International Distinguished Lecturer Program

Transcription

1 U International Distinguished Lecturer Program Ken-ya Hashimoto Chiba University Sponsored by The Institute of Electrical and Electronics Engineers (IEEE) Ultrasonics, Ferroelectrics and Frequency Control (UFFC) Society

2 Basics of RF SAW Resonator Design Ken-ya Hashimoto Chiba University

3 Contents Basic Resonator Theory P-Matrix Representation One-Port SAW Resonator Design Two-Port DMS Resonator Design Influence of Parasitics

4 Contents Basic Resonator Theory P-Matrix Representation One-Port SAW Resonator Design Two-Port DMS Resonator Design Influence of Parasitics

5 Application of Electric Field to Piezoelectric Material, - M i dv dt ηv k vdt = F V v k -1 M Piezoelectric Material C 1 L C 0 V F η C 0 R (a) Electric Mechanical Circuit (b) Electrical Equiv. Circuit Analogies between V F and I v reduce to M L, η R, k 1/C

6 Resonance Characteristics Admittance G B Frequency ωr Resonance Frequency ω r =1/ C 1 L Anti-Resonance Frequency ω a =1/ L(C 1-1 C 0-1 ) -1 ω a

7 C 1 L k η M C 0 R k 0 (a) Electrical Equiv. Circuit F (b) Equiv. Mechanical Circuit Resonance Frequency ω r =1/ C 1 L Anti-Resonance Frequency ω a =1/ L(C -1 1 C -1 0 ) -1 Resonance Q (Steepness of Resonance) Q=ω r L/R Determine Insertion Loss and Skirt Characteristics Capacitance Ratio (Weakness of Piezoelectricity) γ=c 0 /C 1 =[(ω a /ω r ) -1] -1 Determine Insertion Loss and Bandwidth

8 Y G max G max / G What is Q? Stored Energy Q = π Energy Dissipated in Half ( jω / ω ) r j 1 δω ( jω / ω ) / Q r Y Y max Y max / j 1 ( ω / ω ) Cycle r δω =±1/Q j / Q Q=ω r /δω ω r ω ω r ω

9 dφ/dω ω r ω exp(-t/t) t Q=-0.5ω r dφ/dω Q=0.5ω r T Impulse Response φ=tan -1 (B/G)

10 1 Port SAW Resonator Grating (Bragg) Reflectors V in Piezoelectric substrate Interdigital Transducer (IDT) Mass-Production by Photolithography Low Loss, Low Cost and Small Volume Fundamental Operation in VHF-UHF Range

11 Fabry-Perot Model Mirror Image Direct Signal Effective Mirror Multiple Echoes Mirror Image Impulse Response (Input Current)

12 Input Admittance Y 11 Intrinsic IDT Admittance: Y S =G S jb S jωc 0 Transfer Admittance for n-th Echo: Y t =Γ n G S exp[-njβl] Y 11 = YS n= = = Y S jωc 0 1 G S G exp( njβl) Γ exp( jβl) 1 Γ exp( jβl) jb S S Γ n G S 1 Γ exp( 1 Γ exp( jβl) jβl) Γ: Reflectance of Mirror, L: Cavity Length

13 Resonance Characteristics δβl=π Conductance Γ G s Frequency Red: Intrinsic IDT Conductance, Blue: Reflector Characteristics, Black: Total Characteristics

14 Resonance Characteristics Resonance Condition: βl- Γ=mπ Motional Resistance R m : [1- Γ ]/G s Resonance Q: π(l/p I )/[1- Γ ] Motional Capacitance C m : π 1 (p I /L)G s Capacitance Ratio γ: π(l/p I )/(G s /ωc 0 ) Greater G s /ωc 0 and Γ are desirable With L, not only Q but also γ increases

15 One-port SAW Resonator L r L I L L g g L r p I : IDT pitch p r : Reflector pitch L I : IDT length L g : Gap length W: IDT aperture h: Film thickness L r : Reflector length

16 Admittance of Infinte Long IDT Y = jω C θ u κ θ ζ κ 1 8 / u 1 ω C Maximum Difference Between f a and f r (f a -f r )/f r ~4ζ p I /πωc γ={(ω a /ω r ) 1} 1 ~(8ζ p I /πωc) -1 Minimum γ

17 Reflection coefficient at ω r Γ = js tanh( κ 1 L r ) L r >> κ 1 1 Penetration depth at ω r d r = ( κ 1 1 )

18 When κ 1 of IDT ignored When Resonance freq. = Bragg freq. for Reflector Resonance condition: β S (L I κ 1-1 ) Γ=mπ Overtone: f 1 /f r =1p I /(L I κ 1-1 ) Reflector stopband: 1- κ 1 p r /π<f/f r <1 κ 1 p r /π Difference between f r and f a : f a /f r <14ζ /πωc κ 1 >8ζ /ωc L I <(π-1) κ 1-1

19 Rough Estimation Excitation Efficieny 4ζ p I /ωc=0.08 (circa. 18 o YX-LiNbO 3 ) Reflection per period κ 1 p I >0.16 Maximum γ: (8ζ p I /πωc) -1 =19.6 κ 1 >8ζ /ωc L I <(π-1) κ 1-1 L r >> κ 1-1 IDT length L I /p I <33 Ref. Length L r /p I >>7

20 When κ 1 of IDT ignored p I =p r : Resonance at Maximum G p r : For Maximum Γ L I : Larger is better h: Smaller κ 1 is better L r : Allowable Maxim Length L g =±λ/8: Resonance at Bragg Freq. W: Giving Required Impedance Tradeoff Between Spurious and γ

21 When κ 1 =0 only for IDT( L g =-λ/8 ) Relative admittance Y/G L L I =16p I L r =50p r κ 1 p I =0.08π Relative frequency Small γ but large Out-of-Band Ripple γ=5.1 Re Im

22 Reflection Coefficient in db Origin of Ripples κ 1 p=0.0π Relative frequency, θ u p/π Reflection Phase in deg.

23 Contents Basic Resonator Theory P-Matrix Representation One-Port SAW Resonator Design Two-Port DMS Resonator Design Influence of Parasitics

24 P Matrix Representation I(L) V U U - x=0 x=l U U - U (0) U ( L) I( L) p11 = p1 χp 13 p p 1 χp 3 p13 U (0) p3 U ( L) p 33 V χ= or χ=4

25 p = p, p = p Symmetric & Bidirectional IDTs Loss-Less where p p 33 1 = ± G p I 11 = jb I exp( p p p = p p 11 p 1 13 = : IDT Admittance jφ ) ± p = exp( 1 1, / G p j I * 1 φ = ) = χ p p / p * 11 : Transmission Coefficient when U (0)=±U - (L), V=0

26 COM Equation (Bi-direct., Loss-Less) CV j U j U j X I V j U j U j X U V j U j U j X U u u ω ζ χ ζ χ ζ θ κ ζ κ θ = = = 1 1 θ u =β u -π/p I : Detuning Factor(Bragg Cond. At θ u =0) β u : Wavenumber of Unperturbed Mode κ 1 : Mutual Coupling Coef. = Reflectivity/Length ζ : Transduction Coef. (ζ ωck /πp I ) p I (=p): IDT Period, Cp I : Static Capacitance/IDT Period

27 Relative conductance (db) Frequency Response of Re(p 33 ) IDT zero (φ ± =0) IDT peak (φ ± π) κ 1 p I =0 κ 1 p I =0.04π κ 1 p I =0.08π κ 1 p I =0.1π Relative frequency

28 Field Distribution at IDT peak (b) at θ p L=π (φ =π) Field Distribution at IDT zero (a) at θ p L=π (φ =0)

29 Frequency Response of φ ± (κ 1 p I =0.08π) Transmission phase (rad.) π π/ 0 -π/ IDT zero (φ ± =0) IDT peak (φ ± π) φ φ Influence of Internal Reflection Significant -π Relative frequency

30 Contents Basic Resonator Theory P-Matrix Representation One-Port SAW Resonator Design Two-Port DMS Resonator Design Influence of Parasitics

31 One-port SAW Resonator L r L I L L g g L r Boundary Condition: U - (L I /) =Γ U (L I /), U (-L I /) =Γ U - (-L I /) Γ: Reflectivity Looking from IDT Edges

32 Y = = p 33 jb I p 1 jg I χp p Γ cot{( φ 1 φ = Γ jb I ) / } G I 1 1 Γ( Γ( p p 1 1 p p ) ) Resonance ω r : at φ φ Γ =nπ Antiresonance ω a : at φ φ Γ (n-1)π (when G I» B I ) φ Γ = Γ For Wideband Design Larger G I /B I Smaller Gradient in φ with Frequency

33 Designed to resonate at φ =π giving Maximum G I /B I φ Γ =-π (L g =λ/8) Antiresonance at φ =π-φ Ι 0 [φ Ι π/] Spurious Resonance Transmission phase (rad.) π π/ 0 -π/ φ Large γ -π Relative frequency

34 Designed to resonate at φ =π giving Maximum G I /B I Relative admittance Y/G L L I =8p I L r =50p r κ 1 p I =0.08π Relative frequency Large γ and Large Out-of-Band Ripple γ=33.7 Re Im

35 Designed to resonate at φ =π/ giving Large G I /B I φ Γ =-π/ (L g =0) Transmission phase (rad.) Spurious Resonance π π/ 0 -π/ ω r ω a φ Small γ -π Relative frequency

36 QARP Resonator (L g =0) Relative admittance Y/G L L I =13p I κ 1 p I =0.08π p I /p r = Relative frequency γ=5.3 Smaller γ, Smaller Out-of-Band Ripple Re Im

37 Designed to resonate at φ =0 giving Moderate G I /B I φ Γ =0 (L g =-λ/8) Antiresonance at φ =π-φ Ι π [φ Ι π/] Spurious Resonance Transmission phase (rad.) π π/ 0 -π/ φ Smaller γ -π Relative frequency

38 Designed to resonate at φ =0 giving Moderate G I /B I Relative admittance Y/G L L I =8p I L r =50p r κ 1 p I =0.08π -1 Re γ=8.6 Im Relative frequency Generation of Spurious Responses (Limiting IDT Length)

39 p I p r : Higher Mode Suppression φ Γ =-π/ (L g =0) Antiresonance at φ =π-φ Ι π/ [φ Ι π/] Transmission phase (rad.) π π/ 0 -π/ φ Small γ -π Relative frequency

40 IDT Resonator (L g =0) Relative admittance Y/G L L I =L r =40p I κ 1 p I =0.08π 0-1 Re γ=0.0 Im Relative frequency Smallest γ But Strong Close-in Ripple

41 SAW Field Distribution at Resonance Reflector IDT Reflector Reflector (a) Conventional Resonator IDT Reflector (b) Synchronous Resonator with p I =p r

42 Contents Basic Resonator Theory P-Matrix Representation One-Port SAW Resonator Design Two-Port DMS Resonator Design Influence of Parasitics

43 Port SAW Resonator Grating (Bragg) Reflectors Piezoelectric substrate Interdigital Transducers (IDT)

44 Equivalent Circuit for Two Port SAW Resonator with Single Resonance L m SAW Device C m R m R in E in L in C 0 1:-1 C 0 L out R out When two IDTs are Parallel-Connected, Equivalent to One Port SAW Resonator When two IDTs are Parallel-Connected with Sign Inversion, Equivalent to Static Capacitance

45 Two-port SAW Resonator Reflector Gap Space Gap Reflector Boundary Condition for Right IDT: Even or Odd U - (L I /) =Γ U (L I /), U (-L I /) =±Τ U - (-L I /) Γ: Reflectivity Looking from IDT Edges T: Transmission Coefficient Between IDTs

46 1 1 = V V Y Y Y Y I I i t t i o t i V V e t i V V Y Y Y V I Y Y Y V I = = = = ) )( ( ) ( ) ( 1 L o L e o e L t L i t L G Y G Y Y Y G Y G Y Y G S = = Admittance Matrix for DMS Filter IDT Admittances for Symmetric & Antisymmetric Cond. Transmission Characteristics

47 o o I I o e e I I e b a jg jb Y b a jg jb Y = = ψ ψ ψ ψ cos sin sin cos sin sin cos sin sin cos cos cos Γ Γ Γ Γ Γ = = = = = φ φ φ φ φ φ φ φ φ φ φ φ φ φ φ φ φ φ φ φ ψ T o T o T e T e T b a b a Result of P-Matrix Analysis where And φ Γ = Γ φ Τ = T

48 Double-Mode SAW (DMS) Filter Symmetric & Antisymetric Resonances Ymo/ C0 Yme/ 1:-1 C0 Equivalent Circuit

49 Modified Equivalent Circuits Yo-Ye Yo-Ye Ye-Yo Ye-Yo Ye Ye Yo 1:-1 Yo Equivalent to two-stage-cascaded Ladder-Type Filter Resonance Frequency for Series arm Anti-Resonance Frequency for Parallel arm

50 For Wideband DMS Design: G I /B I Should be Large at Resonances Gradient in φ ± with f Should be Small at the Filter Passband Influence of Internal Reflection in IDTs Should be Small at Resonances so that SAW Field Penetrates into IDT

51 ψ ψ ψ ψ cos sin sin cos o I I o e I I e a G jb Y a G jb Y sin cos T o T e T a a φ φ φ φ φ φ φ φ ψ = = = Γ Γ Γ If Internal Reflection insignificant (φ φ - ) Resonance Condition : φ φ Γ φ Τ nπ

52 Resonance Pattern of Lower Two Modes Reflector Gap Space Gap Reflector IDT: Transmission (Out-of-Stopband) Reflector: Bragg Reflection (Stopband) Adjusting Frequency Location by IDT and Gap Lengths

53 Basic DMS Design: Adjusting location of Pole in Y e (or Y o ) to coincide with that of zero in Y o (or Y e ) ω r o ω a o ω r e ω ω a e ω φ Γ φ Τ mπ (when φ φ - ) φ Τ (m1/)π for φ Γ -π/

54 Pole and Zero Location Transmission phase (rad.) π π/ 0 -π/ φ φ -π Relative frequency Use of φ T for Adjustment

55 Current DMS Filter = Multi-Mode SAW (MMS) Filter For Wider Bandwidth ω r o ω a o ω r e ω ω e a ω r o ω ω a o ω

56 How to coincide poles in Y e (or Y o ) with zeros in Y o (or Y e ) Transmission phase (rad.) π π/ 0 -π/ φ φ -π Relative frequency Use of Rapid Change in φ -φ - at Stopband Edge

57 Resonance Pattern of Highest Modes Reflector Gap Space Gap Reflector Significant Internal Reflection in IDT Adjusting Resonance Frequency by Gap Length and IDT Pitch

58 Design Example Relative admittance Y/G L Im Re Y e Y o Relative frequency Gap distance between IDTs: L T =0.36λ

59 Cascaded MMS Filter Response Scattering coefficient S 1 (db) Relative frequency Y e =Y o

60 ) )( ( ) ( ) ( 1 L o L e o e L t L i t L G Y G Y Y Y G Y G Y Y G S = = S 1 =0 When Y e =Y o When φ - φ Γ =(n1) π Resonance Between IDT & Reflector IDT Reflector

61 Cascaded MMS Filter Response Scattering coefficient S 1 (db) Relative frequency Y e =Y o What is this?

62 Reflection Characteristics of SAW Grating Reflection Coefficient in db Relative Frequency Solid-Line: Semi-Infinite Case Broken-Line: Finite Case 90 0 Phase Angle in degree

63 Field Distribution in Grating Reflectors A A in ref A tr (a) Within Stopband (Evanescent) A A in ref A tr (b) Out-of Stopband (Standing Wave Field)

64 DMS Filters with Semi-Infinite Reflectors Scattering Parameter S 1 [db] Relative Frequency Scarcely Influences Passband Characteristics

65 For Suppression of Grating Edge Reflections Cutting Grating Edges

66 For Further Wider Bandwidth Increasing Number of Degrees of Freedom (to Use More Poles) Reduction of IDT Internal Reflection (to Locate Poles out of IDT Stopband) Use of Wideband & Highly-Efficient IDT Controlling IDT Internal Reflection is Essential Use of Modulated IDTs and/or Reflectors

67 DMS Filter Using Pitch-Modulated IDTs Reflector Reflector Variation of Cavity Length No Gap Necessary

68 Design Example Relative admittance Im Re Y e Y o Relative frequency Gap distance between IDTs: L T =0

69 Design Result Scattering coefficient S 1 (db) New Old Relative frequency Without gaps Reduced BAW Scattering Loss

70 Device Operation Scattering coefficient S 1 (db) W Ref. W/o Ref Relative frequency Effective Use of IDT Self-Resonance

71 Contents Basic Resonator Theory P-Matrix Representation One-Port SAW Resonator Design Two-Port DMS Resonator Design Influence of Parasitics

72 Influence of Parasitics C e (a) Lm C0 Cm Ge Rm (a) Capacitance ω a BW Reduction (b) Lm C0 Cm Rm (b) Conductivity Q a (c) L e Lm C 0 Cm Rm (c) Wire Inductance ω r BW Expansion (d) R e Lm C0 Cm Rm (d) Wire Resistance Q r Loss Increase

73 Variation of Reflection Coef. S 11 Z=jR 0 j Group Delay τ = [ Γ] ω -1 Z=R 0 Γ Γ 1 CW Rotation wrt Frequency Z=0 ω Γ Γ 0 Z= Z=-jR 0 -j

74 Smith Chart (Impedance Plot) L R b a ω Solid: Const. R Broken: Const. X b -0. b' R= a L C R R=0 a b (ω=ω r ) a ω C R a b

75 Smith Chart (Admittance Plot) L R b a ω 5 R=0 R= Solid: Const. G Broken: Const. B b -10 a' a ω L C R b a(ω=ω r ) b C R a b

76 R s C 0 L C R ω ω p ω ω a ω=0 Far from Resonance Near Resonance ω R s R s C 0 L C R

77 Influence of Parasitic Impedance Lead Inductance Lead & Electrode Resistance C 0 C m L P R P L m R m L P =1 nh R P =0.5 Ω ω r /π=1 GHz ω r C 0 =0 ms γ=10 R m =1 Ω (Q=500)

78 Admittance [S] With Parasitics W/O Parasitics Frequency [GHz] Reduction in Resonance Q Reduction in Resonance Frequency

79 Impedance [Ω] ω L m (C m -1 C 0-1 ) -1 =1 Q r =ωl m /R m With Parasitics W/O Parasitics Frequency [GHz] ω C m (L m L p )=1 Q r =1/ωC m (R m R p ) ω C m L m =1 Q r =1/ωC m R m

80 Inductance Estimation 10 3 With Parasitics Impedance [Ω] W/O Parasitics Frequency [GHz] Resonance by Parasitic L L P =1/ω C 0 =1 nh

81 Admittance [ms] 1 0 Inductance Estimation ω C 0 L P =1 R P =1/ωC 0 Q Frequency [GHz] With Parasitics W/O Parasitics Impedance [Ω] Frequency [GHz]

82 Estimation of Series Resistance Conductance [ms] Resistance [Ω] Frequency [GHz] With Parasitics W/O Parasitics R P =0.5 Ω Frequency [GHz] Parallel Resistance?

83 Q j Q j j j Y r r r r / 1) / ( 1 1 ) / / ( ) / ( ) / ( ω ω ω ω ω ω ω ω Q j Z r / 1 1) / ( ω ω f r f r f Z Z f Q = I R = ) ( ) ( 1 Q Estimation Q Estimation Impedance [Ω] Frequency [GHz] f Z I ) ( R(Z)

84 Influence of Substrate DUT Port 1 Port C p1 C p Full -port Measurement Conversion to Y Matrix Y 11 Y 1 =jωc p1 -Y 1 =Y DUT

85 Influence of Common Impedance L i SAW Device Chip S 1 S S 3 L o wire SAW chip wire C i C e1 P 1 C e P C e3 P 3 C e4 C o L e1 L e1 L e1 feedthrough L c Origin of L c Equivalent Circuit

86 wire SAW chip wire feedthrough

87 Z s1 Influence of L c out of Band Influence of L c out of Band i 1, i, i 3 are In-Phase When i 1 >> i >> i ) / ( ) / ( ) ( i i L i j Z Z L i j i Z i Z e i i L i j Z Z L i j i Z i Z e i L j Z Z L i j i Z i Z e c p s c p s c p s c p s c p s c p s in ω ω ω ω ω ω L c Z s Z s3 Z p1 Z p Z p3 e 1 e e 1 e 1 i 1 i i 3 i in i out

88 Scattering Parameter, S 1 [db] r=0.4 δ=mhz N=5 L c =0 L c =0.1nH L c =0.nH L c =0.3nH Frequency [GHz]

89 Scattering Parameter, S 1 [db] r=0.4 δ=mhz N=5 L c =0 L c =0.1nH L c =0.nH L c =0.3nH Frequency [GHz]

90 Influence of Parasitic L to DMS Filter jωl c Input Output jωl e

91 Influence of Common Inductance Scattering Coefficient [db] ωl c =0 ωl c =0.005G L ωl c =0.01G L ωl c =0.0G L Relative Frequency

92 Negative Common Inductance Scattering Coefficient [db] ωl c =0 ωl c =-0.005G L ωl c =-0.01G L ωl c =-0.0G L Relative Frequency

93 Influence of Common Inductance M L L L-M L-M M Mutual Inductance is Equivalent to Common One

94 Influence of Mutual Coupling L 1 I SAW Device 1 L 11 L I Cc C 1 C V 1 L 14 L 3 L 13 L L 4 33 L 44 I 3 I L 4 34 V Very Small Values but May Not Negligible

95 Influence of Inductive Coupling EM Feedthrough (db) C 1 =C =3.5pF (b) C c =0.5fF, L 34 =0.5pH (a) C c =0.5fF Frequency (GHz) Tiny Coupling Gives Significant Influence

96 Influence of C Coupling to Common Output? C 13 I 1 I V S I S C 3 C 14 G L ϕ I - C 4 G L ϕ - Coupling with Hot Side Symmetrical Structure Is Not Always Best

97 Influence of L Coupling to Common Output? L 13 I 1 I V S I S L 3 L 14 G L ϕ I - L 4 G L ϕ - Significant Influence by Ground Lines Sign Inversion through Current Direction

98 Common Mistake Disagreement is Due to Use of Lumped Element Model Instead of Distributed one? Distributed Elements Need When Phase Difference is Not Negligible Lumped Model is Enough When Size is less than 0.1λ (λ=ε r cm@1GHz) Mutual Coupling?