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射頻電子 - [第四章] 散射參數網路

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散射參數網路

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射頻電子 - [第四章] 散射參數網路

  1. 1. Department of Electronic Engineering National Taipei University of Technology
  2. 2. • • • • (Power waves) • (Traveling waves) − Department of Electronic Engineering, NTUT2/25
  3. 3. (Traveling Waves) ( ) ( ) ( ) j x j x V x V x V x Ae Beβ β+ − − = + = + ( ) ( ) ( ) ( ) ( ) 0 0 V x V x I x I x I x Z Z + − + − = − = − ( ) ( ) ( ) V x x V x − + Γ = • • • (Normalized traveling waves) ( ) ( ) 0 V x a x Z + = ( ) ( ) 0 V x b x Z − = ( ) ( ) 2 2 0 V x a x Z +   = ( ) ( ) ( ) 2 10log 10log 20log aP a x a x = = ( ) ( ) ( ) ( ) ( )0 0 1 1 2 2 b x v x i x V x Z I x Z = − = −       ( ) ( ) ( ) ( ) ( )0 0 1 1 2 2 a x v x i x V x Z I x Z = + = +       ( ) ( ) ( ) ( ) 0 V x v x a x b x Z = + = ( ) ( ) ( ) ( )0i x a x b x Z I x= − = ( ) ( ) ( )b x x a x= Γ slide 16, 30 3/25 Department of Electronic Engineering, NTUT
  4. 4. Two-port Network ( )2 2a l ( )2 2b l ( )2 2a x ( )2 2b x ( )1 1a l ( )1 1b l ( )1 1a x ( )1 1b x 1oZ 2oZ Input port Output port Port 1 1 1x = l Port 2 2 2x = l • Port 1 ( ) • Port 2 ( ) ( )1 1a l ( )1 1b l1 1x = l ( )2 2a l ( )2 2b l2 2x = l Incident wave Reflected wave • (Scattering Matrix) ( ) ( ) ( )1 1 11 1 1 12 2 2b S a S a= +l l l ( ) ( ) ( )2 2 21 1 1 22 2 2b S a S a= +l l l ( ) ( ) ( ) ( ) 1 1 1 111 12 2 2 2 221 22 b aS S b aS S      =          l l l l xx 4/25 Department of Electronic Engineering, NTUT
  5. 5. ( ) ( ) ( )2 2 1 1 11 1 1 0a b S a = = l l l Input reflection coefficient with output properly terminated ( ) ( ) ( )1 1 2 2 22 2 2 0a b S a = = l l l Output reflection coefficient with input properly terminated Forward transmission coefficient with output properly terminated ( ) ( ) ( )1 1 1 1 12 2 2 0a b S a = = l l l Reverse transmission coefficient with output properly terminated (measured with port 2 properly terminated) (measured with port 2 properly terminated) (measured with port 1 properly terminated) (measured with port 1 properly terminated) ( ) ( ) ( )2 2 2 2 21 1 1 0a b S a = = l l l 5/25 Department of Electronic Engineering, NTUT
  6. 6. ( ) ( ) ( )2 2 1 1 11 1 1 0a b S a = = l l l • Return Loss (RL) ( ) ( ) ( )2 2 2 2 21 1 1 0a b S a = = l l l ( ) ( ) 2 1 12 1 11 2 1 1 1 b a b P S a P = = l l ( )21 11 11 1 10log 10log 20log (dB)b a P S S P   = =    11Return Loss (RL) 10log 20log (dB)in reft P S P   = = −     ( ) ( ) ( ) 2 2 22 2 21 2 1 1 1 b a b P S a P = = l l ( )22 21 21 1 10log 10log 20log (dB)b a P S S P   = =    21Insertion Loss (IL) 10log 20log (dB)transmit receive P S P   = = −    ( )• Insertion Loss (IL) |S11| −12 dB 12 dB 6/25 Department of Electronic Engineering, NTUT
  7. 7. S11 Two-port Network ( )2 2 0a =l ( )2 2b l ( )1 1a l ( )1 1b l 1oZ 2oZ Port 1 1 1x = l Port 2 2 2x = l 2 2oZ Z=+ − 1E 1 1oZ Z= ( ) ( ) ( )2 2 1 1 11 1 1 0a b S a = = l l l OUTZ • Z2=Zo2 (i.e. Zo1=Zo2) 50 ( )2 2 0a =l ( ) ( ) ( )2 2 1 1 11 1 1 0a b S a = = l l l ( ) ( ) ( )1 1 11 1 1 12 2 2b S a S a= +l l l 0 port 2 ( )2 2 0a =l 7/25 Department of Electronic Engineering, NTUT
  8. 8. • Zoi (i=1 to n) n port [ ] [ ][ ]b S a= n-port Network 1oZ Port 1Port 1' 1TZ ( )1 1a l ( )1 1b l 2oZ Port 2Port 2' ( )2 2a l ( )2 2b l onZ Port nPort n' ( )n na l ( )n nb l [ ] 11 12 1 21 22 2 1 2 n n n n nn S S S S S S S S S S ⋅ ⋅   ⋅ ⋅   = ⋅ ⋅ ⋅ ⋅ ⋅   ⋅ ⋅ ⋅ ⋅ ⋅   ⋅ ⋅  8/25 Department of Electronic Engineering, NTUT
  9. 9. • • (i=1 for port 1 and i=2 for port 2) ( )0iP+ ( )0iP− + 1oZ 2oZ Port 1 1 1x = l Port 2 2 2x = l Port 1' 1 0x = ( )1 1I x Port 2' 2 0x = 2l1l − ( )1 1V x ( )2 2I x + − ( )2 2V x ( )0iP+ ( )0iP− ( )0iP+ ( )0iP− 11 12 21 22 S S S S       ( ) ( ) ( ) ( ) 1 1 1 111 12 2 2 2 221 22 b aS S b aS S      =          l l l l ( )0iP+ ( )0iP− ( )a x ( )b x 9/25 Department of Electronic Engineering, NTUT
  10. 10. ( ) ( ) 21 0 0 2 i iP a+ = ( ) ( ) ( ){ } ( ) ( ) ( ) 2 22 , 01 1 1 0 Re 0 0 0 0 2 2 2 i i i i i i rms oi V P V I b b Z − ∗− − −  = ⋅ = = =  • ith port (x1=0, x2=0) • ( ) ( )0i i iP P+ + = l ( ) ( )0i i iP P− − = l ( ) ( ) 2 21 1 0 2 2 i i ia a x= ( ) ( ) 2 21 1 0 2 2 i i ib b x= ( ) ( ) 21 0 0 2 i iP b− = • ith port (x1=0, x2=0) ( ) ( ) ( ){ } ( ) ( ) ( ) 2 22 , 01 1 1 0 Re 0 0 0 0 2 2 2 i i i i i i rms oi V P V I a a Z + ∗+ + +  = ⋅ = = =  ( ) ( ) 0 V x a x Z + = ( ) ( ) 0 V x b x Z − = 10/25 Department of Electronic Engineering, NTUT
  11. 11. ( ) ( )2 2 20 0oV Z I= − ( ) ( ) ( ) ( ) ( )2 2 2 2 2 2 2 2 2 2 1 1 0 0 0 0 0 0 2 2 o o o o o a V Z I Z I Z I Z Z = + = − + =       Two-port Network + 1oZ Port 1 1 1x = l Port 2 2 2x = l Port 1' 1 0x = ( )1 0I Port 2' 2 0x = − ( )1 0V ( )2 0I + − ( )2 2V l 2oZ ( )1 1I l ( )2 2I l ( )1 1V l + − ( )2 2a x ( )2 2b x ( )1 1a x ( )1 1b x + − ( )2 0V + − 1E 1 1oZ Z= 2 2oZ Z= • x2=0 ( ) ( )1 1 1 10 0oV E Z I= − ( ) ( ) ( ) 1 1 1 1 1 1 1 1 0 0 0 2 2 o o o E a V Z I Z Z = + =   ( ) 2 2 1 1 1 0 4 o E a Z =• x1=0 Vpp matched • E1 (available power) x1=0 ( Z1=Zo1 ) ( ) ( ) 2 2 1 1 1 1 1 0 0 2 8 AVS o E P P a Z + = = = ( ) ( ) 2 2 1 1 1 1 1 0 2 2 a a= l matched 11/25 Department of Electronic Engineering, NTUT
  12. 12. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 21 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 01 1 0 0 0 0 0 0 0 2 8 8 o o o o o o o V Z I V Z I a V Z I V Z V I Z I Z Z ∗ ∗ ∗ + +        = = + + +   ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 22 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 2 8 o o o o b V Z I V Z I V Z I Z ∗ ∗ = − − +   ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ){ } 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 Re 0 0 2 2 4 2 P P P a b I V I V I V+ − ∗ ∗ ∗  = − = − = + =  • Z1 Zo1 • port 1' ( port 1 ) ( ) ( ) 2 1 1 1 0 0 2 AVSb P P= − ( ) ( ) 2 1 1 1 1 1 2 AVSb P P= −l l• port 1 ( port 1') ( ) ( ) ( ) 2 1 1 1 1 1 0 0 2 AVSP P P b= = −l • ZT1=Zo1 0 ZT1≠Zo1 port 1 ( ) ( ) ( ) ( ) 2 2 2 2 1 1 1 1 11 2 1 1 0 AVS AVS a b P P S Pa = − = = l l l l ( ) ( ) ( )2 1 1 1 110 1AVSP P P S= = −lor 12/25 Department of Electronic Engineering, NTUT
  13. 13. (Power Waves) (I) • • (Z0) Rs s sV E Z I= − LZ + − sE sZ V I + − source impedance load impedance Department of Electronic Engineering, NTUT L s L s Z Z Z Z ∗ − Γ = + • ( )* L sZ Z= Γ = 0 slide 46 13/25
  14. 14. (Power Waves) (II) ( ) 1 2 p s s a V Z I R = + ( )1 2 p s s b V Z I R ∗ = − LZ + − sE sZ pa pb V I + − s p s L s p s L s s V Zb V Z I Z ZI Va V Z I Z ZZ I ∗ ∗ ∗−− − Γ = = = = + ++ p pa bΓ = • (Normalized power waves) 0pb =L sZ Z∗ = • (Available power) ( ) 1 2 p s s a V Z I R = + s sV E Z I= − ( ) 1 2 2 s p s s s s s E a E Z I Z I R R = − + = 2 2 4 s p s E a R = 2 2 2 , 1 2 8 s AVS p p rms s E P a a R = = = • ( ) { } { } 2 21 1 Re Re 2 2 s L L L s L E P I Z Z Z Z = = + 2 ,max 1 8 s L AVS s E P P R = = 14/25 Department of Electronic Engineering, NTUT
  15. 15. ( )( ) ( )( ) { } 2 2 *1 1 1 1 1 Re 2 2 8 8 2 L p p s s s s s s P a b V Z I V Z I V Z I V Z I V I R R ∗∗ ∗ ∗ = − = + + − − − = 2 2 21 1 1 2 2 2 L p p AVS pP a b P b= − = − 21 2 p AVS Lb P P= − = ( – ) • = ( – ) 15/25 Department of Electronic Engineering, NTUT
  16. 16. − (Traveling Waves) 0 0 s s s Z Z Z Z − Γ = + 0 0 L L L Z Z Z Z − Γ = + 1 11 1 12 2b S a S a= + 2 21 1 22 2b S a S a= + Transistor [S] 2a 2b 1a 1b Port 1 Port 2 + − sE sZ outΓ LZ inΓ sΓ LΓ • [S] Z0 sΓ LΓ ? + − sE sZ sΓ LZ LΓ Transistor [S] 1b 1a 2a 2b 16/25 Department of Electronic Engineering, NTUT
  17. 17. 1 1 in b a Γ = 2 2La b= Γ 2 21 1 22 2Lb S a S b= + Γ 21 1 2 221 L S a b S = − Γ • inΓ [ ]SLΓ 1 12 21 11 1 221 L in L b S S S a S Γ Γ = = + − Γ 12 21 1 11 1 12 2 11 1 1 221 L L L S S b S a S b S a a S Γ = + Γ = + − Γ a1 b1 1 11 1 12 2b S a S a= + a1 b1 = a2 a2 = b2 Transistor [S] 2a 2b 1a 1b + − sE sZ outΓ LZ inΓ sΓ LΓ 1 11 1 12 2b S a S a= + 2 21 1 22 2b S a S a= + inΓ 17/25 Department of Electronic Engineering, NTUT
  18. 18. 2 2 0s out E b a = Γ = 1 1sa b= Γ 1 11 1 12 2sb S b S a= Γ + 12 2 1 111 s S a b S = − Γ 12 21 2 21 1 22 2 2 22 2 111 s s s S S b S b S a a S a S Γ = Γ + = + − Γ 12 212 22 2 110 1 s s out sE S Sb S a S= Γ Γ = = + − Γ • outΓ [ ]SsΓ Transistor [S] 2a 2b 1a 1b + − sE sZ outΓ LZ inΓ sΓ LΓ 1 11 1 12 2b S a S a= + 2 21 1 22 2b S a S a= + outΓ outΓ inΓ 2 21 1 22 2b S a S a= +and 18/25 Department of Electronic Engineering, NTUT
  19. 19. + − sE sZ sΓ 1a 1b • inΓ + − 1V 1I • 1 1s sa a b= + Γ inΓ outΓ Pin 1 1inb a= Γ 1 1 1s s s s ina a b a a= + Γ = + Γ Γ 1 1 s s in a a = − Γ Γ ( ) 2 2 2 2 2 2 1 1 1 2 11 1 1 1 1 2 2 2 2 1 in in in s s in P a b a a − Γ = − = − Γ = − Γ Γ • 2 2 2 2 2 2 2 22 2 1 11 1 1 1 2 2 2 11 1 in s s s AVS in s s s ss s P P a a a∗ ∗ Γ =Γ − Γ − Γ = = = = − Γ− Γ − Γ ( )( )2 22 2 2 2 1 111 2 1 1 s inin in s AVS AVS s s in s in P a P P M − Γ − Γ− Γ = = = − Γ Γ − Γ Γ • Ms (source mismatch factor) (mismatch loss) inΓ s o s o so E Z a Z ZZ = + 19/25 Department of Electronic Engineering, NTUT
  20. 20. LZ LΓ outΓ + − thE outZ 2a 2b + − LV LI LZ LΓ outΓ ( )2 2 2 2 2 2 2 1 1 1 1 2 2 2 L LP b a b= − = − Γ • ZL 2 2 2 11 2 1 L L th out L P b − Γ = − Γ Γ • ( source) 2 2 1 1 2 1L out AVN L th out P P b∗ Γ =Γ = = − Γ ( )( )2 2 2 1 1 1 L out L AVN AVN L out L P P P M − Γ − Γ = = − Γ Γ • ML (load mismatch factor) (mismatch loss) ( source) outΓ 2 2La b= Γ 20/25 Department of Electronic Engineering, NTUT
  21. 21. Transistor [S]+ − sE sZ LZ PAVNPAVS PLPin Ms interface interface ML • (power gain) L p in P G P = • (transducer power gain) L T p s AVS P G G M P = = • (available power gain) AVN T A AVS L P G G P M = = p TG G> A TG G> • p T AG G G= = 21/25 Department of Electronic Engineering, NTUT
  22. 22. Gp (Operating Power Gain) ( ) ( ) 2 2 2 2 2 1 1 1 2 1 1 2 L L p in in b P G P a − Γ = = − Γ 21 1 2 221 L S a b S = − Γ 2 2 212 2 22 11 1 1 L p in L G S S − Γ = − Γ − Γ • The Operating Power Gain Gp where Transistor [S]+ − sE sZ LZ PAVNPAVS PLPin Ms interface interface ML slide 17 22/25 Department of Electronic Engineering, NTUT
  23. 23. GT (Transducer Power Gain) • The Transducer Power Gain GT in inL L T p p s AVS in AVS AVS P PP P G G G M P P P P = = = = 2 2 2 2 2 2 21 212 2 2 2 22 11 1 1 1 1 1 1 1 1 s L s L T s in L s out L G S S S S − Γ − Γ − Γ − Γ = = − Γ Γ − Γ − Γ − Γ Γ ( )( )2 2 2 1 1 1 s in s s in M − Γ − Γ = − Γ Γ where Transistor [S]+ − sE sZ LZ PAVNPAVS PLPin Ms interface interface ML slide 19 23/25 Department of Electronic Engineering, NTUT
  24. 24. GA (Available Power Gain) • The Available Power Gain GA AVN AVN AVNL T A T AVS AVS L L L P P PP G G G P P P P M = = = = 2 2 212 2 11 1 1 1 1 s A s out G S S − Γ = − Γ − Γ Transistor [S]+ − sE sZ LZ PAVNPAVS PLPin Ms interface interface ML ( )( )2 2 2 1 1 1 L out L out L M − Γ − Γ = − Γ Γ where slide 20 24/25 Department of Electronic Engineering, NTUT
  25. 25. • (1) ( ) (2) (power waves, [Sp]) (3) (traveling waves, [S]) { }Re 2L L LP V I∗ = • ( ) 2 2 2 , 1 2 8 s AVS p p rms s E P a a R = = = 2 2 21 1 1 2 2 2 L p p AVS pP a b P b= − = − • L p inP G P= L T AVSP G P= • (defined with traveling waves, circuitries are separately measured in a Zo system) : 25/25 Department of Electronic Engineering, NTUT

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