modes can bc trapped in much the same way as the shearing modes [70],which leads us to suspect that other new configurations will be dcvelopcd in the next, few ye:~rs. A large amount of technology has been devoted to the nlonolithic mechanical filter manufacturing process^ for inst:lnce in :~reas such as the we of a laser to vary the couplingbetween electrode pirs and the fahrication of extremelyflat and parallel crgstd blanks. It is certain that this work will continue for a long period of time and shoultl he app1ic:tt)lc to nmhnnical filtertechnology in gencr:~l. neve1opwcnts in (Ithe/. C’orcntries ~h~l~anicalfiltcr dcvelopnent~outside of ,Japan, West Germany, and thc Is. S. llas1)rimarily bccn concen- trated on distributed linc, filters of the type shon.11 in Fig. 7(a). This has Ileen the case in Great Britain [71], Poland [ 721, the USSR [ 731, and East’ Germany, where they have becn Innnufnctureclfor some years. Recent papers publiwhctl in Englnnd have reflected an interest in transducer dcaign [74] antllow-frequency flexure mode resonators 1751. A study of flexure modes in mechanical filtcrsis also a subject of interestin Czechoslovakia [E].At this time, channel filters of the configuration of Fig. 511)) arc manufacturedin East Gennany (200 kHz) [771 antlin Czechoslovakia (64-108 kHz) [78].

[31 M. L. Doclz and J. C. Ra,thnwny, “How to use mechnnicnl I-I.’ filters,” Electronics, vol. 26, Mar. 1953: pp. 138-142. I41 (i. A.C:lmpbell, ”Physicnl theory of the rlectric ~vavc-filter,” Bell Syst. Yech. J., vol. 1, Nov. 1922, pp. 1-32. 151 R. V. L. Hartleg, “Frequency selective transmission system,” L.S. Pntcmt 1654 123, Dec. 1927. I61 J. 1’. Mnxfield and H. C. Hnrrkon, “Methods of high qunlity rcvording and rt,producing of music and speech based on kle- phoneresearch,” Bell Syst. Tech. J., vol. 5, July IWG, pp. 493-523. [TI JV. 1’. Mason, “W:lve transmission network,” US. Patent 2 345 491. Mar. 1944. [SI R. A. Sykrs and W. D. Beavcr, “High frequency monolitllic filtexs with possible application to singlc freclucwcy and single sideband us~,”Proc. Annu. Fwquencv Control Sum- posi~m,Apr. 1966, pp. 28S-308. [91 l’. Nnkaznwa, “High frequency crystal t~l~~~tron~cc.l~n~~ic~alfil- ter,” PTOC.A~tnu, Frequency Control Sgrmposirtrn, Bpr. 1962, on. 373-300.

Ovt. 1952. 1121 31. Btimvr. E,Tict,icl, ant[ H. Olln.;orgc. “hlcclrnnisrhe filter fiir die nnc.hriclrtentcrhnik,” Tekjzlnkeu J.; vol. 31, June 1958. IIP. 105-114. [l31 31. Kjrncr: E. Diirre, and I€. Schiislrr, “RI(~ll:lniscl1r I~~i~wc.iten-\~:u~~tliilter,”Tekfunken J., vol. 36, hhy 1933, pp. 272-280. [l41 T. Tanaka Rntl T. Inoguchi. “Studies on electronics materials and their npplic:~tion.;,” Division of Elrctronics Mntr,ri:ils. Inslitule for Chemical Research, Kyoto Univ., Kyoto, Japan, 1959, p1J. 22-25. 170 IEEE TRANSACPIOSS ON SONICS AND ULTRASONICS, JULY 1971 L431 M. Onoe and T. Yano, “Analysis of flexural vibrations of a polfilter,” Diplom-Arbeit, Institut fiir HF-Technik und HF- circular disk,” ZEEE Trans. Sonics Ultrason., vol. SU-15, Physikder Technischcn Hochschule Karlsruhe, Munich, JuI~1968, pp. 182-185. Germany, 1%. 1441 R. L. Sharma.“Enuivalent circuit of a resonant. finitr,. iso- l661 H. Schiisler.“Filter nlit mechanischen resonatoren.” Bull. tronic. elastic’circular disk.”~, J.- Acoust. Soc. Am‘er.. vol. 28. Schweizerischer Electrotechn. Verein (Zurich), Ma;. 1969, xot.-i956, pp. 1153-1158. pp. 216-222. L451 W. P. Mason, Electromechanicnl Tramducers and Wave Fil- 1671 R. il. Johnson, “New single sidchand mechanical filters,” 19’70 ters. NewYork: Van Nostrand, 1948, pp. 291-297. WESC‘ON Tech. Papers, Aug. 1970, pp. 1-10, 1461 E. Frymover, J. Klovstad, and R. A. Johnson, “Equivalent I681 K. Shibayama,“Elcctromechanical filters,” Eleclron. Com- mass of a thick vibratine disk.” unoublished. mun. Jap., vol. 48, Kov. 1965, pp. 6672. 1471 M. OI~K,“Contour vibrations’ of i$otropiccircular plates,” 1691 H. Yoda, Y. Xakazama, and N. Kobori,“High frcqucncy J. ACO~LS.SOC. AWLET.,vol. 28, NOV. 1056, pp. 11561162. crystal monolithic (HCM) filters,” Proc. 2Srd Annu. Symp. I481 J. 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MAG- (in Polish), Rozpr. Elektrotech., vol. 15,1969, pp. 717-749. 2. Sept,. 1966, pp. 613-620. 1731 A. IC. Losev, “Filterswith multielemrnt coupling,” Tele- 1521 C. M. van der Burgt,, “Performance of ceramic ferrite resona- cornrnun. Radio Bng. (USSR), Jan. 1964, pp. 1-8. tors as transducers and filter elements,”J. Acuusi. Soc. Amer., L741 R. P. Wa.lters, “Balanced actlon toroidal transducer for clrc- vol. 28, XOV.1956, pp. 1020-1032. tromechanical filters,” Electron. Eng., Mar. 1969, pp. 238-245. L531 S.Srhweitzerhof, “Fber ferrite fiir magnetoslriktiveschwingcr 1751 P.Kagaaa and G. M. L. Gladwell, “Finite clenlrnt analysis in filterkreisen,” niaChrichte?ltec/k Z., vol. 11, Apr. 1958, pp. of flrsure-typevibrators with elcctrostrictivetransducers,” -179-1 . . - 8.5- - . ZEEE Trans. Sonics Ulirason., vol. SU-17, Jan. 1970, pp. 41- I541 M.Biirner and H. Schiissler, “Miniaturisi~rllngmechanischrr 49. I’ilt,er:” Telefztnken J., vol. 37, 1964, pp. 228-246. C761 Z. 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