rfic-lecture7-0
合集下载
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
is is
2 2
Ys
ig
2
C gs
g m V gs
id
2
Ys
Ys = Gs + jBs
z
For zero mean random variables:
2 2
Γs − Γopt 4 Rn F = Fmin + Z 0 (1 − Γ 2 ) 1 + Γ s opt z When Γs= Γopt, F=Fmin
RF transceiver -LNA
z
Gain of LNA
2005-6
Institute of Microelectronics
z
RF transceiver -LNA Gain circle of LNA
2005-6
Institute of Microelectronics
Common Source MOS Transistor
+
vgs
gmvgs
Rds
g 1 1 + m Ls ≈ sL g + sLs + + ω T Ls sC gs C gs sC gs
f0 = 1 2π C gs ( Lg + Ls )
-
– Center frequency
Ls
– Input impedance at center frequencyR – Output current to source voltage
ωT 2ω 0 Rs
(Input matching)
Institute of Microelectronics
Noise figure optimization
The correlation between the input referred noise voltage and current ensures the existence of an optimal source impedance such that minimum noise figure can be achieved, unfortunately, this is not for power matching Under the condition of power matching and limited power consumption, a minimum noise figure is reached with a device of width Wopt-P gm γ ω Fmin − P ≈ 1 + 2.4 , α= α ωT gd 0
γ ω0 ⎡ F = 1 + ( ) ⎢2 c α ωT ⎣
QL = ( Lg + Ls )ω 0 Rs
⎤ 1 p + 2p+ (1 + p ) + pQL ⎥ QL ⎦
δα 2 p= 5γ
Fopt
2005-6
QLopt = 1 + 1/ p
2γ ω 0 = 1+ ( ) p ( c + p + 1+ p )
2005-6
Institute of Microelectronics
Practical issues
z More
noise contributors
– Cascode transistor – Limited Q of spiral inductors – Poly gate resistance Rg =
RsqW 12n 2 L
– Substrate loss at input pad
2005-6
Institute of Microelectronics
is
2
Ys
is
2
Ys
ig
2
C gs
g m V gs
id
2
Ys = Gs + jBs
z
For zero mean random variables:
* * VAR[iog + iod ] = VAR[iog ] + VAR[iod ] + E[iog iod ] + E[iog iod ]
Rn F = Fmin + Ys − Yopt Gs
α ωT
Institute of Microelectronics
RF transceiver -LNA
z z
NF circle of LNA At given gain, you should rotate around the gain circle and choose the reflection coefficient as close as Γopt
2005-6
Institute of Microelectronics
Common Source: Minimum Noise Figure
Gsopt = αωC gs
δ 5γ
(1 − c )
δ 5γ
2
NFmin = 1 + 2
δγ
5
(1 − c )
2
ω ωT
Bsopt = −ωC gs (1 + α
γ αδ ⎛ ω ⎜ NF = 1 + + α 5 ⎜ ⎝ ωT
⎞ ⎟ ⎟ > 5dB ⎠
2
(γ=2, δ=4, α=0.85)
2005-6
Institute of Microelectronics
Inductive source degeneration LNA schematic
z
z
Cascode amplifier with resonance at both the input and output Inductive source degeneration provides the input matching
δ 5γ
NFmin = 1 + 2
(1 − c )
ω ωT
Bsopt = −ωC gs (1 + α
c)
= 1 + 2.32
ω ωT
(γ=2, δ=4)
Yin = g m + jωC gs
z z
Simultaneous noise and power match is impossible For power match (Gs=gm, Bs=-ωCgs):
2005-6 Institute of Microelectronics
Device width optimization with Matlab
gamma=2.7; delta=1.35; Leff=0.24E-6; ueff=0.0300978; vsat=103237.4; esat=2*vsat/ueff; c=0.4j; Vdd=2.5; Cox=6.054E-3; Rs=50; pi=3.14; Vod=0.1:0.001:0.8; Id=0.002; PD=0.005; f0=2.44E9; W0=2*pi*f0; lo=Vod./(Leff*esat); a=(1+lo/2)./((1+lo).^2); P0=3*Vdd*vsat*esat/(2*W0*Rs); QL=P0*(lo.^2)./((1+lo)*PD); W=1./(W0*Rs*2/3*QL*Cox*Leff); WT=3*vsat*a.*lo/Leff; ft=WT/(2*3.14); X=1+2*sqrt(delta*a.^2/(5*gamma)).*QL*abs(c)+delta*a.^2.*(1+QL.^2)/(5*gamma); F=1+gamma*W0*X./(a.*QL.*WT); NF=10.*log10(F); WLR=W./Leff; plot(WLR,NF,'b');
I I V gs 1 = Gm = d = d = gm Vin V gs Vin ωC gs ( Rs + ω T Ls )
in
=
gm Ls ≈ ω T Ls C gs
transconductance
ωT ω 0 Rs (1 +
ω T Ls
Rs
)
(at center frequency)
=
2005-6
RF transceiver -LNA
z
Stability of LNA
Γ <1
2005-6
Institute of Microelectronics
z
RF transceiver -LNA Input and output matching of LNA (S11, S22)
2005-6
Institute of Microelectronics
c)
= 1 + 2.32
ω ωT
(γ=2, δ=4)
Yin = jωC gs
z z
Simultaneous noise and power match is impossible For power match (Gs=0, Bs=-ωCgs), NF → ∞
2005-6
Institute of Microelectronics
Input
VDD Ld
Cd Output
Bias
M2
M1 Lg Ls
2005-6
Institute of Microelectronics
Example: Inductive source degeneration
– Input impedance
Z in = sL g + sLs +
Lg
Rs
Hale Waihona Puke CgsCommon Gate MOS Transistor
NF = 1 +
2 αδω 2C gs
5 g m Gs
+
γ αg mGs
2
[Gs2
+ ( Bs + ωC gs ) ] + 2 c
2
δγ ωC gs
5 g m Gs
δγ
5
( Bs + ωC gs )
2
Gsopt = αωC gs
δ 5γ
(1 − c )
z
2
Fmin is minimum noise figure, Rn is equivalent noise resistor, Yopt=Gopt+jBopt is the optimal source admittance
2005-6 Institute of Microelectronics
Common Source MOS Transistor
RF transceiver -LNA
z
Inductor source degeneration LNA
2005-6
Institute of Microelectronics
RF transceiver -LNA
z
Inductor source degeneration LNA
2005-6
Institute of Microelectronics
2 2
Ys
ig
2
C gs
g m V gs
id
2
Ys
Ys = Gs + jBs
z
For zero mean random variables:
2 2
Γs − Γopt 4 Rn F = Fmin + Z 0 (1 − Γ 2 ) 1 + Γ s opt z When Γs= Γopt, F=Fmin
RF transceiver -LNA
z
Gain of LNA
2005-6
Institute of Microelectronics
z
RF transceiver -LNA Gain circle of LNA
2005-6
Institute of Microelectronics
Common Source MOS Transistor
+
vgs
gmvgs
Rds
g 1 1 + m Ls ≈ sL g + sLs + + ω T Ls sC gs C gs sC gs
f0 = 1 2π C gs ( Lg + Ls )
-
– Center frequency
Ls
– Input impedance at center frequencyR – Output current to source voltage
ωT 2ω 0 Rs
(Input matching)
Institute of Microelectronics
Noise figure optimization
The correlation between the input referred noise voltage and current ensures the existence of an optimal source impedance such that minimum noise figure can be achieved, unfortunately, this is not for power matching Under the condition of power matching and limited power consumption, a minimum noise figure is reached with a device of width Wopt-P gm γ ω Fmin − P ≈ 1 + 2.4 , α= α ωT gd 0
γ ω0 ⎡ F = 1 + ( ) ⎢2 c α ωT ⎣
QL = ( Lg + Ls )ω 0 Rs
⎤ 1 p + 2p+ (1 + p ) + pQL ⎥ QL ⎦
δα 2 p= 5γ
Fopt
2005-6
QLopt = 1 + 1/ p
2γ ω 0 = 1+ ( ) p ( c + p + 1+ p )
2005-6
Institute of Microelectronics
Practical issues
z More
noise contributors
– Cascode transistor – Limited Q of spiral inductors – Poly gate resistance Rg =
RsqW 12n 2 L
– Substrate loss at input pad
2005-6
Institute of Microelectronics
is
2
Ys
is
2
Ys
ig
2
C gs
g m V gs
id
2
Ys = Gs + jBs
z
For zero mean random variables:
* * VAR[iog + iod ] = VAR[iog ] + VAR[iod ] + E[iog iod ] + E[iog iod ]
Rn F = Fmin + Ys − Yopt Gs
α ωT
Institute of Microelectronics
RF transceiver -LNA
z z
NF circle of LNA At given gain, you should rotate around the gain circle and choose the reflection coefficient as close as Γopt
2005-6
Institute of Microelectronics
Common Source: Minimum Noise Figure
Gsopt = αωC gs
δ 5γ
(1 − c )
δ 5γ
2
NFmin = 1 + 2
δγ
5
(1 − c )
2
ω ωT
Bsopt = −ωC gs (1 + α
γ αδ ⎛ ω ⎜ NF = 1 + + α 5 ⎜ ⎝ ωT
⎞ ⎟ ⎟ > 5dB ⎠
2
(γ=2, δ=4, α=0.85)
2005-6
Institute of Microelectronics
Inductive source degeneration LNA schematic
z
z
Cascode amplifier with resonance at both the input and output Inductive source degeneration provides the input matching
δ 5γ
NFmin = 1 + 2
(1 − c )
ω ωT
Bsopt = −ωC gs (1 + α
c)
= 1 + 2.32
ω ωT
(γ=2, δ=4)
Yin = g m + jωC gs
z z
Simultaneous noise and power match is impossible For power match (Gs=gm, Bs=-ωCgs):
2005-6 Institute of Microelectronics
Device width optimization with Matlab
gamma=2.7; delta=1.35; Leff=0.24E-6; ueff=0.0300978; vsat=103237.4; esat=2*vsat/ueff; c=0.4j; Vdd=2.5; Cox=6.054E-3; Rs=50; pi=3.14; Vod=0.1:0.001:0.8; Id=0.002; PD=0.005; f0=2.44E9; W0=2*pi*f0; lo=Vod./(Leff*esat); a=(1+lo/2)./((1+lo).^2); P0=3*Vdd*vsat*esat/(2*W0*Rs); QL=P0*(lo.^2)./((1+lo)*PD); W=1./(W0*Rs*2/3*QL*Cox*Leff); WT=3*vsat*a.*lo/Leff; ft=WT/(2*3.14); X=1+2*sqrt(delta*a.^2/(5*gamma)).*QL*abs(c)+delta*a.^2.*(1+QL.^2)/(5*gamma); F=1+gamma*W0*X./(a.*QL.*WT); NF=10.*log10(F); WLR=W./Leff; plot(WLR,NF,'b');
I I V gs 1 = Gm = d = d = gm Vin V gs Vin ωC gs ( Rs + ω T Ls )
in
=
gm Ls ≈ ω T Ls C gs
transconductance
ωT ω 0 Rs (1 +
ω T Ls
Rs
)
(at center frequency)
=
2005-6
RF transceiver -LNA
z
Stability of LNA
Γ <1
2005-6
Institute of Microelectronics
z
RF transceiver -LNA Input and output matching of LNA (S11, S22)
2005-6
Institute of Microelectronics
c)
= 1 + 2.32
ω ωT
(γ=2, δ=4)
Yin = jωC gs
z z
Simultaneous noise and power match is impossible For power match (Gs=0, Bs=-ωCgs), NF → ∞
2005-6
Institute of Microelectronics
Input
VDD Ld
Cd Output
Bias
M2
M1 Lg Ls
2005-6
Institute of Microelectronics
Example: Inductive source degeneration
– Input impedance
Z in = sL g + sLs +
Lg
Rs
Hale Waihona Puke CgsCommon Gate MOS Transistor
NF = 1 +
2 αδω 2C gs
5 g m Gs
+
γ αg mGs
2
[Gs2
+ ( Bs + ωC gs ) ] + 2 c
2
δγ ωC gs
5 g m Gs
δγ
5
( Bs + ωC gs )
2
Gsopt = αωC gs
δ 5γ
(1 − c )
z
2
Fmin is minimum noise figure, Rn is equivalent noise resistor, Yopt=Gopt+jBopt is the optimal source admittance
2005-6 Institute of Microelectronics
Common Source MOS Transistor
RF transceiver -LNA
z
Inductor source degeneration LNA
2005-6
Institute of Microelectronics
RF transceiver -LNA
z
Inductor source degeneration LNA
2005-6
Institute of Microelectronics