Su, Q., R. N. Miles, M. G. Weinstein, R. A. Miller, L. Tan, W. Cui, Respnse f a bilgially inspired MEMS differential mirphne diaphragm, Preedings f the SPIE AerSense 00, Orland Fl. Paper number [4743-15]. Respnse f a bilgially inspired MEMS differential mirphne diaphragm L. Tan, R. N. Miles, SUNY/Binghamtn; M. G. Weinstein, R. A. Miller, Charles Stark Draper Lab., In.; Q. Su, W. Cui, SUNY/Binghamtn ABSTRACT The develpment f a nvel, bilgially inspired austi sensr is presented. The primary gal f this effrt is t nstrut a miniature devie that is apable f deteting the rientatin f an inident sund sure with an auray f. The design apprah fllws frm ur investigatin f the mehanis f diretinal hearing in the parasitid fly, Ormia hraea. This animal has been shwn t be able t detet hanges in the line f bearing f an inident sund that are as small as [1]. The tympanal strutures f the ears f this animal suggest a nvel apprah t designing very small diretinally sensitive mirphnes. A mirphne diaphragm design is presented that has been fabriated using silin mirfabriatin tehnlgy. Measurements f the stati defletin due t intrinsi stress and f the respnse t sund are shwn t be in exellent agreement with preditins. Predited results indiate that this mirphne nept uld lead t a pratial differential mirphne with self-nise as lw as 0 dba. Keywrds: Mirphne, austi sensr, bimimeti, MEMS 1. INTRODUCTION Any austi sensr that respnds preferentially t sund frm a speifi diretin must detet the spatial gradient f the sund that is inident n it. In urrent mirphne tehnlgy, this is typially ahieved either by nstruting a pressure sensitive diaphragm driven n either side by sund sampled at different latins in the sund field, r by using tw islated mirphnes and pressing the signals eletrnially. The distane between the latins at whih the sund is sampled is nrmally smaller than the sund wavelength. It is well knwn that as the verall dimensins f the sensr are redued, with a rrespnding redutin in the spatial separatin in the sensed pressures, the deteted pressure differene will als be redued. This lss f sensitivity pses numerus engineering hallenges in the design f very small diretinal mirphnes. In the present study, we desribe an imprved design apprah inspired by the auditry systems f small animals that are adept at lalizing sunds. Our apprah t designing miniature diretinal mirphnes fllws frm ur previus study f the auditry system f the parasitid fly Ormia hraea []. This animal has shwn exemplary ability t lalize sunds even thugh its ears span nly abut 1mm. The fly an detet hanges in the angle f inidene f the sund that are as small as [1]. In this fly, the detetin f the pressure gradient is ahieved by mehanially upling the mtins f the tw ears. As a result, a differene in pressure at the exterir f the tw ears auses them t mve ut-f-phase. The mbinatin f this mtin with an in-phase mtin exited by the average pressure leads t a diretinally sensitive respnse []. If ne wishes t detet the pressure gradient using a very small devie, this system suggests that an effetive way t amplish this is t design a sensr that rks abut a fulrum due t differenes in pressure at tw pints n its exterir. This differs frm the usual apprah f sampling the sund pressure at tw pints and arranging the devie s that these pressures drive either the exterir r interir side f a single mirphne diaphragm. The aim f this paper is t desribe ur urrent results in fabriating this bilgially inspired diretinal mirphne nept. A mdel fr the respnse f a nventinal differential mirphne is first desribed in whih sund drives bth the internal and external surfaes f the mirphne diaphragm. Results frm this mdel are then mpared t thse f a simplified mdel f the respnse f a mirphne diaphragm based n Ormia s ears. The use f this apprah pens up numerus design pssibilities that have nt previusly been available. Beause ur urrent interest is in develping very small differential mirphnes, an apprpriate means f nstruting the devies is t use silin mirfabriatin tehniques. Detailed designs have been develped with nsideratin given t a wide range f design
parameters. Results are presented that shw that ur preditins f the defrmatin f the diaphragm due t intrinsi stress alng with the vibratin respnse due t sund are in exellent agreement with measurements.. BIOLOGICAL INSPIRATION In a previus study, we disvered that the mehanial struture f the ears f the parasitid fly Ormia hraea endws the fly with a remarkable ability t sense the diretin f an inident sund wave []. The fly s auditry system has evlved in suh a way that it is ideally suited t hearing and lalizing a riket s mating all. Measurements f the mehanial respnse f the ears f this fly indiate that when sund arrives frm ne side, the ear that is lser t the sund sure respnds with signifiantly greater amplitude than the ear that is further frm the sure. The interaural differene in mehanial respnse is due t the upling f the ears mtin by a utiular struture that jins the tw tympana, whih we have named the intertympanal bridge. This is the first reprt f the use f a mehanial link between a pair f ears t ahieve diretinally sensitive hearing []. An examinatin f the analytial mdel fr the austi respnse f the tympana f Ormia hraea shws that the system an be represented in terms f tw, unupled resnant mdes f vibratin that are exited by a sund wave as shwn in figure 1 belw. A primary gal f the present investigatin is t apply ur understanding f the mehanis f this and similar auditry systems and mimi the perating priniples used in rder t nstrut an austi mirsensr that is insensitive t unwanted nise disturbanes. The ears f Ormia hraea serve t demnstrate that suh a small diretinal mirphne, r "rmiaphne," an be develped. Anti-symmetri mde Symmetri mde Cmbined respnse Figure 1. Mdes f vibratin f the intertympanal bridge. The antisymmetri mde invlves rking f the bridge abut the fulrum and respnds t the pressure gradient. The symmetri mde is a translatinal bending mtin in whih the tw sides mve in-phase and respnds t the average pressure n the tw sides. When the mehanial prperties f the system are apprpriate, the general respnse nsists f a mbinatin f the tw mdes where their ntributins anel n ne side and add n the ther. 3. DIFFERENTIAL MICROPHONE CONCEPT A simplified representatin f a nventinal differential mirphne is depited in figure (a) in whih a diaphragm is driven n bth the tp and bttm sides by sund that travels thrugh tw duts having penings that are separated by a distane d. Our alternative apprah, inspired by the ears f the fly, is depited shematially in figure (b). In this ase, sund drives nly the tp surfae f the diaphragm. The differene in pressure at pints 1 and n the tp surfae prdue a rking mtin abut the pivt pint. The right and left sides f the diaphragm thus mve in ppsite phase in respnse t a spatial pressure gradient. This nstrutin intrdues entirely new design pssibilities fr sensing pressure gradients. (a) Cnventinal Differential Mirphne (b) Ormia-Inspired Mirphne Figure. Cnstrutins f the differential mirphne
T develp a mirphne diaphragm based n the nept shwn in figure (b), a detailed finite element mdel was reated fr a 1 mm diaphragm made f plyrystalline silin as shwn in figure 3(a). This design nsists f a stiffened plate that is supprted n flexible pivts. The diaphragm was designed in rder t minimize the mass while preventing unwanted strutural resnanes. Figure 3(b) shws a plysilin devie that we have fabriated. (a) FEA Mdel (b) Fabriated Plysilin Devie Figure 3. Diaphragm Struture f the Ormia Differential Mirphne 4. PREDICTIONS OF ACOUSTIC PERFORMANCE In this setin, predited results fr the sensitivity and nise perfrmane f the Ormia mirphne (depited in figure 3) are mpared with a nventinal design (depited in figure a). The perfrmanes f speifi designs are mpared t illustrate sme f the advantages f the present apprah. Sine ur urrent interest is in the develpment f very small austi sensrs, it is assumed that eah design will be fabriated using silin mirfabriatin tehniques. The diaphragm shwn in figure 3(a) is designed using a detailed finite element mdel s that it respnds as a rigid plate that is supprted n trsinal springs at the pivts. The sensitivity f the differential mirphne nepts shwn in figures (a) and 3(a) may be mputed frm: S Vb = h d sα iω s( φ) / m ω ω + iωω ζ and S 3 Vb siω( L / ) s( φ) /( Ih) = ω ω + iωζ ω 3
Where, i= 1, is the sund speed, φ is the angle f inident sund, ω andω are the resnant frequenies f the k k nventinal and rmia diretinal mirphne respetively, ω =, ω t =, and ω is the driving frequeny. m I The dimensins f the mirphnes are bth 1 mm, and the strutures are nstruted ut f 1µm thik plysilin. Bth mirphnes thus have the same area s. Fr the Ormia mirphne, the ttal mass is m = 0.975 10-8 kg, the mass mment f inertia abut the axis thrugh the supprts is I = 3.99 10-15 kgm, The resnant frequeny f the rtatinal mde ω is predited t be 1409Hz. Fr the nventinal mirphne, the mass is m = 0.46 10-8 kg, the resnant frequeny f the diaphragm ω is fund t be abut 10kHz. The bias vltage V b = 1 vlts and the bakplate gap h = 3µm. The damping nstants in eah design are seleted t ahieve ritial damping, i.e. ζ =ζ = 1. Predited austi respnses fr the tw mirphne diaphragm designs are shwn in figure 4 belw. It is apparent that the Ormia mirphne has substantially higher sensitivity than the nventinal apprah ver the audible frequeny range f interest here. Figure 4. Predited Frequeny Respnses f the Differential Mirphnes Alng with the austi sensitivity, it is als very imprtant t examine the lwest sund levels that an be measured with a given mirphne. This is limited by the self-nise f the mirphne as desribed in [3]. Nise perfrmane f mirphnes is usually haraterized by using the A-weighted verall equivalent sund pressure due t the nise. In rder t nstrut a fair mparisn f the nise perfrmane f andidate designs, a mpensatin filter is develped s that the signals frm the mirphnes are adjusted t have idential frequeny respnses. The mpensatin filter fr eah mirphne signal was applied t ahieve the flat frequeny respnse frm 50Hz t 8kHz. The nise f the mirphne results frm energy dissipatin in the system that an be thught f as being due t equivalent dashpts that are distributed ver the diaphragm surfae. The mirphne nise was mputed frm N 10 SPL b +10lg P sd =, where, SPL b is the tave band sund pressure level, P sd is the white nise pwer spetrum due t thermal nise, P sd = 4k b TR/s [3]. k b is Bltzmann s nstant, k b = 1.38 10-3 J/K, T is the abslute temperature, s is the area ver whih the dashpt at, R is the equivalent dashpt nstant. 4
The predited nise perfrmanes f the tw mirphnes are shwn in figure 5 belw. Figure 5. Predited Output Nise Spetra f the Differential Mirphnes As shwn in figure 4, the peak f the sensitivities always appear near the resnant frequeny f the system, thus the mpensatin filters and nise levels are lwest near this pint. The sensitivities f the Ormia mirphne are ver ne rder f magnitude higher than nventinal mirphne ver mst f the frequeny range f interest here. The lw signal level f the nventinal mirphne at lw frequenies auses it t require abut 40 db f gain in rder fr it t utput the same signal level as the Ormia mirphne. It an be seen in figures 4 and 5 that beause the use f the partiular mehanial struture in the Ormia mirphne, the frequeny respnse and the nise perfrmane are nsiderably imprved in the miniature design. The nise level predited fr the Ormia design is nly abut 0 dba. This is a remarkably lw nise level and rivals that f high perfrmane nn-diretinal mirphnes. 5. EVALUATION OF FABRICATED DEVICES Results f fabriatin f the design shwn in figure 3(a) are shwn in figure 3(b). Charaterizatin f the devies inluded the measurement f the flatness and dimensinal auray alng with the respnse t sund. As shwn in figure 6 belw, measurements and analysis f the stati defrmatin f the mirphne were mpleted t verify that the design preditin mathed the experimental data. The results shwn in the figure indiate the defletin alng the mm lng axis f the diaphragm at its midline. The stati defrmatin f the diaphragm resulted frm the intrinsi stress in the plysilin that is reated during the fabriatin press. Measurements f the urvature f unifrm wafers with plysilin films indiated that the plysilin was subjeted t apprximately 0 MPa f mpressive stress. Despite this signifiant mpressive stress, the results shwn in the figure indiate that the diaphragm is remarkably flat with a maximum defletin f nly 0.3 µm. The results based n ur analysis are extremely lse t the measured data. 5
defletin (um) 0.3 0. 0.1 0-0.1-0. -0.3 Defletin: lng-axis Defletin(mirn) 0.3 0. 0.1 0.0-0.1-0. -0.3 X-axis Defletin -D prfile -0.4 0 0.5 1 1.5.5 x-axis distane (mm) (a) Measured X-axis-D prfile frm WYCO -0.4 0 500 1000 1500 000 500 X-Axis distane(mirn) (b) Predited X-axis -D prfile frm ANSYS Figure 6. Stati Defrmatin Alng the mm Lng Axis Alng with a haraterizatin f the stati defletin f the devies, measurements were perfrmed t examine the dynami perfrmane. The strutures are designed t have a rking mde and a translatinal mde f vibratin. The measured mdes f vibratin are pressed frm frequeny respnse measurements f pints n the test struture. The sund-indued vibratin f the diaphragm was measured using a Plyte laser vibrmeter. A retangular measurement grid ver the surfae f the diaphragm is used. The imaginary part f the mplex transfer funtin is pltted ver the retangular grid fr a partiular frequeny band. The data was pressed and viewed using a ustm written Matlab GUI. Measured results are shwn in figure 7 belw alng with preditins based n ur detailed finite element mdel. The figure shws that the measured results are in exellent agreement with preditins. Alng with prediting the resnant frequenies and mde shapes, it is ruial that we are able t aurately predit and measure the respnse f the mirphnes t an inident sund field. Figure 8 shws a mparisn f the measured and predited respnse relative t the sund pressure inident n the enter f the diaphragm. This figure shws the magnitude and phase f the respnse versus frequeny n the side f the diaphragm that is lsest t the sund sure (ipsilateral). The predited results were btained using a Matlab prgram (written by us) that pst-presses the utput frm ur detailed ANSYS FEM mdel. This Matlab prgram alulates the vibratin f the struture t a distributed, traveling austi field. The results shwn here indiate the displaement at a pint ne-quarter f the way alng the length f the diaphragm and half-way arss the width, where the length is mm and the width is 1mm. 6
0.0000 Relative Respnse 0.00015 0.00010 0.00005 0.00000-0.00005-0.00010 1.0-0.00015 0.8 0.6-0.0000 0.4 0.0 0. 0.4 0.6 0.8 1.0 0. 1. 1.4 1.6 1.8.0 0.0 mm Mdeshape at 400 Hz mm Relative Respnse 0.000014 0.00001 0.000010 0.000008 0.000006 0.000004 0.00000 0.000000-0.00000 0.0 0.0.40.6 0.8 1.0 1. 0. 1.4 1.6 Mdeshape at 40,000 Hz 1.8.0 0.0 mm 0.4 1.0 0.8 0.6 mm Predited 663 Hz (a). The rking mde Predited 40,895 Hz (b). The translatinal mde Figure 7. Measured and predited mde shapes The data in figure 8 shw that the diaphragm respnse ntains tw resnant peaks. The peak that urs at relatively lw frequenies, apprximately 400 Hz, rrespnds t the mde in whih pure rking urs abut the entral supprts as shwn in the left panels f figure 7. The next mde f vibratin, at a frequeny f abut 40 khz, nsists f in-phase mtin f the tw sides f the diaphragm as shwn in the panels at the right f figure 7. This mde is well abve the frequeny range f nrmal human hearing and will have negligible influene n the perfrmane f the diaphragm. The fat that nly ne resnant frequeny (rrespnding t the rking mde) urs in the frequeny range f interest auses this design t perfrm with exellent fidelity. Many mirphne designs suffer frm unwanted resnanes that adversely impat the frequeny and phase respnse. It is apparent frm figure 8 that the resnane at 400 Hz is rather lightly damped and has a higher Q value than is desirable. A predure we have develped fr identifying the damping parameters fr vibrating systems indiates the damping rati f this mde is ζ 0.0051 s that Q = 1/(/ζ) 97.7. It is imprtant t nte that the devies we have fabriated thus far d nt inlude bakplates and hene lak an imprtant sure f damping. It is well knwn that visus fres due t air flw in the gap between the bakplate and the diaphragm results in signifiant damping f the diaphragm mdes. 7
Figure 8. Cmparisn f measured and predited respnse f ur differential mirphne diaphragm (with n bakplate) due t an inident sund. Data are nrmalized relative t the inident sund pressure. 6. CONCLUSIONS A bilgially inspired nept fr a differential mirphne is presented that has the ptential f allwing the develpment f higher perfrmane mirphne designs. Fabriated results are presented that shw exellent agreement with preditins. 7. ACKNOWLEDGEMENTS This wrk has been funded by DARPA grant DAAD17-00-C-0149 t RNM. 8. REFERENCES 1. A. Masn, M. Oshinsky, and R. Hy, Hyperaute diretinal hearing in a mir-sale auditry system, Nature 4/5/01. Miles, R. N., Rbert, R., and Hy, R. R. [1995] "Mehanially upled ears fr diretinal hearing in the parasitid fly Ormia hraea." Jurnal f the Austial Siety f Ameria 98 (6) 3059-3070. 3. Gabrielsn, T. [1993] Mehanial-thermal nise in mirmahined austi and vibratin sensrs. IEEE Transatins n Eletrn Devies 40 (5) 903-909. 4. Rnald N. Miles, Lin Tan, Weili Cui, Quang Su, Mihir Shetye, Design f a Bilgially Inspired Diretinal Mirphne, Preedings f the 001 Meeting f the MSS Speialty Grup n Battlefield Austi and Seismi Sensing, Magneti and Eletri Field Sensrs Jhns Hpkins University, Laurel MD, Ot. 3, 001 8