优化噪声系数的LNA匹配设计.pdf-资料库

(LNA) RF I1 V1 1. RF IF I2 I1 Vn1 Vn2 I2 V2 V1 NOISELESS TWO-PORT NETWORK (b) V2 NOISY TWO-PORT NETWORK (a) (a) (b) Vn1 Vn2 In1 In2 2 5 6 = I Y V Y V In 1 1 12 2 11 1 + + — ( 1a) 2 In1 In2 7 8 = I Y V Y V I n 2 22 2 21 1 + + 2 ( ( ( ( 5) 6) 7) 8) Vn1 Vn2 ( 1b) Vn1 Vn2 1b 1 2 = = + + + + V Z I Z I Vn 1 1 12 2 11 1 V Z I Z I Vn 2 22 2 21 1 2 Z ( ( 1 2 Vn1 Vn2 (I1 = I2 = 0) ( 3 4) V n1 = V I 1 1 = I 2 = 0 V n2 = V I 2 1 = I 2 = 0 ( ( Vn1 Vn2 = I V V 1 2 1 = I V V 2 2 1 = 0 = 0 = I n1 = I n2 1b 2 I1 V1 In1 NOISELESS TWO-PORT NETWORK In2 I2 V2 2. In1 In2 1) 2) 3) 4) 12

( 3) ABCD 9 10 3 − V AV B I 1 2 = + ( 2 + ) Vn = − I CV D I 1 2 + ( 2 + ) In 9 10 Vn In I1 V1 3 In Vn In Vn 1b I2 V2 NOISELESS TWO-PORT NETWORK ( ( 9) 10) I n V n In2 In1 n = −  V    2 I n Y 21 = I n I n 1 −     Y 11 Y 21 I n 2 ( 4) Vn1 Vn2 Ys I2 sc) (I2 s) F = 2 I I SC 2 S 3. ( 1b Z − + I n ) = V Z I ( 11 1 1 Vn In ) 3 V n1 V n2 3 Vn In Vn Ys Is I2 V2 In NOISELESS TWO-PORT NETWORK INPUT PORT + Z I V Z I Z I 12 2 12 2 11 1 n = + + ( − V Z I 11 n ) n ( 11) 4. 2 ( ( 17) 18) ( F ( 19) Isc = V Z I ( 21 1 2 − + I n ) Z I Z I Z I 22 2 22 2 21 1 = + − ) n Z I 21 ( 1 2 11 = 1 V n 12 − V Z I 11 n n = − V n 2 Z I 21 n 13 14 Vn In: n= V V n 1 −     I n2 Z Z 11 21 = −   I n   2 V n Z 21 ( ( ( ( 12) 13) 14) 15) 16) 13 = −( + I s 2 I sc 20 20 Isc = -Is + In + VnYs 20 ) − 2 2 + I V Y n s n ) = 2 +( I 2 s + I V Y n s n ( I I V Y s s + n n ) ( ( ( ( 20) 21) 22) 23) ) 2 ( I I V Y s n s + n ) = 0 2 I sc = I 2 s +( + I V Y n s n 19 = + 1 F ( ) 2 + I V Y n s n 2 s I

Vn In In — Vn (Inu) 34 Vn (Inc) = I n I nu + I nc ( 24) Yc Inc Vn = I nc Y V c n 24 = I n I nu + Y V c n 25 ( ( 25) 26) Yc 26 Vn* InuVn *= 0 ( 27) Gs * = I V n n Y V c 2 n 26 = + 1 F 23 ( I nu + ( Y c = * V I n n 2 V n F Y Y V n ) s + 2 s c I ) 2 ( ( ( ( ( ( 28) 29) 30) Gu 31) 32) 33) + 1 kT G B 0 s 4= I 2 s Gs = Re [Ys] Rn V 2 n 4= I 2 nu 4= 29 30 31 kT R B 0 n kT G B 0 u 28 + = Y G jB c c c = Y G jB s s s + 4 = + 1 F kT G B G jB G jB 0 u s + + 4 s + + c kT G B 0 s 2 4 c kT R B n 0 = = + 1 G u G s + R n G s [ ( G G c + s ) +( 2 B B c + s ] ) 2 ( 34) Ys 34 F = − B c B s F Bs = − = + 1 Bc G u G s + ( R n G s 34 Gs + G G c s ( ( 35) 36) ) 2 ( + G G s ) ) 2 c ( ( = 0 38) 39) dF = − Bs dG s Bc = 0 ( 37) ( 2 dF = − Bs dG s Bc = − G u 2 G s + R n ( G G G s s + )− c G 2 s = G s G +2 c G R u n 39 35 Gs Bs ) ( Yopt = Gopt + jBopt Y opt = G opt + jB opt = + G 2 c G R u n − jB c ( 40) 36 F min = F = Ys Yopt = + 1 u + G G opt 3 9 G u / G o p t Fmin ( n opt R G G ) 2 + G c opt ( 41) 4 1    R G n − opt 42 = ( G 2 opt + 2 G G G opt c + ) = 2 c Fmin n R G opt   +  G G 2 c opt ( R G n ) + G c opt ( 42) + 1 2 34 ( = F F − min 2 + c n R G G ) + + ( 2 G G s c )+ G G opt − B B s opt u s ) + 2   ( 43) (   R n G s 14

opt = g opt + jb opt ( 47) LNA ( 50) Smith − 4 F F r n min + 1 Γ opt 2 = − Γ s −( 1 Γ opt Γ 2 s 2 ) = N − Γ s −( 1 Γ opt Γ 2 s 2 ) with N = − 4 F F r n min 2 + 1 Γ opt 2 Γ opt Γ Γ s opt Γ 2 s + ) 2 1 −( ) = 2 Γ s Γ s 2 − Γ Γ s opt 2 + Γ opt 2 ) Γ s 2 = N + Γ Γ −− s opt 2 −( N 1 +( 1 N 2 = Γ s N +( 1 N ) + 2 Γ s − Γ s ) + − Γ Γ 2 s opt +( 1 N Γ opt +( 1 N 2 ) = ) − Γ Γ 2 s opt +( N 1 2 Γ opt +( 1 N 2 ) −   2 N 1 +( N 1 ) 2 2 ) N Γ opt Γ opt +( 1 Γ ) = opt +( 1 N − 1  N + 2 2 2 2 Γ opt +( 1 ) N N +( 1 N Γ opt 2   ) −   = O N Γ opt +( N 1 ) with N = − F F 4 r n min 2 + 1 Γ opt = R N 1 +( N 1 )   2 N N + ( 51) − 1  2Γ opt     ( 52) 51 52 Smith LNA (SNR) ( ) Yopt = Gopt + jBopt Fmin F 2 Γ s = N − 39 Gu 43 F − G G s ) + 2 ( opt − B B s ) 2   opt ( 44) + R n G s (   F = F F min 44 Ys = F F min + R n G s − y y s opt 2 = + rn F min Re ( al y ) s − Y Y s opt 2 rn = Rn/Z0 : = y s = Y s Y 0 G jB s s + Y 0 ( 45) ys = YsZ0 = g s + jb s ( 46) yopt = y opt Y opt Y 0 G opt = jB + Y 0 ys yopt y s = − 1 + 1 Γ s Γ s ← → Γ s = − 1 + 1 y y s s = y opt − + 1 1 Γ opt Γ opt ← → Γ opt = − + 1 1 y y opt opt ( 48) ys yopt ( LNA 45) LNA Gopt S Γ s Γ opt − Γ opt 2 −( 1 = F F min + 4 rn + 1 Smith 2 ) 2 Γ s ( 49) F ( 49) 15

LNA ( ) MAX2656 ) LNA LNA ( Rollet 1 (K (K) ) LNA (ΓL) LNA Γ L =   S  + 22 S 1 21 − Γ s S 11 S 12 Γ s   *,  ( 53) ΓS ( LNA MAX2656—— LNA ( 5) ΓL) (IP3) PCS (14.5dB VCC = 3V 1 3 RBIAS L1 = 1.2nH C2 = 1.5pF Cb 4 BIAS MAX2656 2 5 RF C1 = 1.8nF 5. MAX2656 LNA 0V : HIGH GAIN VCC : LOW GAIN 10kΩ 6 C3 = 3.6pF RF OUTPUT 0.8dB ( MAX2656 IP3 ) 1.9dB RBIAS ) MAX2655/ (RBIAS) 5 MAX2656 LNA 1960MHz ) PCS MAX2656 (RBIAS) 2dB 50Ω ( 715Ω 1960MHz (Fmin = 1.79dB) Γopt Γ opt = ° 0 130 124 48 . / . ( 54) RN = 43.2336Ω 1960MHz MAX2656 LNA S ( / ) • S11 = 0.588/-118.67° • S21 = 4.12/149.05° • S12 = 0.03/-167.86° • S22 = 0.275/-66.353° (K = 2.684) 5 ) 2dB 3dB 3.5dB 2dB 50Ω ΓS = 0.3/150° arc ΓSA ( arc BO ( C1 ΓS L1 Smith ( 6) ( 2.5dB ) ) arc Γ SA 0.3 50 x 0.3 = 15Ω [2π x (1.96 x 109)] = 1.218nH Z = L1 = 15/ω = 15/(2πf) = 15/ 1.2nH arc BO 1/Y = Z = 50 /0.9 = 55.55Ω C2 = 1/(55.55 x ω) = 1/ (55.55 x 2πf) = 1/[55.55 x 2π x (1.96 x 109)] = 1.46pF 0.9 1.5pF 16

6. Smith MAX2656 PCS LNA ( ) 2dB 17

13dB Constant Gain Circle ΓL = 0.236 / 70.5° O 13.6dB Desired Constant Gain Circle 7. MAX2656 PCS LNA 2dB 18

C1 ΓS LNA 5 LNA Γ L =   S  + 22 S 1 21 − Γ s S 11 S 12 Γ s   = *  ° 0 236 70 5 . . / ( 55) C3 MAX2656 50Ω 50Ω 7 ΓL arc OΓL ( C3 arc OΓL Z = 50 x 0.45 = 22.5Ω C3 = 1/(22.5 x ω ) = 1 / (22.5 x 2πf ) = 1/ [22.5 x 2π x (1.96 x 109) ] = 3.608pF 3.6pF ) 0.45 1. Gonzalez, Guillermo; Microwave Transistor Amplifiers, Analysis & Design ; , Prentice Hall, Upper Saddle River, New Jersey 07458. 2. Bowick, Chris; RF Circuit Designs ; Howard W. Sams & Co., Inc., ITT 19

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优化噪声系数的LNA匹配设计.pdf

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