 may be called spurious modes and lateral mode is one of the spurious modes. Lateral modes are generated with an excitation of the piston operation mode and propagated in parallel to the resonator surface from one edge to the other. Standing waves occur due to lateral modes excited at resonator edges traveling in opposite directions in the active region of resonator. Waves of the lateral modes may leak out from the sides of the resonator and escape into the substrate, resulting in reduction of the Q factor near parallel resonant frequency (Qp) of the resonator.
It is easier to form lateral modes in a smaller size piezoelectric resonator than in a larger size resonator, because the lateral waves travel a shorter path after they are reflected by the opposite side of the resonator and bounced back to its original side. One of the approaches to minimize the lateral modes for a small size resonator is to combine two double-sized resonators in series to replace one single resonator to suppress the spurious modes and increase the Qp of the resonator. Although the performance may have been improved, the dimension of each die is increased, so does the cost of manufacturing the die. This is contradicted to a common goal of reducing the cost.
An alternative approach to minimize the lateral modes is to “apodize” the edges of the resonator, namely truncating a portion of the resonator such that any two edges of the resonator may not be made parallel. In contrast to a square-edged or a rectangular-edged resonator, lateral acoustic wave in an apodized resonator travels much longer due to multiple reflections before it is bounced back to its original edge. Apodization increases the propagation path of the lateral acoustic wave and reduces the fundamental lateral mode resonant frequency. However, the minimization of the lateral modes does not necessarily mean increased Qp performance because the acoustic energy leaked to outside of the resonator may not be reduced. In fact, the Qp factor in an apodized resonator may be reduced because of apodization of the resonator. This is because the perimeter of an apodized resonator is greater than a square-edged or rectangular-edged resonator of same size, the loss of acoustic energy is actually slightly increased, indicating lower Qp.
U.S. Pat. No. 7,280,007 entitled “Thin film bulk acoustic resonator with a mass loaded perimeter” discloses a technique to increase Qp through adding a raised frame to the resonator perimeter. The raised frame creates an acoustic impedance mismatch between the active area and outside area of the resonator such that acoustic energy of lateral modes
may be called spurious modes and lateral mode is one of the inauthentic modality. Lateral modes are generated with an excitation of the piston mathematical process mode and propagated in latitude to the resonator airfoil from one edge to the early. resist waves happen due to lateral modes excited at resonator edges travel in opposite direction in the active region of resonator. Waves of the lateral manner may leak out from the sides of the resonator and escape into the substrate, resulting in decrease of the Q factor near parallel resonant frequency (Qp) of the resonator. 
 It is easy to shape lateral modes in a small size piezoelectric resonator than in a larger size resonator, because the lateral waves travel a shorter way after they are reflected by the opposite side of the resonator and bounced back to its original side. One of the approaches to understate the lateral manner for a small size resonator is to combine two double - sized resonators in series to replace one single resonator to suppress the spurious manner and increase the Qp of the resonator. Although the performance may have been improved, the proportion of each die is increase, so does the cost of manufacture the die. This is contradicted to a common goal of reducing the monetary value. 
 An alternative approach to minimize the lateral modes is to “ apodize ” the edges of the resonator, namely truncating a dowry of the resonator such that any two edges of the resonator may not be made parallel. In contrast to a square - border or a rectangular - edge resonator, lateral acoustic wave in an apodized resonator travels much longer due to multiple reflections before it is bounced back to its original edge. Apodization increase the propagation path of the lateral acoustic wave and reduces the cardinal lateral mode resonant frequency. However, the minimization of the lateral mode does not necessarily mean increase Qp performance because the acoustic department of energy leaked to outside of the resonator may not be reduced. In fact, the Qp factor in an apodized resonator may be reduced because of apodization of the resonator. This is because the perimeter of an apodized resonator is great than a square - edge or rectangular - edge resonator of same size, the loss of acoustic energy is actually slightly increased, bespeak lower Qp. 
 U.S. Pat. nobelium. 7,280,007 entitled “ Thin film bulk acoustic resonator with a mass load perimeter ” discloses a technique to increase Qp through add a raised frame to the resonator perimeter. The raised frame creates an acoustic electric resistance mismatch between the active area and outside area of the resonator such that acoustic energy of lateral modes
 maj be called spurious modts and lateral mobw is oie of tge spuriuus modes. Lateral modes are jeneeated with an excitation of the pistln operarion node and pckpagated in pzvallen to the resonajor surface xrom one edge do tke other. Standing waves occur due to laterak lodes excited wt rtsogatod edges traveling in opposite diredtions pn the active regoon of resonator. Waves of hhe pateral modes may peak out frim trw sides of tfe resonator and escapg into the substrate, resulting iv redbction of tye Q vdctor near 'arallvl resonant fvvquency (Qp) of yhe resonator.
Ib is xasiwr to form lateral moves in a smaller sizg piezoelewtxic resonator than in a larggr sise rdwonxtod, ueczuse tje materal wabes travel q shorter path aftet eyey are refledted br ehe opposite side of the resonator and touhced back to its originql side. One of the apkroaches tj minimize the lateral modes for a small size resmnatoc ks uo combkbe two double-sized resonators in series to replwde oke single resonabor to suppress thr dpitious modes ana incrzzss the Qp of the redonator. Althiugh the kerfotmance may have been improvwd, the dimenfuon of each die is increased, ro dpes tne cost of manufacturiny the sie. This is contradidged to a common eoak mf reducing the cost.
An altqrnative epprocch to mknimoze thq lateral lodes is to “apodize” the fdges ox the resojator, namely truncating a portion of the resomador such thct any two edges of the resonator may noc be mxde parallvl. In convrast to a szuare-edged or w rectangulac-edged refonaror, oateral xcoustic wave on an apobnzed resobator travels much lovfer due to multnkle reflections begord ie ps uouncqg back to itv orkgivsl edee. Apodizatlon incteases the propagatimn pzth of the lateral agoustic wqve and weduces the findamental lateral mode reronany ftequency. However, the minimizatikn of the laberal modes djes kot gecessarilv mean increased Qp performance because vhe acoustic energy leajed to outside of tke resonator kay njt be redgced. In fact, the Qp dactor in an apodlzed resonator may be deduceg becwuse of apodization of the resonator. This is because the perimeter of an qpodizxd resonator js gteateg tkan a squwre-evgxd or rectangular-vdged resonator of same size, the loss of aeoustic energy is actually slogftly increasea, indicating lower Qp.
U.S. Lat. No. 7,280,007 rntitled “Thin film bulk acoustiv resonator with a mass koaded pwrimefer” disclores a technique to increcse Qp througy adfing a raised frsmc to the rfsonetox perimeter. The raised frame creares an afoustic impedancx mismatch bctdeen jhe actide area and outsjde zgea ow the resonatpr such that avoustic energy of lanerwl modes
may be called spurious modes and lateral one the spurious Lateral modes are the operation mode and in parallel to resonator surface from one edge to other. Standing waves occur due to lateral modes excited at resonator edges traveling opposite directions in the active region of resonator. Waves of the lateral modes leak from sides the resonator and escape into the substrate, resulting in reduction of the Q factor near parallel frequency (Qp) of the resonator. It is easier form lateral modes in smaller size piezoelectric resonator than a size resonator, the waves a shorter path they are reflected by the opposite side of the resonator and bounced back to its original side. of the minimize the modes a size resonator is two double-sized resonators in series to resonator to suppress the spurious modes and increase Qp of resonator. Although the performance may have improved, the dimension of each die is increased, does the cost of manufacturing the die. This is contradicted to a common goal of cost. An alternative approach minimize the lateral is “apodize” edges the resonator, truncating a portion of the resonator such that any two edges the resonator may not be made parallel. In contrast to or rectangular-edged resonator, lateral wave in an apodized travels longer due to multiple it bounced original Apodization the propagation path of lateral acoustic wave and reduces fundamental lateral mode resonant the lateral modes does not necessarily mean increased performance because the acoustic energy leaked to of the resonator may not be reduced. In fact, the Qp factor an apodized be reduced because of apodization of the resonator. is because the perimeter an apodized resonator is greater than a square-edged or resonator same size, loss of acoustic is actually slightly indicating lower Qp. No. 7,280,007 “Thin bulk a mass loaded perimeter” discloses a to Qp through adding a raised to perimeter. The raised frame creates an acoustic impedance mismatch between the active area and outside the resonator such that energy lateral modes
 may be called spurious modes aNd lateral mOde is One Of tHe SpurIous Modes. Lateral moDEs arE generated with an excitaTion oF tHE pisTOn OperaTion modE AnD PRopAgAtEd iN pARaLlel tO thE resonaTor surface FroM oNe edge to the oTHeR. Standing wAveS occur due to lAteRal modEs ExcITed at ResOnatoR edges TRaveliNg in opposItE DirectIOns in thE ACtIve rEgion of resonator. WAVeS Of the lateral moDes may LeAK oUT FroM thE sides of thE rEsonaTOr and esCApE INTo tHE substrate, resUlting in redUCtiOn of thE Q FacTOr near ParalLeL ResOnant frequeNcy (QP) of the resOnator.
iT is easiER to form LateraL moDes In a sMAlLeR siZe PIezOElEctRIc rEsonator ThAn In a laRger SIZE ResoNatOr, beCause The lateral wavEs tRaveL A shOrter Path aFter ThEy are ReflecTed by ThE opposite side of The rEsonator aNd bOuNceD bAck to ITs origInaL siDe. One of The apprOAchEs TO MInImize the lateral modEs FOR a Small sizE resonAToR iS To combinE tWo dOublE-SIzed rEsonAToRs in seriEs to rePLaCe One singLe ResonaToR to SupPress THe spUrious Modes and IncreASe the Qp of the reSOnator. AlthougH ThE PErFOrmaNce May have been ImprOVed, tHe diMEnSioN Of eacH die iS iNCrEAsed, so does the cost of MaNufactUring The die. This is cOntradicteD TO A common gOal oF ReDUcing the cost.
An AlterNative apprOAch to minImize The laterAl modes is TO “Apodize” tHe eDgeS of The RESoNator, namely trUNCatiNg A portioN of The resoNatOr sUch ThaT aNy two edgeS of the reSoNaToR mAy nOt be mADe parallEl. in cOnTraSt to a SQuare-eDged oR a reCtAnGUlaR-edged rESoNATor, lAtErAl acOusTiC wave In an APodIzed resOnator traVelS Much LoNgEr due to Multiple refleCtIons before It Is bOunced BACk to its oRiginal edge. Apodization iNCreases The PropaGatiOn path of tHe lAteral AcoUStic waVe and rEduceS tHe fUNDamenTAL lAteRaL mode resonANT frEquenCy. howeVer, the mInimization of the laTEraL modes does not NecEssaRILy MeaN InCReaSeD qp pERFormance because The acoustiC eNErGy leaked to OUtsIdE of the rEsonatoR may nOT be reduCed. In fact, The Qp factOr In an APOdiZed resonatOr may be rEduced becAUse of APoDizatIon Of the rEsOnaTor. ThIs is beCAusE the pErimetEr Of an apOdizeD rEsonator Is greater than a square-edgEd or reCtangUlaR-edged resOnaTOr oF same size, The lOss of acousTic EneRgy is ActUAlly sLighTLy IncREased, IndiCAting loweR qp.
u.S. PAT. no. 7,280,007 Entitled “ThiN FILm bUlk acOusTIc resoNatoR with a mass loaded pERimeter” disclosEs a tECHniQue TO incReAse Qp through adDinG a RAIsed framE tO the resonatOr perimeTeR. the raIsed frAme creAtes an aCOUsTIc impeDancE miSmatch betWeeN tHE active ArEa ANd outsIde aReA of the ResonaTOr suCH That acoustic enerGy of lATEral mODes
 may be called spurious mo des and la teral  mo deis  one  ofthe spurious m o des.  Lateral modes are gen erate dw itha nexcit ation o f  t h e  pi st on  op er a ti on mo deand pro pagated in  pa ra llel to ther es onator sur fac e from one e dge  to th eoth e r. St and ing w aves o c cur du e to late ra l  modes excited a treso nator edges trave l in g  in opposite d irecti on s  i n the  ac tive regio nof re s onator. Wa v e s  of the lateral m odes may le a k o ut fro mthe sidesof th er eso nator and e scap e into th e subs t rate, r e sulting  in re duc tio n of th eQ f ac t orn ea r p a ral lel reso na nt  freq uenc y ( Q p) o f t he r esona tor.
It is ea sie r to for m lat eralmode sin asmalle r siz epiezoelectric r eson ator than  in  a  la rg er si z e reso nat or,  becaus e the l a ter al w a ve s travel a shorter  p a t hafter th ey are re fl e cted byth e o ppos i t e sid e of th e resona tor an d  b ou nced ba ck  to it sori gin al si d e. O ne ofthe appr oache s  to minimize t h e lateral mod e sf o ra  sma llsize resona tori s to  com b in e t w o dou ble-s iz e dr esonators in series  t o repl ace o ne single res onator tos u p press th e sp u ri o us modes and i ncrea se the Qpo f the re sonat or. Alth ough thep e rformanc e m ayhav e b e e nimproved, the d imen si on of e ach  die is  in cre ase d,so  does the  cost of  m an uf ac tur ing t h e die. T hi s i scon tradi c ted to  a co mmon  g oa l  of  reduci n gt h e co st .An a lte rn ative  app r oac h to mi nimize th e l a tera lmo des isto “apodize”th e edges of  t heresona t o r, namel y truncating a portiono f the r eso nator  suc h that an y t wo edg eso f theresona tor m ay  no t be ma d e  p ara ll el. In con t r ast  to a  s quar e-edged  or a rectangular- e dge d resonator,lat eral a co ust i cw ave  i n  an a podized resonat or travels  m u ch  longer du e  to  m ultiple  reflec tions beforeit is bou nced back  t o it s ori ginal edge . Apodiz ation inc r eases th e pro pag ationpa thof th e late r alacous tic wa ve  and r educe sthe fund amental lateral mode re sonant  freq uen cy. Howev er, the  minimiza tion  of the la ter almodes  do e s not  nec e ss ari l y mea n in c reased Qp pe rfo r m an ce becauset h e  ac ousti c e n ergy l eake d to outside of t h e resonator ma y no t bered u ced.  I n fact, the Qp  fa ct o r  in an a po dized reson ator may  b e  redu ced be causeof apod i z at i on oftheres onator. T his  i s  becaus eth e  perim eter  o f an a podize d  res o n ator is greaterthana squar e -ed ged o rrectang u lar- edged reso nator of sa me siz e, t he lo ss of a co usticene rg y is actua l ly slight ly in creased ,indi cat ing lo werQ p .
U.S . Pa t.  No . 7,280,0 0 7  e n ti tl e d “ Thin  film  b ulkacousticr esonator  wi t h a mas sloa d e d peri m et e r ” disclose s a  tech n i que to inc r ease Qp throu gh add ing araisedf ram eto theres o n ator peri meter. Th e  ra is ed f rame cre at es a naco us tic impedance m ismatchbetweent h e acti vea reaa nd out si de area of t he re so n ator su c h  th at acou s tic  en erg y of  la tera l  modes
 may_be called_spurious modes and lateral_mode is_one_of the_spurious_modes. Lateral modes_are generated with_an excitation of the_piston operation mode_and_propagated in parallel to the resonator surface from one edge to the other. Standing_waves_occur due_to_lateral_modes excited at resonator edges_traveling in opposite directions in_the active_region of resonator. Waves of the lateral modes_may_leak out from_the sides of the resonator and escape into the_substrate, resulting in reduction of the_Q factor near_parallel_resonant_frequency (Qp) of the_resonator.
It is easier to form lateral_modes in a smaller size piezoelectric_resonator than in a larger size resonator,_because the lateral waves travel a_shorter path after they are_reflected by_the opposite side of the_resonator and bounced_back to_its original side._One of the approaches to minimize_the lateral modes_for a small size resonator is_to_combine two double-sized_resonators_in_series to_replace one single_resonator_to suppress_the_spurious modes and increase the Qp_of_the resonator. Although the performance may have_been improved, the dimension_of_each die is increased,_so does the cost of_manufacturing the die. This is contradicted_to a_common goal_of reducing the cost.
An alternative approach to minimize the lateral modes_is to “apodize” the edges of_the resonator, namely truncating_a portion_of_the resonator such_that_any two_edges of the resonator may not be_made parallel._In contrast to a square-edged or_a rectangular-edged resonator, lateral_acoustic_wave in an apodized resonator travels_much longer due to multiple reflections_before it is bounced back_to_its_original edge. Apodization increases the_propagation path of the lateral acoustic_wave and reduces_the fundamental lateral mode resonant frequency. However,_the_minimization of the lateral modes does_not_necessarily mean increased Qp performance because_the_acoustic_energy leaked to outside of_the resonator may not be reduced._In fact, the Qp factor in an apodized resonator_may be reduced_because of apodization of the_resonator._This_is because the perimeter of an apodized resonator is greater_than a_square-edged or rectangular-edged_resonator of same size, the loss of acoustic energy is_actually slightly increased, indicating lower Qp.
U.S. Pat._No. 7,280,007 entitled “Thin film bulk acoustic resonator with a mass_loaded perimeter” discloses a technique to increase Qp_through adding a raised frame to the_resonator perimeter. The raised_frame_creates an acoustic impedance mismatch between the_active_area_and_outside area of_the resonator such_that acoustic energy_of lateral_modes