Introduction to Surface Acoustic Wave (SAW) Devices

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April, 8 Introduction to Surface Acoustic Wave (SAW) Devices Part 4: Resonator-Based RF Filters Ken-ya Hashimoto hiba University k.hashimoto@ieee.org http://www.te.chiba-u.jp/~ken

ontents Basic Filter Design Ladder Type Filter Design Lattice Filter Design Stacked Resonator Filter Design oupled Resonator Filter Design

ontents Basic Filter Design Ladder Type Filter Design Lattice Filter Design Stacked Resonator Filter Design oupled Resonator Filter Design

H (db) N-th Order Butterworth Filter Maximally Flat Response: H (n) ()= for n=,,---n H ( ) N ( / ) - -4-6 N=3 N=5-8 N=7 - N=9.5.5.5 3 3.5 4 Relative frequency H (db) - N=3 - N=5 N=7-3 N=9..4.6.8..4 Relative frequency Gradual Skirt & Group Delay haracteristics

S (db) N-th Order hebyshev Filter Equal-Ripple haracteristics (: parameter) H ( ) T N ( / ) cos( N cos hebyshev polynomial T N x) cosh( N cosh -.db -4-6 N=3 N=5-8 N=7 N=9 -.5.5.5 3 3.5 4 Relative frequency S (db) ( - x) x).db N=3 - N=5 N=7 N=9-3..4.6.8..4 Relative frequency Good Skirt but Bad Group Delay haracteristics x x

7 Element T-type Butterworth LPF Various values R =5 f =MHz

L' ' ' ' L' L' ' L' ' ' L' L' ' L' ' L L LPF to HPF LPF to BPF LPF to BEF / ' / ' L L c c c c ' ', ' ' L L ' ) /( ' ) ( ' ) /( ' ) ( L L L c c c c c c / ' ) /( ' ) ( / ' ) /( ' ) ( L L L c c c c c c ' ', ' ' L L Original LPF (ut-off c )

R =5=%, f c =MHz

Infinite Q Q= for Parallel-L Q= for Series-L Round Left Shoulder Increased Insertion Loss Round Right Shoulder

Influence of Mutual L M L L L -M L -M M V V di L dt di M dt M L di dt di dt ( L ( L di M ) M dt di M ) M dt d dt ( I d ( I dt I I ) )

Null Generation! Equivalent to L 4 & L 6 oupling Equivalent to L & L 3 oupling

onstant K Filter E S R L L/=R R Uniform Impedance Values V L L L L V I I I L L L I V ascade-onnection with Inversion (Equivalent ircuit for Transmission Line)

V L L L L V H = When Equivalent Transmission Line I I Length is n/ H (db) - -4 - -6 N=3 N=3 N=5 - N=5-8 N=7 N=7 N=9 N=9 -.5.5.5 3 3.5 4-3..4.6.8...4 Relative frequency Relative frequency H (db) Similar Response to Butterworth Filter

Fabry-Perot Resonator A A T T L Interference Between Two Reflected Waves % Transmit When L=n/

Image Parameter Z i, Z o & Z i Z i Z o Z o Z i Z i Z Z o Example Z s ascade onnection with Inversion Z p Z i Z o Z o Z i Z i Z o Z i Z s ( Z s Z p ) F Z i cosh Zi sinh 3 Z o Z i sinh cosh Y o Z o sinh Y Z p s ( Y p / Z Y p s ) where =Z i /Z o

Analysis i i i 3 i M+ e e e3 [Fe] e M+ R [Fo] [Fe] [Fo] or [Fo] R e out e in # # #3 #M. ascade onnection with Inversion cosh M Z i sinh M Zi sinh M cosh M F cosh M Zi sinh M Zi sinh M cosh M ( M ( M :odd) :even)

i i R e F F e E in R F F S F F R F G F ( )cosh M ( Zi / R cosh M ( Zi / R R R / Zi )sinh / Z )sinh M i M ( M :odd) ( M :even) When jn / M, S =

R R L E S L L K j K Z K Z c c c o c i /, / / sin ) / ( / ) / ( When < c Imag., Z i & Z o Real Passband =jn / c =sin(n When > c Real, Z i & Z o Imag. Rejection band Zero Insertion Loss

Derived m Filter E S R L R =L/ R onstant K Filter ml (m - -m) m (m - -m)l ml m R =L/ m Null Due to Series Resonance Null Due to Parallel Resonance

ml L L ml m (m - -m)l m (m - -m)l ombination of Derived m and onstant K Filters H (db) - -4-6 -8 -.5.5.5 3 3.5 4 Relative frequency H (db) -3..4.6.8..4 Relative frequency Steep Skirt and Good Out-Band Rejection - - m=.6 m=.7 m=.8 m=.9 m=

ontents Basic Filter Design Ladder Type Filter Design Lattice Filter Design Stacked Resonator Filter Design oupled Resonator Filter Design

Ladder-Type Filter onfiguration (Resonator-Based onstant K Filter) Fabrication of Multiple Resonators on a hip Low Loss High Power Durability Moderate Out-of-Band Rejection

Performance of Ladder-Type SAW Filter Scattering Parameter S (db) -5 - -5 - -5-3 -35-4 -45-5 Tx W-DMA-Rx Rx 9 3 4-5 Frequency (MHz) Fujitsu FAR-F6P-G4-LM - - -3-4 Scattering Parameter S (db)

- r s - Y s a s -3.9.95..5. Frequency [GHz] Scattering Parameter, S [db]

- a p - r p Y p -3.9.95..5. Frequency [GHz] Scattering Parameter, S [db]

- Y s Y p Y p r s a p - r p a s -3.9.95..5. Frequency [GHz] Scattering Parameter, S [db]

r r r r a a Q j j Q j j j Y ) / / ( ) / ( ) / / ( ) / ( p Resonator Model for Y p & Y s. Q r Identical for Z s Z p. rs = a p Assumption R L Z s Z p s p s p p o o p s s i Y Y Y Y Y Z Y Z Z Z Z / sinh ) ( ) ( Passband When -<Y p /Y s < (Either Y s or Y p Inductive)

Relative admittance Y p r p Null Y s a s ap r s Null Passband When -<Y p /Y s < (Either Y s or Y p Inductive) Larger Y s Offers Wide Bandwidth

At the Resonance(=) ) ( ) / / ( NrM Z R R Z N S p s s r where s p R Loss Minimum ondition = / Q r M (FOM) s p r / NrM S s r Low Loss When NrM - «:even) ( )sinh / / ( cosh :odd) ( )sinh / / ( )cosh ( M M Z R R Z M M M Z R R Z M S i i i i

Bandwidth s r ( )( r ( )( r ) ) r ( )( r where ) p s r / Out-of-Band Rejection When =, S cosh( N) T N r where T N (x)=cosh(ncosh - x): hebyshev Polynomial N Influences IL and OoB Rejection r Influences IL, Bandwidth and OoB Rejection

Scattering Parameter, S [db] -5 - N= -5 N= - N=3 N=4-5 r=.4 N=5-3.9.95..5. Frequency [GHz]

Scattering Parameter, S [db] - - r=.4 N= N= N=3 N=4 N=5-3.97.98.99....3 Frequency [GHz]

Scattering Parameter, S [db] -5 - N=5-5 - r=. -5 r=.4-3 r=.6 r=.8-35 r=. -4.9.95..5. Frequency [GHz]

Scattering Parameter, S [db] - - N=5 r=. r=.4 r=.6 r=.8 r=. -3.97.98.99....3 Frequency [GHz]

Scattering Parameter, S [db] - - -3 N=5 r=.4 =MHz =MHz =4MHz =6MHz =8MHz.97.98.99....3 Frequency [GHz]

Scattering Parameter, S [db] -.5 - N=5 r=.4 -.5 d=mhz Q p =, Q s = - Q p =, Q s = Q -.5 p =, Q s = Q p =Q s = -3.97.98.99...3 Frequency [GHz]

Influence of ommon Impedance L i SAW Device hip S S S 3 L o wire SAW chip wire i e P e P e3 P 3 e4 o L e L e L e feedthrough L c Origin of L c Equivalent ircuit

Scattering Parameter, S [db] -5 - -5 - -5-3 -35-4 r=.4 =MHz N=5 L c = L c =.nh L c =.nh L c =.3nH.9.95.5. Frequency [GHz]

Scattering Parameter, S [db] -5 - -5 - -5-3 -35-4 r=.4 =MHz N=5 L c = L c =.nh L c =.nh L c =.3nH.5.5.5 3 3.5 Frequency [GHz]

Design of Ladder-type Filters Resonator Limits Achievable Band Width For IL Minimization, r p s R S For Wide bandwidth, rs should be a little larger than p a With smaller r= p / s, IL and Band Width Improved but OoB Rejection Deteriorated. With N, OoB Rejection Improved but IL Increases IL is Very Sensitive to Motional Resistance of Y s Very Sensitive to Parasitics Q Influences IL and Shoulder haracteristics

ontents Basic Filter Design Ladder Type Filter Design Lattice Filter Design Stacked Resonator Filter Design oupled Resonator Filter Design

Lattice Filter Resonator Y o R Y e R e out Balanced I/O e in Y o Y o / Y e / :- Equivalent ircuit Unbalanced I/O

Y o -Y e Y o -Y e Y e -Y o Y e -Y o :- Y e Y e Y o Y o Modified Equivalent ircuit Equivalent to -Stage ascaded L-type (or -type) Filter Res. Freq. for Series Arm Anti-Res. Freq. for Parallel Arm Y e =, Y o = or Y o =, Y e =

Resonance ondition Res. Freq. for Y o Anti-Res. Freq. for Y e Or Res. Freq. for Y e Anti-Res. Freq. for Y o S R ( Yo Ye ) ( Y R )( Y e o R ) At Resonance ( M S o r ( M M ) M ) IL Min. ondition Where M=Q r / R S o r M M

Frequency Response S (db) 5-5 - 5-5 Y o 5 - Y e -5-5 -3 S - -5-35 - -4.9.95.5. -5 Relative frequency Good OoB Rejection Relative admittance (db)

Wideband When ro > a e -5 - S (db) - -5 - S (db) - -5.96.98..4 Relative frequency -3-4 = =.% =.4% =.6%

Better OoB Rejection When o > e - S (db) - -3-4 -5.9.95.5. Relative frequency r= r=.95 r=.9 r=.85 r=.8 Null Generation Near Passband

Relative admittance Y e r o Y o a e ao r e S R ( Yo Ye ) ( Y R )( Y e o R ) Null Generation When Y e =Y o

Influence of Mutual oupling L I SAW Device L L I c V L 4 L 3 L 3 L L 4 33 L 44 I 3 I 4 L 34 V Very Small Values but May Not Negligible

Influence of Inductive oupling EM Feedthrough (db) -5-6 -7-8 -9 - - = =3.5pF (b) c =.5fF, L 34 =.5pH (a) c =.5fF - 3 4 5 6 7 8 9 Frequency (GHz) Tiny oupling Gives Significant Influence

ontents Basic Filter Design Ladder Type Filter Design Lattice Filter Design Stacked Resonator Filter Design oupled Resonator Filter Design

Stacked FBAR Filter Electrodes Si Good OoB Rejection Moderate IL L m m R m R Z R Equivalent ircuit for Fundamental Resonance E Static apacitance When Parallel-onnected -Port Resonator When Parallel-onnected with Inversion

Frequency Response of Stacked Resonator Filter From TFR Technologies 53

i L m m R m e e Transfer Function S ( j R Z i ){ ZR ( i i Where j R Y Y Y Y Z ) } Y Y j Z jl e e m Z R m / j m Ideal ase (R m =), ZR ( j R ) /( j R ) At Satisfying S j R j R Z ( R S jr ) (Loss Less)

}] ) ( /{ / ) ( [ ) ( G G R L j j G G S m ) ( ) ( R R j R L j Z m Gives }/ ) ( { R R R S m M R S m R IL Min. ondition / / Q M R L R Q m m m m m Determined by M

] ) / ( [ M j j S G When ] [ M S ] ) / ( [ M -3dB Bandwidth ) ( M S / / Q M R L R Q m m m m m When Determined by M and

Response of Stacked Resonator Filter S [db] R =5 - -4 R =.5-6 -8 -.5.5.5 3 3.5 Frequency [GHz] ZnO (L=.6 m, S=66 m ) S is Set to Z-Match at GHz

ascaded Stacked Resonator Filters L m m R m L m m R m L m m R m R R E in R R E in F N jr jr cos e cos N e sin sin N jre sin cos N jre sin N cos N where cos jr jr e e Z sin Z sin jl m j j R m Z / ( j j m Z)

S [db] -5 - -5 - -5-3 -35-4 N= N= N=3 N=4.9.9.94.96.98. Frequency [GHz] ZnO (L=.6 m, S=66 m ) Widened Passband Steeper Skirt haracteristics

ontents Basic Filter Design Ladder Type Filter Design Lattice Filter Design Stacked Resonator Filter Design oupled Resonator Filter Design

Uncoupled State k M M k Resonance Frequency: r =(k/m).5 oupled State k M k c M k Resonance Frequency Symmetric Resonance: rs ={(k+k c )/M}.5 Antisymmetric Resonance: ra =(k/m).5

oupled Resonator + + M M V - dv dt dv dt v i v v k k v v M k - dt dt k - k c k c M ( v ( v V - v v ) dt ) dt v i V V V F k c - F V (a) Electric + Mechanical ircuit

i v M k - k - M v i V F k c - F V (a) Electric + Mechanical ircuit M k - k - M k c - (b) Mechanical ircuit

M k - k - M k c - M k - k - M (k c ) - (k c ) - (a) Symmetric Resonance M k - k - M (b) Antisymmetric Resonance

Transversally oupled Double-Mode Filter Electrodes Si Symmetrical & Antisymmetrical Resonances R in E in L m L m a m a s m s a R m s R m :- Equivalent ircuit R out -Port Resonator When Parallel- onnected Another -Port Resonator When Parallel-onnected with Inversion

Equivalent ircuit of Double-Mode Filter Y e =(Y me +j ) Y o =(Y mo +j ) Y me, Y mo :Motional Y, j :Static apacitances Equivalent to Lattice Filter Y mo / Y me / :- Y o / Y e / :-

Design Principle of Wideband DMS Filters oincidence of Multiple Resonance for Y e (or Y o ) with Antiresonance for Y o (or Y e ) r o a o r e e a r o a o Employing More Resonances Results in More Bandwidths

Double Mode SAW (DMS) Filter Scattering parameter. S [db] - - -3-4 -5-6 -7-8 8 85 9 95 5 Frequency [MHz] Symmetrical & Anti-symmetrical Resonances - - -3-4 -5-6 -7-8 Scattering parameter. S [db] Fujitsu FAR-F5EB-94M5-B8E

oupled Resonator Filter (RF) Input Output Si S [db] Overcoupling -5 - riticalcoupling -5 - Undercoupling -5-3.85.9.95.5..5 Frequency [GHz] ZnO (L=.6 m, S= m ) oupler R=GRayls (Very hard),.8 How to Realize?

S [db] S [db] - -4-6 N= -8 N= N=3 -.5.5.5 3 3.5 Frequency [GHz] N= - N= N=3-4 -6-8 -.5.5.5 3 3.5 Frequency [GHz] ascaded RF ZnO (L=.6 m, S= m ) oupler GRayls,.8 Extremely hard ZnO (L=.6 m, S=66 m ) oupler MRayls,. Extremely soft

Design of oupled Resonator Filters Band Width Governed by For Loss Minimization, r R S oupling Layer Should be Designed to Adjust Multiple Poles to oincide with Nulls (But Very ritical!) Slight Difference Between Poles & Nulls Effective ascade-onnection is Effective IL is Sensitive to Motional Resistances & Parasitics

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