Introduction of Surface Acoustic Wave (SAW) Devices

Transcription

1 April, 018 Itroductio of Surface Acoustic Wave (SAW) Devices Part 6: D Propagatio ad Waveguide Ke-a Hashimoto Chiba Uiversit k.hashimoto@ieee.org te.chiba-u. jp/~ke

2 Cotets Wavevector ad Diffractio Waveguide Scalar Potetial Theor

3 Cotets Wavevector ad Diffractio Waveguide Scalar Potetial Theor

4 Diffractio (a) Fresel Regio (Beam Propagatio) W (a) (b) (b) Frauhofer Regio (Clidrical Wave Propagatio) c Critical Legth: c =(1+)W / Parameter Determied b Aisotrop(=0 for Isotropic)

5 (a) For Wide Aperture (b) Narrow Aperture Variatio with Aperture Size For Weighted IDT

6 Wave Vector =/:Phase Dela per Uit Legth Wave Propagatio Wave Propagatio =/ / =/ V p (=fdoes ot Follow Vector Decompositio Rule! ep( j X) ep[ j( z)] z

7 D Wave Equatio u C u ep[ j( t )] 0 3 S 3 where 0 / V (- 1,+ 3 ) (-S 1,+S 3 ) (+ 1,+ 3 ) (+S 1,+S 3 ) S 0 1 S 1 (- 1,- 3 ) (-S 1,-S 3 ) (+ 1,- 3 ) (+S 1,-S 3 )

8 Sell s Law Cotiuit of Wave Frot at Boudar Medium 1 Medium Cotiuit of Lateral Wavelegth Cotiuit of Lateral Wavevector Compoet

9 At Boudar Betwee Two media, S () / t t / / S () i S (1) i i r r i / r / (a) Trasmissio S (1) i / r / (b) Total Reflectio Slowess Surface (S=1/V p ) Whe S (1) >S () si si si i r r I optics, =/c, where is refractive ide ad c is wave velocit i vacuum t t

10 Evaescet Field (at Total Reflectio) () j () 0 Field Peetratio Epoetial Deca (Eerg Storage)

11 Tuelig Eve for Total Reflectio State, Wave Trasmissio Occurs whe Medium is Thi No Phase Dela Through Trasmissio

12 0 0 0 ) / ( ) / ( V V V ) / ( ) / ( ) / ( V V V V Parabolic Approimatio /V 0 /V 0 Aisotrop Case )] ( ep[ t j u

13 Whe Aisotrop eists, V p =S Phase Velocit V g : Group Velocit S z (+S,+S z ) V g -1 S V g S V p Beam Steerig cf. Birefrigece

14 Gree Fuctio Aalsis q(,) (X,Y) ( X, Y ) G( X, Y ) q(, ) dd F Where G(X,Y) is Gree Fuctio G( r) ep( jr) r Para-Aial Approimatio for X» Y Approimatig 0, The F G( X, Y ) ep( j X jy X / 4 X )

15 Cotributio of -th Electrode (Width w, Positio (, )) +w / (,) -w / (X,Y) ( X, Y ) A N 1 w w G( X / /, Y ) d

16 (X m,y) -w / +w / (,) Y m -W m / Y m +W m / ddy Y X G A dy Y X Q M m N W Y W Y w w m M m W Y W Y m m m m m m m m m 1 1 / / / / 1 / / ), ( ), ( Detectio b m-th Electrode (Width W m, Positio (X m,y m ))

17 Amplitude i db Simulatio With Diffractio Without Diffractio Frequec i MHz Sigificat at Higher Out-of-Bad Rejectio

18 Cotets Wavevector ad Diffractio Waveguide Scalar Potetial Theor

19 Ifluece of Diffractio i SAW Resoators Couter Measure

20 Iharmoic Resoaces Admittace G Iharmoic Resoace B Frequec r a Desig Challege: Suppressio of Iharmoic Resoaces Without Badl Affectig Mai Resoace

21 Closed Waveguide Waveumber of Mode = h For Phase Matchig Betwee Icidet ad -Bouced Waves - h csc+= coth cos : Reflectio Coef. at Boudaries Trasverse Resoace Coditio - h +=

22 Resoace Coditio h 0 h 0 h h Trasverse Resoace Coditio

23 ad 0 h Waveumber of Guided Mode ( / V ) ( / h ) Normalized frequec = =1 = Normalized waveumber Relatio Betwee ad 0 Whe =0 or

24 (a) Near Cutoff (b) Far from Cutoff Propagatio of Waveguide Mode V p =/ : Phase Velocit Frequec ta -1 (V p ) Waveumber ta -1 (V g ) Propagatio Speed of Phase Frot V g =/ : Group Velocit Propagatio Speed of Eerg

25 Ifluece of Group ad Phase Velocities o Sigal Trasfer =L/V g t (a) Iput Sigal =-L/V p t (b) Output Sigal

26 Uder Cutoff Frequec Normalized frequec 3 =6 =5 =4 =3 1 = =1 0-3j -j -j Normalized waveumber Behavior as Evaescet Field

27 At Cutoff (a) cut-off (b) (c) R cut-off (d) R R Behavior as Evaescet Field

28 Eve if ot Cutoff 1 R1 R 1 R 1 R Ifluece of Higher-Order Cutoff Modes

29 Ope Waveguide h Use of Total Reflectio at Surfaces Eerg Peetratio to Outsides Trasverse Resoace Coditio - h += is Frequec or depedet

30 Similarit with Closed Waveguide at Total Reflectio Normalized frequec Critical Coditio Normalized wavevector Relatio betwee ad 0 If Total Reflectio Coditio is Not Satisfied?

31 Leak Waveguide h Whe Reflectio Coefficiet at Surfaces is Large, Pseudo Mode Propagates with Eerg Leakage to Outside If Reflectio Coefficiet at Surfaces is Small?

32 Propagatio as Free Wave(Not Guided) Appearig Whe Velocities of Waveguide Mode ad Free Wave are Close (Near Cutoff)

33 Ecitatio ad Propagatio of No-Leak Compoet source c SAW c =cos -1 (V S /V B ): critical agle V S : SAW velocit, V B : BAW velocit

34 Ecitatio ad Propagatio of Leaked-BAW Compoet source c Leaked BAW c =cos -1 (V B /V S ): critical agle V S : SAW velocit, V B : BAW velocit Field Amplitude Grows Toward the Depth!

35 Resoace Frequec of Cuboid Cavit z z z h h h 0 z z h h h

36 Wavevector of Propagatio Mode i Rectagular Waveguide z 0 h h

37 Cotets Wavevector ad Diffractio Waveguide Scalar Potetial Theor

38 Scalar Potetial Aalsis w B w G w B Regio B Regio G Regio B -D Aalsis Approimatio as Uiform (Flat) IDT Field Epressio(Whe w B = is Assumed for Simplicit) B ep( B )ep( j) ( wg / ) { G ep( jg ) G ep( jg )}ep( j) ( wg / ) B ep( B )ep( j) ( wg / )

39 Due to Cotiuit of ad at =w G / Smmetric Mode ( B+ = B-, G+ = G- ) B G cos( GwG / ) ep( BwG ta( w / ) B G G G / ) Ati-Smmetric Mode ( B+ =- B-, G+ =- G- ) B B jg si( GwG / ) ep( BwG / ) G cot( G w G / )

40 Parabolic Approimatio for Slowess Surface S S S S (a) For Regio G For Regio B V G0-1 V G0-1 (b) >0 <0 G 0 B 0 G B G B / / G0 B0 For Isotropic Case, =0.5

41 Slowess Surface of SH-tpe SAW o 36-LT S sec/km S sec/km

42 Waveumber of Gratig Mode ad Slowess Surface For Eerg Trappig i Waveguide Real B S S V -1 p S V p -1 S V B0-1 V G0-1 V G0-1 (a) For >0 (b) For <0 V G0 <V p <V B0 V B0 <V p <V G0 Higher-order Modes Appear i Higher Frequecies V B0-1 Higher-order Modes Appear i Lower Frequecies

43 Smmetric Mode ˆ 1 ˆ ta ˆ 1 ˆ 1 G V w V V ˆ 1 ˆ cot ˆ 1 ˆ 1 G V w V V Ati-Smmetric Mode Whe V B0 /V G0-1 «1, Where :Relative Phase Velocit :Relative Waveguide Width G0 G0 B0 p G G G0 B0 G0 B0 p ˆ ˆ V V V w w V V V V V V

44 Relative SAW Velocit vs. Relative Aperture Relative phase velocit A 3 S 0.6 A 0.4 S 1 0. A S Relative aperture width Velocit i Regio B Velocit i Regio G

45 Equivalet Circuit for Multi-Mode Resoators () L m (3) L m () L m (1) L m C m () C m (3) C m () C m (1) C 0 R m () R m (3) R m () R m (1) ( ) r C 1 ( ) m L ( ) m V p ( ) p I

46 Modes Propagate without Mutual Power Iteractio ( ) ( ) d ( ) d ( ) k Mode Orthogoalit * k ( ) ( ) d Field ca be Epressed as Sum of Mode Fields Mode Completeess k k P k where P k ( ) k d d ( ) k 1 A ( ) / k k P k

47 Fourier Trasform ()=p -0.5 ep(j/p) Orthogoalit p 0 ( ) ( ) d k * Completeess ( ) p 0 k 1 * p p A ( ) k k p 0 k 1 ep[j( m) / p] d p 0.5 k k k 1 A k * ep(kj ( ) ( ) d A ( ) ( ) d A k / p) Multiplicatio of * () & Itegratio give p 0.5 A p ( )ep( j 0 / p) d

48 Differece of Waveguide Width w g with Figer Overlap Width w e w e w g Amplitude at Ecitatio Source ( ) 0 0 ( ( w e w e /) /)

49 / / * 0 ) ( e e w w m m m d P A 1 * * ) ( ) ( / ) ( ) ( k m k k k m d P A d Multiplig m* () ad Itegratig The 1D Aalsis Gives A 0 = 0 w e 1 / / 0 (0) ) ( ) ( ) ( d w d A A C C e w w m m e e Sice Motioal Capacitace Power Ecitatio Efficiec,

50 Effective Electromechaical Couplig Factor vs. Relative Aperture Width (Whe w e =w g ) Relative couplig factor S Relative aperture width Zero Ecitatio Efficiec for Ati-Smmetric Modes S 1 S

51 Wh Effective Couplig Factor Chages? (a) S 0 Mode (Whe w is small) Large Peetratio (b) S 0 mode (Whe w is large) Small Peetratio (c) S 1 mode Eistece of Sig Iverted Regio