低噪声放大器匹配技术

LNA
5 LNA C3 50Ω MAX2656
(
55)
50 Ω
7 ΓL 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
I1 Vn
(
18)
Vn 1b
In V n1 V n2 Ys
(
4)
I2 NOISELESS TWO-PORT NETWORK
( I2
sc )
V1
In
V2
(I 2 s )
F
F=
3. Vn In
Vn
I 2SC I 2S
(
19)
I2 NOISELESS TWO-PORT NETWORK
( 1b Z
) Vn1 3
) R BIAS IP3
1.9dB )
MAX2655/ (RBIAS)
Rollet
(K) )
1 (K
5 MAX2656 LNA 2dB ( 1960MHz PCS 50Ω ) MAX2656 (RBIAS) 715Ω 1960MHz (F min = 1.79dB) Γopt
Γopt = 0.130 / 124.48°
Γs
2
Γopt 2 Γs Γopt N = + − (1 + N) (1 + N) (1 + N) 2 Γs Γopt Γopt
2
Γs −
( 46)
(1 + N)
+ =
Γopt
2
(1 + N)2 (1 + N)2
1 (1 + N)2
−
Γopt
2
Γopt N = − (1 + N) (1 + N)
2
Γs −
( 54)
LNA (ΓL) LNA
S ΓS ΓL = S22 + 21 s 12 *, 1 − S11Γs
( 53)
RN = 43.2336 Ω 1960MHz / MAX2656 LNA ) S
( • • • •
ΓS ( ΓL)
S11 = 0.588/-118.67° S21 = 4.12/149.05° S12 = 0.03/-167.86° S22 = 0.275/-66.353° (K = 2.684) 5
13
14
Vn
In:
( 15)
Is I n + VnYs = 0
(
)
(
21)
20
I 2sc = I 2s + In + VnYs
Z Vn = Vn1 − 11 In2 Z 21
(
)
2
(
22)
20
V In = − n2 Z 21
( 16)
19
F = 1+
(I n + VnYs)
( 12)
Isc = -Is + In + VnYs
I 2sc = − Is + I n + VnYs
20
Isc
1
2
11
12
( 13)
Vn 1 = Vn − Z11In Vn2 = − Z 21In
(
)
2
= I 2s + I n + VnYs − 2 Is I n + VnYs
(
(
)
2
(
பைடு நூலகம்
)
20)
(
14)
LNA MAX2656— — LNA ( 5)
(IP3) PCS (14.5dB
VCC = 3V 4 1 Cb
) 3dB 3.5dB
2dB
Smith ( 6)
( 2.5dB
BIAS 0V : HIGH GAIN VCC : LOW GAIN
RBIAS
MAX2656
L1 = 1.2nH RF C1 = 1.8nF C2 = 1.5pF 2 5 3 6
ABCD 9 10
3 I n1
( 9)
Vn I n2
In
2
V1 = AV2 + B( − I2 ) + Vn I1 = CV2 + D( − I2 ) + In
I Vn = − n2 Y21 Y In = In1 − 11 In2 Y21
(
17)
(
10)
9 Vn
10 3 In
( 52)
ys
yopt ( LNA 45) S
51
52 LNA
Smith
LNA Gopt
F = Fmin + 4 rn
Γs − Γopt 1 + Γopt
2
2 2
(1 − Γ )
s
(
49)
(SNR) 49)
(
)
F( Smith
15
LNA ( ) LNA MAX2656 LNA ( )
0.8dB ( MAX2656
G s = Re [Y s] Rn
V 2n = 4 kT0 RnB
( 30)
36
Fmin = F Ys =Yopt = 1 +
Fmin
Gu R + n G opt + G c G opt G opt
(
Gu
I 2nu = 4 kT0 Gu B
( 31)
(
)
2
41)
39
Gu /Gopt
Fmin =
41
29
3 Vn2
Vn
In
Ys Is INPUT PORT In
V2
V1 = Z11( I1 − In ) + Z12 I2 + Vn = Z11I1 + Z12 I2 + (Vn − Z11In )
( 11) 4.
V2 = Z 21( I1 − In ) + Z 22 I 2 = Z 21I1 + Z 22 I 2 − Z 21In )
I 2s
2
(
23)
13
Vn Vn (Inc)
In — Vn (Inu)
(
In 34
Ys F
Bs = − Bc
( 35)
I n = I nu + I nc
24)
34
FBs = − Bc = 1 + Gu Rn + ( Gs + Gc)2 Gs Gs
( 36)
Yc
I nc = YcVn
Inc
(
Vn
25)
10kΩ
2dB ΓS = 0.3/150° 50Ω ΓS arc ΓSA ( L1 arc BO ( C1
) )
RF OUTPUT
C3 = 3.6pF
5. MAX2656 LNA
arc ΓSA 0.3 Z = L1 = 15/ω = 15/(2πf) = 15/ 50 x 0.3 = 15Ω 9 1.2nH [2π x (1.96 x 10 )] = 1.218nH arc BO 0.9 1/Y = Z = C 2 = 1/(55.55 x ω ) = 1/ 50 /0.9 = 55.55 Ω (55.55 x 2πf) = 1/[55.55 x 2π x (1.96 x 109)] = 1.46pF 1.5pF
( 34)
(
2 Rn 2 G + G c ) + Bs − Bopt ( s Gs
(
)
(
43)
14
39
Gu
Rn G − G opt s Gs
43
F
F − Fmin 1 + Γopt 4 rn
( 44)
2
=
Γs − Γopt
s
2
F = Fmin +
(
) + (B
2
s
(
8)
1b
2
(
2)
I1 NOISELESS TWO-PORT NETWORK I2
1
2
Vn1
Vn2 ( 3 4)
( 3)
(I1 = I2 = 0)
V1
In1
In2
V2
Vn1 = V1 I1 = I 2 = 0 Vn2 = V2 I1 = I 2 = 0
(
4)
2. In1 In2
Vn1
Vn2
12
(
3)
16
6. Smith
MAX2656 PCS LNA
(
17
)
2dB
13dB Constant Gain Circle ΓL = 0.236 / 70.5°
O
13.6dB Desired Constant Gain Circle
7. MAX2656 PCS LNA
2dB
18
C1 ΓS
S ΓS ΓL = S22 + 21 s 12 * = 0.236 / 70.5° 1 − S11Γs
2 − Bopt
)
(1 − Γ )
2
N=
Γs − Γopt
s
2
44 Ys
F
Yopt = Gopt + jBopt F
Fmin
N=
(1 − Γ )
2 2 2
with N =
2
F − Fmin 1 + Γopt 4 rn
2
Γs − 2 Γs Γopt + Γopt
2 s
2 R rn F = Fmin + n y s − y opt = Fmin + Ys − Yopt Gs Re al( y s )
(
42)
F = 1+ = 1+
4 kT0 G u B + G s + jBs + G c + jBc 4 kT0 R n B 4 kT0 Gs B
2
42
=
34
Gu R n + ( Gs + Gc)2 + (Bs + Bc)2 Gs Gs
[
]
F = Fmin − 2 R n G c + G opt +
arc OΓL (
C3 Z= arc O Γ L 0.45 50 x 0.45 = 22.5 Ω C 3 = 1/(22.5 x ω ) = 1 / (22.5 x 2 π f ) = 1/ [22.5 x 2 π x (1.96 x 10 9 ) ] = 3.6pF 3.608pF )
19
(
5)
(
6)
— ( Vn1 V n1 V n2 1b
V1 = Z11I1 + Z12 I 2 + Vn1 V2 = Z 21I1 + Z 22 I 2 + Vn2
( 1)
2 1a ) 1b) Z
In1
In2 7 8
( 7)
Vn2 1 2
(
I n1 = I1 V1 = V2 = 0 I n2 = I2 V1 = V2 = 0
34
Gs
dFBs = −Bc =0 dGs
Yc 24
I n = I nu + YcVn
(
25
(
37)
26)
26
Vn*
I nVn* = Yc V 2n Yc =
InuVn* = 0
V *n In V 2n
( 27)
2 G s (G s + G c ) − (G s + G c ) Gu dFBs = −Bc =− 2 + Rn dGs Gs G 2s
I1
I2 NOISY TWO-PORT NETWORK (a)
I1
Vn1 NOISELESS TWO-PORT NETWORK (b)
Vn2
I2
(LNA)
RF RF IF
V1
V2
V1
V2
1. (b)
(a) Vn1 Vn2
2 I n1 I n2 5 6
I1 = Y11V 1+ Y 12V 2 + In1 I2 = Y21V1 + Y22V2 + I n2
yopt
y opt = Yopt Y0 = G opt + jBopt Y0 = g opt + jb opt
( 47)
(1 + N)
N 2 + N 1 − Γ 2 opt
( 50)
LNA
Γopt
Smith
F − Fmin 1 + Γopt 4 rn
(
ys
yopt
ys = 1 − Γs 1 − ys ← → Γs = 1 + Γs 1 + ys
ON =
(1 + N)
with N =
2
51)
RN = y opt = 1 − Γopt 1 + Γopt ← → Γopt = 1 − y opt 1 + y opt
( 48)
1 N 2 + N 1 − Γ 2 opt (1 + N)
30
31
28
Yc = Gc + jBc Ys = Gs + jBs
( 32)
G2c Rn 1 + R n G opt − G 2opt + 2G opt G c + G 2 c = +G G opt opt
(
)
(
33)
1 + 2 R n G opt + Gc
(
) )
Gu + Gs
2
N 1 − Γs
(
(1 − Γ ) ) = Γ − 2Γ Γ
2 s
s opt
+ Γopt
2 2
2
(
45)
2 (1 + N) Γs = N + 2Γs Γopt − Γopt 2
rn = Rn /Z0 :
Y G + jBs ys = s = s = g s + jb s Y0 Y0
ys = Ys Z0
(
(
2
)=0
38) 39)
Gs
G s = G 2c + Gu Rn
(
26
23
F
2
(I nu + (Yc + Ys )Vn ) F = 1+
I 2s I 2s = 4 kT0 GsB
(
28)
39
Gs Bs ( ) Yopt = Gopt + jBopt
Gu − jBc Rn
( 40)
35
(
29)
Yopt = G opt + jBopt = G 2c +