低噪声放大器简介
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0dB frequency
i ω out T 1 iin ωT
f
21
Small-Signal Model of MOSFET
i2 i1 V1 V2
i1
Rg Cgs V1
Cgd V’gs ri rds
i2
Cdb
V2
• • • • • •
Cgs Cgd rds Cdb Rg: Gate resistance ri: Channel charging resistance
a10
a10
15
S-Parameters
I1 I2
Z1
Vs1 V1
S
V2
Z2
Vs2
V1 I1Z1* S11 V1 I1Z1 V V1 I1Z1* S12 V2 I 2 Z 2
s 2 0
* V2 I 2 Z 2 Re(Z1 ) S21 V1 I1Z1 Re(Z 2 ) V * V2 I 2 Z 2 S22 V2 I 2 Z 2 V
Rs 4kTRs Vs Vgs gmVgs
• Effective transconductance io gm Zin Gmeff Vs Rs Zin 4kTgg
m 18
Power Gain
• Voltage input • Current output
ii g m Z in 2 G | Gmeff | * VsVs Rs Z in
• Definition
SNRin Sin Nin NF SNRout Sout N out
• As a function of device
N device G N source NF G N source
G: Power gain of the device
5
NF of Cascaded Stages
Frequency
8
Power Transfer and Impedance Matching
• Power delivered to load
Rs Vs I jXs V jXL RL
Vs Pdel RL Rs jX s RL jX L
2
• Maxim available power VsVs* Pmax PL R R , X X 0 4Rs
S S11S22 S12 S21
| S |2 L L 1
| S11 |2 | S22 |2 L | S12 S21 | 2
17
A First LNA Example
Rs Vs io
• Assume
– – – – No flicker noise ro = infinity Cgd = 0 Reasonable for appropriate bandwidth
Sin/Nin G1, N1, NF1 Gi, Ni, NFi Sout/Nout GK, NK, NFK
NF2 1 NF3 1 NFK 1 NF 1 NF1 1 ... G1 G1G2 G1G2...GK 1
• Overall NF dominated by NF1 [1] F. Friis, “Noise Figure of Radio Receivers,” Proc. IRE, Vol. 32, pp.419-422, July 1944.
• Power ratio @ output
– Device noise + input-induced noise – Input-induced noise
N device G N in NF 1 G N in 1 1 4kTg g m 2 gm 4kTRs 1 2 ( RsCgs ) 2
– Transmission coefficients – Reflection coefficients
13
S-Parameters
a1
S21
S11
b2
S22
S12
b1
b1 S11a1 S12 a2 b2 S 21a1 S22 a2
a2
14
S-Parameters
b1 S11 a1 a 20 b2 S 21 a1 a 20 b1 S12 a2 b2 S 22 a2
25
Review of First Example
• No impedance matching
– Capacitive input impedance – Output not matched
• Power transfer
– S11=(1-sRCgs)/(1+sRCgs) – S21=2Rgm/(1+sRCgs), R=Rs=RL
22
gmV’gs
T Calculation
i1 Rg Cgs V1 Cgd V’gs ri rds Cdb gmV’gs i2 i1 Rg Cgs V1 Cgd V’gs ri gmV’gs i2
s(Cgs Cgd ) s 2 riCgsCgd I1 Y11 V1 V 0 1 s(Cgs Cgd ) Rg sriCgs s 2 Rg riCgsCgd
2
g m (1 sriCgs ) sC gd s 2 riCgsCgd I2 Y21 V1 V 0 1 s(Cgs Cgd ) Rg sriCgs s 2 Rg riCgsCgd
2
23
T of NMOS and PMOS
Set:
Y11 ( j T ) Y21 ( j T )
• Power consumption
– High power for NF – High power for S21
26
Impedance Matching for LNA
• • • • Resistive termination Series-shunt feedback Common-gate connection Inductor degeneration
* o o 2
gm Rs 1 ( jC gs ) 1 jRs C gs T 1 g 2 2 1 ( Rs C gs ) R s
2 m 2
g m 1 ( jC gs )
2
2
19
Noise Figure Calculation
Low-Noise Amplifier
1
RF Receiver
Antenna BPF1 LNA BPF2 Mixer BPF3 IF Amp
Demodulator RF front end LO
2
Low-Noise Amplifier
• First gain stage in receiver
– Amplify weak signal
g
Rs g m
2 (1 2 Rs2Cgs )
g
Rs g m
gRsቤተ መጻሕፍቲ ባይዱg m
2
( g m / Cgs ) 2
gm T C gs
20
Unity Current Gain Frequency
Device
iin
iout
iout Ai iin Ai
T
Ai fT
• 0.25um CMOS Process*
1
Solve for T
gm T gm Cgs Cgd
[2] Tajinder Manku, “Microwave CMOS - Device Physics and Design,” IEEE J. Solid-State Circuits, vol. 34, pp. 277 - 285, March 1999.
6
Simple Model of Noise in MOSFET
Vg Id
k • Flicker noise V ( f ) WLC f ox – Dominant at low frequency
2 g
• Thermal noise Id2 ( f ) 4kTg gm
– g: empirical constant 2/3 for long channel much larger for short channel – PMOS has less thermal noise
V IZs* b 2 Rs
b Z L Z s* a ZL Zs
11
Reflection Coefficient
No reflection Maximum power transfer
12
S-Parameters
• Parameters for two-port system analysis • Suitable for distributive elements • Inputs and outputs expressed in powers
24
Noise Performance
g 2 NF 1 g Rs gm 2 Rs gm T
• Low frequency
– Rsgm >> g ~ 1 – gm >> 1/50 @ Rs = 50 ohm – Power consuming
• CMOS technology
– gm/ID lower than other tech – T lower than other tech
3
LNA Design Consideration
• • • • • • • Noise performance Power transfer Impedance matching Power consumption Bandwidth Stability Linearity
4
Noise Figure
• S11 – input reflection coefficient with the output matched • S21 – forward transmission gain or loss • S12 – reverse transmission or isolation • S22 – output reflection coefficient with the input matched
s 2 0
Re(Z 2 ) Re(Z1 ) V
s 1 0
s 1 0
16
Stability Condition
• Necessary condition 1 | S22 |2 | S11 |2 | S |2 K 1 2 | S12 S21 | where • Stable iff where
s L s L
• Impedance matching
– Load and source impedances conjugate pair – Real part matched to 50 ohm
9
Available Power
Equal power on load and source resistors
Vi
• Input-inferred noise
Vi 2 ( f ) 4kT
g
gm
k WLC ox f
7
Noise Approximation
Noise spectral density
1/f noise
Thermal noise dominant Thermal noise
Band of interest
• Significant impact on noise performance
– Dominate input-referred noise of front end
NFfrontend NFLNA NFsubsequent 1 GLNA
• Impedance matching
– Efficient power transfer – Better noise performance – Stable circuit
10
Reflection Coefficient
Rs Vs I
jXs
V
jXL
RL
V IZL
V IZs a 2 Rs
* I I * (Z L Z L ) Pdel 2
VsVs* (V IZs )(V IZs )* Pmax aa* 4 Rs 4Rs (V IZs* )(V * I *Z s ) Pref Pmax Pdel bb* 4Rs
i ω out T 1 iin ωT
f
21
Small-Signal Model of MOSFET
i2 i1 V1 V2
i1
Rg Cgs V1
Cgd V’gs ri rds
i2
Cdb
V2
• • • • • •
Cgs Cgd rds Cdb Rg: Gate resistance ri: Channel charging resistance
a10
a10
15
S-Parameters
I1 I2
Z1
Vs1 V1
S
V2
Z2
Vs2
V1 I1Z1* S11 V1 I1Z1 V V1 I1Z1* S12 V2 I 2 Z 2
s 2 0
* V2 I 2 Z 2 Re(Z1 ) S21 V1 I1Z1 Re(Z 2 ) V * V2 I 2 Z 2 S22 V2 I 2 Z 2 V
Rs 4kTRs Vs Vgs gmVgs
• Effective transconductance io gm Zin Gmeff Vs Rs Zin 4kTgg
m 18
Power Gain
• Voltage input • Current output
ii g m Z in 2 G | Gmeff | * VsVs Rs Z in
• Definition
SNRin Sin Nin NF SNRout Sout N out
• As a function of device
N device G N source NF G N source
G: Power gain of the device
5
NF of Cascaded Stages
Frequency
8
Power Transfer and Impedance Matching
• Power delivered to load
Rs Vs I jXs V jXL RL
Vs Pdel RL Rs jX s RL jX L
2
• Maxim available power VsVs* Pmax PL R R , X X 0 4Rs
S S11S22 S12 S21
| S |2 L L 1
| S11 |2 | S22 |2 L | S12 S21 | 2
17
A First LNA Example
Rs Vs io
• Assume
– – – – No flicker noise ro = infinity Cgd = 0 Reasonable for appropriate bandwidth
Sin/Nin G1, N1, NF1 Gi, Ni, NFi Sout/Nout GK, NK, NFK
NF2 1 NF3 1 NFK 1 NF 1 NF1 1 ... G1 G1G2 G1G2...GK 1
• Overall NF dominated by NF1 [1] F. Friis, “Noise Figure of Radio Receivers,” Proc. IRE, Vol. 32, pp.419-422, July 1944.
• Power ratio @ output
– Device noise + input-induced noise – Input-induced noise
N device G N in NF 1 G N in 1 1 4kTg g m 2 gm 4kTRs 1 2 ( RsCgs ) 2
– Transmission coefficients – Reflection coefficients
13
S-Parameters
a1
S21
S11
b2
S22
S12
b1
b1 S11a1 S12 a2 b2 S 21a1 S22 a2
a2
14
S-Parameters
b1 S11 a1 a 20 b2 S 21 a1 a 20 b1 S12 a2 b2 S 22 a2
25
Review of First Example
• No impedance matching
– Capacitive input impedance – Output not matched
• Power transfer
– S11=(1-sRCgs)/(1+sRCgs) – S21=2Rgm/(1+sRCgs), R=Rs=RL
22
gmV’gs
T Calculation
i1 Rg Cgs V1 Cgd V’gs ri rds Cdb gmV’gs i2 i1 Rg Cgs V1 Cgd V’gs ri gmV’gs i2
s(Cgs Cgd ) s 2 riCgsCgd I1 Y11 V1 V 0 1 s(Cgs Cgd ) Rg sriCgs s 2 Rg riCgsCgd
2
g m (1 sriCgs ) sC gd s 2 riCgsCgd I2 Y21 V1 V 0 1 s(Cgs Cgd ) Rg sriCgs s 2 Rg riCgsCgd
2
23
T of NMOS and PMOS
Set:
Y11 ( j T ) Y21 ( j T )
• Power consumption
– High power for NF – High power for S21
26
Impedance Matching for LNA
• • • • Resistive termination Series-shunt feedback Common-gate connection Inductor degeneration
* o o 2
gm Rs 1 ( jC gs ) 1 jRs C gs T 1 g 2 2 1 ( Rs C gs ) R s
2 m 2
g m 1 ( jC gs )
2
2
19
Noise Figure Calculation
Low-Noise Amplifier
1
RF Receiver
Antenna BPF1 LNA BPF2 Mixer BPF3 IF Amp
Demodulator RF front end LO
2
Low-Noise Amplifier
• First gain stage in receiver
– Amplify weak signal
g
Rs g m
2 (1 2 Rs2Cgs )
g
Rs g m
gRsቤተ መጻሕፍቲ ባይዱg m
2
( g m / Cgs ) 2
gm T C gs
20
Unity Current Gain Frequency
Device
iin
iout
iout Ai iin Ai
T
Ai fT
• 0.25um CMOS Process*
1
Solve for T
gm T gm Cgs Cgd
[2] Tajinder Manku, “Microwave CMOS - Device Physics and Design,” IEEE J. Solid-State Circuits, vol. 34, pp. 277 - 285, March 1999.
6
Simple Model of Noise in MOSFET
Vg Id
k • Flicker noise V ( f ) WLC f ox – Dominant at low frequency
2 g
• Thermal noise Id2 ( f ) 4kTg gm
– g: empirical constant 2/3 for long channel much larger for short channel – PMOS has less thermal noise
V IZs* b 2 Rs
b Z L Z s* a ZL Zs
11
Reflection Coefficient
No reflection Maximum power transfer
12
S-Parameters
• Parameters for two-port system analysis • Suitable for distributive elements • Inputs and outputs expressed in powers
24
Noise Performance
g 2 NF 1 g Rs gm 2 Rs gm T
• Low frequency
– Rsgm >> g ~ 1 – gm >> 1/50 @ Rs = 50 ohm – Power consuming
• CMOS technology
– gm/ID lower than other tech – T lower than other tech
3
LNA Design Consideration
• • • • • • • Noise performance Power transfer Impedance matching Power consumption Bandwidth Stability Linearity
4
Noise Figure
• S11 – input reflection coefficient with the output matched • S21 – forward transmission gain or loss • S12 – reverse transmission or isolation • S22 – output reflection coefficient with the input matched
s 2 0
Re(Z 2 ) Re(Z1 ) V
s 1 0
s 1 0
16
Stability Condition
• Necessary condition 1 | S22 |2 | S11 |2 | S |2 K 1 2 | S12 S21 | where • Stable iff where
s L s L
• Impedance matching
– Load and source impedances conjugate pair – Real part matched to 50 ohm
9
Available Power
Equal power on load and source resistors
Vi
• Input-inferred noise
Vi 2 ( f ) 4kT
g
gm
k WLC ox f
7
Noise Approximation
Noise spectral density
1/f noise
Thermal noise dominant Thermal noise
Band of interest
• Significant impact on noise performance
– Dominate input-referred noise of front end
NFfrontend NFLNA NFsubsequent 1 GLNA
• Impedance matching
– Efficient power transfer – Better noise performance – Stable circuit
10
Reflection Coefficient
Rs Vs I
jXs
V
jXL
RL
V IZL
V IZs a 2 Rs
* I I * (Z L Z L ) Pdel 2
VsVs* (V IZs )(V IZs )* Pmax aa* 4 Rs 4Rs (V IZs* )(V * I *Z s ) Pref Pmax Pdel bb* 4Rs