1 low-noise amplifier. 2 rf receiver bpf1bpf2lna lo mixerbpf3if amp demodulator antenna rf front end
TRANSCRIPT
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Low-Noise Amplifier
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2
RF Receiver
BPF1 BPF2LNA
LO
Mixer BPF3 IF Amp
Demodulator
Antenna
RF front end
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3
Low-Noise Amplifier• First gain stage in receiver
– Amplify weak signal
• Significant impact on noise performance– Dominate input-referred noise of front end
• Impedance matching– Efficient power transfer– Better noise performance– Stable circuit
LNA
subsequentLNAfrontend G
NFNFNF
1
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4
LNA Design Consideration
• Noise performance
• Power transfer
• Impedance matching
• Power consumption
• Bandwidth
• Stability
• Linearity
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5
Noise Figure• Definition
• As a function of device
G: Power gain of the device
outout
inin
out
in
NS
NS
SNR
SNRNF
source
sourcedevice
NG
NGNNF
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NF of Cascaded Stages
• Overall NF dominated by NF1
[1] F. Friis, “Noise Figure of Radio Receivers,” Proc. IRE, Vol. 32, pp.419-422, July 1944.
Sin/Nin
G1, N1, NF1
Gi, Ni, NFi
GK, NK, NFK
Sout/Nout
12121
3
1
21
11111
K
K
...GGG
NF...
GG
NF
G
NFNFNF
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Simple Model of Noise in MOSFET
fWLC
kfV
oxg )(2
• Flicker noise– Dominant at low frequency
• Thermal noise– : empirical constant
2/3 for long channel
much larger for short channel– PMOS has less thermal noise
• Input-inferred noise
md gkTfI 4)(2
Vg
Id
Vi
fWLC
k
gkTfV
oxmi
4)(2
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Noise Approximation
Thermal noise
1/f noise
Band of interest Frequency
Noise spectral density
Thermal noise dominant
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Power Transfer and Impedance Matching
LLLss
sdel R
jXRjXR
VP
2
s
ssXXRRL R
VVPP
LsLs 4
*
0,max
• Power delivered to load
• Maxim available power
Rs
Vs
jXs jXL
RLI V
• Impedance matching– Load and source impedances conjugate pair– Real part matched to 50 ohm
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Available Power
Equal power on load and source resistors
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Reflection Coefficient
***
max 4
))((
4aa
R
IZVIZV
R
VVP
s
ss
s
ss
s
s
R
IZVa
2
****
max 4
))((bb
R
ZIVIZVPPP
s
ssdelref
Rs
Vs
jXs jXL
RLI V
s
s
R
IZVb
2
*
sL
sL
ZZ
ZZ
a
b
*
2
)( **LL
del
ZZIIP
LIZV
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12
Reflection Coefficient
No reflectionMaximum power transfer
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S-Parameters• Parameters for two-port system analysis
• Suitable for distributive elements
• Inputs and outputs expressed in powers– Transmission coefficients– Reflection coefficients
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S-Parameters
2221212
2121111
aSaSb
aSaSb
a1
b1
b2
a2
S11
S12
S22
S21
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S-Parameters• 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
012
222
012
112
021
221
021
111
a
a
a
a
a
bS
a
bS
a
bS
a
bS
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S-Parameters
SZ1 Z2
Vs1 Vs2
I1
V1
I2
V2
0222
*222
22
01
2
222
*111
12
02
1
111
*222
21
0111
*111
11
11
22
)Re(
)Re(
)Re(
)Re(
ss
ss
VV
VV
ZIV
ZIVS
Z
Z
ZIV
ZIVS
Z
Z
ZIV
ZIVS
ZIV
ZIVS
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Stability Condition
• Necessary condition
where• Stable iff
where
1||2
||||||1
2112
2211
222
SS
SSK S
21122211 SSSSS
1|| 2 LLS
2
||||||
222
211
2112
SSSSL
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A First LNA Example
• Assume– No flicker noise
– ro = infinity
– Cgd = 0
– Reasonable for appropriate bandwidth
• Effective transconductance
Rs
Vs
Vs
Rs 4kTRs
Vgs gmVgs 4kTgmins
inm
s
omeff ZR
Zg
V
iG
io
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19
Power Gain• Voltage input
• Current output
2
22
2
22
2
2*
*
1
)(1
1)(1
)(1
||
s
T
gss
m
gss
m
gss
gsm
ins
inmmeff
ss
oo
RCR
g
CRj
g
CjR
Cjg
ZR
ZgG
VV
iiG
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20
Noise Figure Calculation• Power ratio @ output
– Device noise + input-induced noise– Input-induced noise
2
2
222
22
2
)/(1
)1(1
)(14
41
gsmms
ms
gssms
gss
ms
m
in
indevice
CggR
gR
CRgR
CRg
kTR
gkT
NG
NGNNF
gs
mT C
g
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Unity Current Gain Frequency
Device ioutiin
1ω
ω
Tin
Touti
in
outi
i
iA
i
iA
T
1ω
ω
Tin
Touti
in
outi
i
iA
i
iA
T
0dB
fT
Ai
ffrequency
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22
Small-Signal Model of MOSFET
• Cgs
• Cgd
• rds
• Cdb
• Rg: Gate resistance
• ri: Channel charging resistance
V’gs
gmV’gs
Cgdi1 i2
ri
Cgs
i1
i2
Cdb
rds
Rg
V1 V2
V1
V2
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T Calculation
gdgsiggsiggdgs
gdgsigdgs
VCCrRsCsrRCCs
CCrsCCs
V
IY
2
2
01
111 )(1
)(
2
V’gs
gmV’gs
Cgdi1 i2
ri
CgsCdb
rds
Rg
V1
V’gs
gmV’gs
Cgdi1 i2
ri
Cgs
Rg
V1
gdgsiggsiggdgs
gdgsigdgsim
VCCrRsCsrRCCs
CCrssCCsrg
V
IY
2
2
01
221 )(1
)1(
2
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T of NMOS and PMOS
• 0.25um CMOS Process*
[2] Tajinder Manku, “Microwave CMOS - Device Physics and Design,” IEEE J. Solid-State Circuits, vol. 34, pp. 277 - 285, March 1999.
mgdgs
mT g
CC
g
1)(
)(
21
11 T
T
jY
jY
Set:
Solve for T
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Noise Performance
• Low frequency– Rsgm >> ~ 1– gm >> 1/50 @ Rs = 50 ohm– Power consuming
• CMOS technology– gm/ID lower than other tech– T lower than other tech
2
2
1T
msms
gRgR
NF
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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
• Power consumption– High power for NF
– High power for S21
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Impedance Matching for LNA• Resistive termination
• Series-shunt feedback
• Common-gate connection
• Inductor degeneration
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Resistive Termination
2
/1/1 gsIs
m
CjRR
gG
• Current-current power gain
• Noise figure
Rs
Vs Is Rs
4kT/Rs
Vgs gmVgs
io
RI RI
4kT/RI4kTgm
2
2211
1T
smIsm
s
I
s RgRRg
R
R
RNF
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Comparison with Previous Example
• Previous example
• Resistive-termination
2
22
11T
smI
s
smI
s RgR
R
RgR
RNF
2
2
1T
msms
gRgR
NF
Introduced by input resistance Signal attenuated
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Summary - Resistive Termination• Noise performance
– Low-frequency approximation
– Input matched Rs = RI = R
• Broadband input match• Attenuate signal
• Introduce noise due to RI
• NF > 3 dB (best case)
RgNF
m
42
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Series-Shunt Feedback• Broadband matching
• Could be noisy
Rs
Vs
Ra
RF
RL
Vgs gmVgs
RFiout
Ra
Cgs
Rs
Vs
RL
gsLFaaLm
gsaamLFin CRRRsRRg
CsRRgRRR
)()(1
)1)((
))((1
)(
))((1
))(1(
asgsm
saFsFags
asgsm
sFamout
RRsCg
RRRRRRsC
RRsCg
RRRgR
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Common-Gate Structure
RsRL
Vs
Rs 4kTRs
VgsgmVgs
RL
4kTgm
Vs
Rs 4kTRs
Vgs gmVgs
RL
4kTgm
gm
gsssm
m
s
outeff
CsRRg
g
V
IG
1
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Input Impedance of CG Structure
• Input impedance
Yin=gm+sCgs
• Input-impedance matching– Low frequency approximation– Direct without passive components
1/gm=Rs=50 ohm
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Noise Performance of CG Structure
2
2
2222
222
2
41
)1(1
)()1(4
41
T
gsssmms
gsssm
ms
m
in
indevice
CRRggR
CRRgg
kTR
gkT
NG
NGNNF
222
22
)()1( gsssm
meff CRRg
gGG
Signal attenuated
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Power Transfer of CG Structure• Rs = RL = R = 50 ohm
• S11=0, S21=1 @ Low frequency
gss
gss
gsssm
gsssm
sin
sin
CsR
CsR
CsRRg
CsRRg
ZZ
ZZS
2
1
1*
11
gs
gsssm
mLeffL
sC
CsRRg
gRGRS
2
2
1
2221
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Summary – CG Structure• Noise performance
– No extra resistive noise source– Independent of power consumption
• Impedance matching– Broadband input matching– No passive components
• Power consumption– gm=1/50
• Power transfer– Independent of power consumption
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Inductor Degeneration Structure
Rs
Vs
Ls
Lg
Vgs gmVgs
iout
Cgs
Rs
Vs
Lg
Ls
Zin
Vin
iin
gs
sm
gssgin
sgs
inmings
ingin
sgsmings
inginin
C
Lg
sCLLsI
sLsC
IgIsC
IsLI
sLVgIsC
IsLIV
1)(
)1
(1
)(1
Zin
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38
Input Matching for ID Structure
• Zin=Rs
– IM{Zin}=0
– RE{Zin}=Rs
gs
sm
gssgin C
Lg
sCLLsZ
1)(
gssg CLL )(
120
sgs
sm RC
Lg
Vgs gmVgs
iout
Cgs
Rs
Vs
LgLs
Zin
gmLs/Cgs
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39
Effective Transconductance
Vgs gmVgs
iout
Cgs
Rs
Vs
LgLs
Zin
gmLs/Cgs
)()(1
)(
2sggssmgss
m
ins
gsm
s
outeff
LLCsLgCRs
g
ZR
sCg
V
IG
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40
Noise Factor of ID Structure
• Calculate NF at 0
22
22
2
)(1
)(4
41
0
smgssms
smgss
ms
m
in
indevice
LgCRgR
LgCRg
kTR
gkT
NG
NGNNF
2222
22
)()](1[ smgsssggs
meff LgCRLLC
gGG
= 0 @ 0
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41
Input Quality Factor of ID Structure
CRRII
CII
powerLost
powerStoredQ
1*
*
Cgs
Rs
Vs
LgLs
gmLs/Cgs
C
R
V
L
gsssmgss
gssmsgsin
CRLgCR
CLgRCCRQ
2
1
)(
1
)/(
11
I
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42
Noise Factor of ID Structure
2
22
11
)(1
0
inms
smgssms
QgR
LgCRgR
NF
)(
1
smgssin LgCR
Q
• Increase power transfer
gmLs/Cgs = Rs
• Decrease NF
gmLs/Cgs = 0
• Conflict between– Power transfer– Noise performance
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43
Further Discussion on NF
sg
s
sggsms
sm
smgssms
LL
L
LLCgR
Lg
LgCRgR
NF
41
)(
1)(41
)(1
2
22
0
• Frequency @ 0
2 ~= 1/Cgs/(Lg+Ls)
• Input impedance matched to Rs
RsCgs=gmLs
• Suitable for hand calculation and design
• Large Lg and small Ls
Tss RL
gsgs CLL 201
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44
Power Transfer of ID Structure
• Rs = RL = R = 50 ohm
• @
)()(1
)(1
)(1
)(1
2
2
2
2*
11
sggsgsssm
sggs
gsssmsggs
gsssmsggs
sin
sin
LLCsCRLgs
LLCs
CsRLsgLLCs
CsRLsgLLCs
ZZ
ZZS
)()(1
22
221sggssmgss
LmLeff LLCsLgCRs
RgRGS
)(
1
smgssin LgCR
Q
gssg CLL )(
120
s
LTinLm
smgss
Lm
R
RjQRgj
LgCRj
RgSS
002111 2
)(
2 ;0
![Page 45: 1 Low-Noise Amplifier. 2 RF Receiver BPF1BPF2LNA LO MixerBPF3IF Amp Demodulator Antenna RF front end](https://reader035.vdocuments.site/reader035/viewer/2022081506/56649da75503460f94a929e9/html5/thumbnails/45.jpg)
45
Computing Av without S-Para
Rs
Vs
Ls
Lg
)(
2/1
22
;2
:matchimput and resonanceAt
0
00
0
oos
T
s
ov
sTssgssmo
gsinmgsmossin
sin
YYRj
V
VA
RjVRCjVgI
CjIgVgIRVI
RZ
![Page 46: 1 Low-Noise Amplifier. 2 RF Receiver BPF1BPF2LNA LO MixerBPF3IF Amp Demodulator Antenna RF front end](https://reader035.vdocuments.site/reader035/viewer/2022081506/56649da75503460f94a929e9/html5/thumbnails/46.jpg)
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Power Consumption
DDTgsox
DDD VVVL
WCVIP 2)(
2
WLCC oxgs 3
2)( Tgsoxm VV
L
WCg
222
2
3Tgsox
gs
m VVL
WC
C
Lg
gs
sms C
LgR
s
gssm L
CRg
)/1(3
1
)(3
1
3
)(333
320
2222
0
22
20
2
22
2
2222
sgs
DDs
sg
DDTDDgs
T
sg
DD
s
sDDgs
s
sDD
gs
m
LLL
VRL
LL
VLVC
LP
LL
V
L
RLVC
L
RLV
C
LgP
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47
Power Consumption
)/1(
132
0
22
sgs
s
LLL
RLP
• Technology constant– L: minimum feature size– : mobility, avoid mobility saturation region
• Standard specification– Rs: source impedance
– 0: carrier frequency
• Circuit parameter– Lg, Ls: gate and source degeneration inductance
sg
s
LL
LNF
41
0
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48
Summary of ID Structure• Noise performance
– No resistive noise source– Large Lg
• Impedance matching – Matched at carrier frequency– Applicable to wideband application, S11<-10dB
• Power transfer– Narrowband– Increase with gm
• Power consumption– Large Lg
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49
Cascode
• Isolation to improve S12 @ high frequency– Small range at Vd1
– Reduced feedback effect of Cgd
• Improve noise performance
Rs
Vs
Ls
Lg
Vbias
LL
M2
M1
Vd1
Vo
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50
Rs
Vs
Ls
Lg
LL
M1
Vo
Vgs gmVgsCgs
Rs
Vs
Lg
Ls LL
Vo
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51
LNA Design Example (1)
Rs
Vs Ls
Lg
Ld
M2
M1
Lvdd
Vbias
M4
Lb1
Cb1
Tm
Cm
M3
Lgnd
Lout
Input bias Off-chip
matching[3] D. Shaeffer and T. Lee, “A 1.5-V, 1.5-GHz CMOS low noise amplifier,” IEEE J. Solid-State Circuits, vol. 32, pp. 745 – 759, May 1997.
Lb2Cb2 Vout
Output bias
Vdd
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52
LNA Design Example (1)
Rs
Vs Ls
Lg
Ld
M2
M1
Lvdd
Vbias
M4
Lb1
Cb1
Tm
Cm
M3
Lgnd
Lout
[3] D. Shaeffer and T. Lee, “A 1.5-V, 1.5-GHz CMOS low noise amplifier,” IEEE J. Solid-State Circuits, vol. 32, pp. 745 – 759, May 1997.
Unwanted parasitics
Supply filtering
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Circuit Details
• Two-stage cascoded structure in 0.6 m
• First stage– W1 = 403 m determined from NF
– Ls accurate value, bondwire inductance
– Ld = 7nH, resonating with cap at drain of M2
• Second– 4.6 dB gain
– W3 = 200 m
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54
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55
LNA Design Example (2)
[4] A. Karanicolas, “A 2.7-V 900-MHz CMOS LNA and Mixer,” IEEE J. Solid-State Circuits, vol. 31, pp 1939 – 1944, Dec. 1996.
Cs
M2
M1
M3
Off-chip matching
Ns
RB
VRF
CB
IREF
IB1
VB1M4
M5
M7
M6
Vout1
RX
CX
NL
Off-chip matching
NF = 1 + K/gm
gm = gm1 + gm2
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56
Simplified view
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57
LNA Design Example (2)
[4] A. Karanicolas, “A 2.7-V 900-MHz CMOS LNA and Mixer,” IEEE J. Solid-State Circuits, vol. 31, pp 1939 – 1944, Dec. 1996.
Cs
M2
M1
M3Bias feedback
Ns
RB
VRF
CB
IREF
IB1
VB1M4
M5
M7
M6
Vout1
RX
CX
NL
M8
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58
LNA Design Example (2)
[4] A. Karanicolas, “A 2.7-V 900-MHz CMOS LNA and Mixer,” IEEE J. Solid-State Circuits, vol. 31, pp 1939 – 1944, Dec. 1996.
Cs
M2
M1
M3Bias feedback
Ns
RB
VRF
CB
IREF
IB1
VB1M4
M5
M7
M6
Vout1
RX
CX
NL
M8
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59
LNA Design Example (2)
[4] A. Karanicolas, “A 2.7-V 900-MHz CMOS LNA and Mixer,” IEEE J. Solid-State Circuits, vol. 31, pp 1939 – 1944, Dec. 1996.
Cs
M2
M1
M3Bias feedback
Ns
RB
VRF
CB
IREF
IB1
VB1M4
M5
M7
M6
Vout1
RX
CX
NL
M8
VA
DC output = VB1
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60
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61
LNA Design Example (3)
• Objective is to design tunable RF LNA that would:
– Operate over very wide frequency range with very fine selectivity
– Achieve a good noise performance
– Have a good linearity performance
– Consume minimum power
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62
LNA Architecture • The cascode architecture
provides a good input – output isolation
• Transistor M2 isolates the Miller capacitance
• Input Impedance is obtained using the source degeneration inductor Ls
• Gate inductor Lg sets the resonant frequency
• The tuning granularity is achieved by the output matching network
VDD
LS
LG
M1
M2
LD
R2
R1
M3
Output to Mixer
Input to LNA
Matching Network
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63
Matching Network • The output matching tuning
network is composed of a varactor and an inductor.
• The LC network is used to convert the load impedance into the input impedance of the subsequent stage.
• A well designed matching network allows for a maximum power transfer to the load.
• By varying the DC voltage applied to the varactor, the output frequency is tuned to a different frequency.
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64
Simulation Results - S11• The input return loss
S11 is less than – 10dB at a frequency range between 1.4 GHz and 2GHz
Input return loss
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65
Simulation results - NF • The noise figure is 1.8
dB at 1.4 GHz and rises to 3.4 dB at 2 GHz.
Noise Figure
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66
Simulation Results - S22
S22 at 1.7725 GHz S22 at 1.77 GHz
• By controlling the voltage applied to the varactor the output frequency is tuned by 2.5 MHz.
• The output return loss at 1.77 GHz is – 44.73 dB and the output return loss at 1.7725 GHz – 45.69 dB.
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Simulation Results - S22
S22 at 1.9975 GHz S22 at 2 GHz
• The output return loss at 2 GHz is – 26.47 dB and the output return loss at 1.9975 GHz – 26.6 dB.
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Simulation Results - S21• The overall gain of
the LNA is 12 dB
S21 at 1.4025 GHz
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Simulation Results - Linearity
-1dB compression point IIP3
• The third order input intercept is –3.16 dBm
• -1 dB compression point ( the output level at which the actual gain departs from the theoretical gain) is –12 dBm
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70
From an earlier slide:
fWLC
kfV
oxg )(2
• Flicker noise– Dominant at low frequency
• Thermal noise– : empirical constant
2/3 for long channel
much larger for short channel– PMOS has less thermal noise
• Input-inferred noise
md gkTfI 4)(2
Vg
Id
Vi
fWLC
k
gkTfV
oxmi
4)(2
Not accurate for low voltage short channel devices
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71
Modifications
is called excess noise factor = 2/3 in long channel = 2 to 3 (or higher!) in short channel NMOS (less in PMOS)
m
dod
gkTgkTfI 44)(2
Thermonoise
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gdo vs gm in short channel
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gdo vs gm in short channel
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Fliker noise• Traps at channel/oxide interface randomly
capture/release carriers
– Parameterized by Kf and n • Provided by fab (note n ≈ 1) • Currently: Kf of PMOS << Kf of NMOS due to buried channel
– To minimize: want large area (high WL)
f
K
f
KfI
fWLC
kfV
f
n
fd
oxg
)(
)(
2
2
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Induced Gate Noise• Fluctuating channel potential couples
capacitively into the gate terminal, causing a noise gate current
– is gate noise coefficient• Typically assumed to be 2
– Correlated to drain noise!
2
2
54
T
dong gkTi
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76
Input impedance
Set to be real and equal to source resistance:
real
gs
m
gsgin C
Lg
sCLLssZ deg
deg
1)()(
gsg CLL )(
1
deg
20
sgs
m RC
Lgdeg
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Output noise current
)14(21)( 222 QcgkTfI dddod
Noise scaling factor:
)14(214
1 22 Qc dd
Where for 0.18 process
c=-j0.55, =3, =6, gdo=2gm,
d = 0.32
5do
md g
g
s
g
gss R
LL
CRQ
2
)(
2
1 deg0
0
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Noise factor
Noise factor scaling coefficient:
22 )14(212 dd
m
donf Qc
g
g
QK
22 )14(212
1 ddm
do
T
o Qcg
g
QF
42
1)(41 0220
0 QCR
gRNG
NGNNF
Tgss
msin
indevice
Compare:
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Noise factor scaling coefficient versus Q
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Example
• Assume Rs = 50 Ohms, Q = 2, fo = 1.8 GHz, ft = 47.8 GHz
• From gss CR
Q02
1
fFeQR
Cs
gs 442)2(98.12)50(2
1
2
1
0
nHe
R
g
CRL
T
s
m
gss 17.098.472
50deg
nHLC
LCLL gs
ggsg
5.171
)(
1deg2
0deg
20
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Have We Chosen the Correct Bias Point?
IIP3 is also a function of Q
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If we choose Vgs=1V
• Idens = 175 A/m
• From Cgs = 442 fF, W=274m
• Ibias = IdensW = 48 mA, too large!
• Solution 1: lower Idens => lower power, lower fT, lower IIP3
• Solution 2: lower W => lower power, lower Cgs, higher Q, higher NF
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Lower current density to 100
Need to verify that IIP3 still OK (once we know Q)
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We now need to re-plot the Noise Factor scaling coefficient - Also plot over a wider range of Q
Lower current density to 100
43.05
268.0
568.0
15.1
78.0
do
md
do
m
g
g
g
g
GHz 8.4229.2
78.0
fF
mS
C
g
gs
mT
22 )14(212
11 dd
m
do
T
o QcQg
gF
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Recall
We previously chose Q = 2, let’s now choose Q = 6 - Cuts power dissipation by a factor of 3! - New value of W is one third the old one
mm
W 91
3
274
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• Rs = 50 Ohms, Q = 6, fo = 1.8 GHz, ft = 42.8 GHz
• Ibias = IdensW =100A/m*91m=9.1mA• Power = 9.1 * 1.8 = 16.4 mW• Noise factor scaling coeff = 10• Noise factor = 1+ wo/wt * 10
= 1+ 1.8G/42.8G *10 = 1.42• Noise figure = 10*log(1.42) = 1.52 dB• Cgs=442/3=147fF• Ldeg=Rs/wt=0.19nH• Lg=1/(wo^2Cgs) –Ldeg = 53 nH
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Other architectures of LNAs
•Add output load to achieve voltage gain•In practice, use cascode to boost gain
•Added benefit of removing Cgd effect
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Differential LNAValue of Ldeg is now much better controlled
Much less sensitivity to noise from other circuits But: Twice the power as the single-ended version
Requires differential input at the chip
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LNA Employing Current Re-Use
•PMOS is biased using a current mirror •NMOS current adjusted to match the PMOS current •Note: not clear how the matching network is achieving a 50 Ohm match
Perhaps parasitic bondwire inductance is degenerating the PMOS or NMOS transistors?
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Combining inductive degeneration and current reuse
Current reuse to save power
Larger area due to two degenerationinductor if implemented on chip
NF: 2dB, Power gain: 17.5dB, IIP3: -6dBm, Id: 8mA from 2.7V power supply
Can have differential version
F. Gatta, E. Sacchi, et al, “A 2-dB Noise Figure 900MHz Differential CMOS LNA,” IEEE JSSC, Vol. 36, No. 10, Oct. 2001 pp. 1444-1452
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At DC, M1 and M2 are in cascodeAt AC, M1 and M2 are in cascadeS of M2 is AC shortedGm of M1 and M2 are multiplied.Same biasing current in M1 & M2
LIANG-HUI LI AND HUEY-RU CHUANG, MICROWAVE JOURNAL® from the February 2004 issue.
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•IM3 components in the drain current of the main transistor has the required information of its nonlinearity•Auxiliary circuit is used to tune the magnitude and phase of IM3 components•Addition of main and auxiliary transistor currents results in negligible IM3 components at output
Sivakumar Ganesan, Edgar Sánchez-sinencio, And Jose Silva-martinezIEEE Transactions On Microwave Theory And Techniques, Vol. 54, No. 12, December 2006
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MOS in weak inversion has speed problemMOS transistor in weak inversion acts like bipolarBipolar available in TSMC 0.18 technology (not a parasitic BJT)Why not using that bipolar transistor to improve linearity ?
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Inter-stage Inductor gain boost
Inter-stage inductor withparasitic capacitance formimpedance match network betweeninput stage and cascoded stageboost gain lower noise figure.
Input match condition will beaffected
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Folded cascode
Low supply voltage
Ld reduces or eliminatesEffect of Cgd1
Good fT
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Design Procedure for Inductive Source Degenerated LNA
Noise factor equations:
22 )14(212
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Targeted Specifications
• Frequency 2.4 GHz ISM Band
• Noise Figure 1.6 dB
• IIP3 -8 dBm
• Voltage gain 20 dB
• Power < 10mA from 1.8V
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Step 1: Know your process• A 0.18um CMOS Process• Process related
– tox = 4.1e-9 m
– = 3.9*(8.85e-12) F/m– = 3.274e-2 m^2/V.s
– Vth = 0.52 V
• Noise related– = gm/gdo– ~ 2– ~ 3– c = -j0.55
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Step 2: Obtain design guide plots
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Insights:
• gdo increases all the way with current density Iden
• gm saturates when Iden larger than 120A/m– Velocity saturation, mobility degradation ----
short channel effects– Low gm/current efficiency– High linearity
• deviates from long channel value (1) with large Iden
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Obtain design guide plots
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Insights:
• fT increases with Vod when Vod is small and saturates after Vod > 0.3V --- short channel effects
• Cgs/W increases slowly after Vod > 0.2V
• fT begins to degrade when Vod > 0.8V
– gm saturates
– Cgs increases
• Should keep Vod ~0.2 to 0.4 V
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Obtain design guide plots
3-D plot for visualinspection
2-D plots fordesign reference
knf vs input Q and current density
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Design trade-offs
• For fixed Iden, increasing Q will reduce the size of transistor thus reduce total power ---- noise figure will become larger
• For fixed Q, reducing Iden will reduce power, but will increase noise factor
• For large Iden, there is an optimal Q for minimum noise factor, but power may be too high
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Obtain design guide plots
Linearity plots :IIP3 vs. gate overdrive and transistor size
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Insights:• MOS transistor IIP3 only, when embedded into
actual circuit:– Input Q will degrade IIP3– Non-linear memory effect will degrade IIP3– Output non-linearity will degrade IIP3
• IIP3 is a very weak function of device size• Generally, large overdrive means large IIP3
– But the relationship between IIP3 and gate overdrive is not monotonic
– There is a local maxima around 0.1V overdrive
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Step 4: Estimate fT
Small current budget ( < 10mA )does not allow large gate over drive :
Vod ~ 0.2 V ~ 0.4 VfT ~ 40 ~ 44 GHz
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Step 4: Determine Iden, Q andCalculate Device Size
Select Iden = 70 A/m, =>Vod~0.23V
Gm/W~0.4
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If Q = 4, IIP3 will have enough margin:Estimated IIP3:IIP3(from curve) – 20log(Q) = 8-12 = -4dBmSpecs require: -8 dBm
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Q=4 and Iden = 70A/m meet thenoise factor requirement
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Gm=0.4*128 ~ 50 mS fT = gm/(Cgs*2pi) = 48 GHz
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Step 6: Simulation Verification
Large deviation
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Comparison between targeted specs and simulation results
Parameter Target Simulated
Noise Figure 1.6 dB 0.8 dB
Drain Current < 10mA 8 mA
Voltage gain 20 dB 21 dB
IIP3 -8 dBm -6.4 dBm
P1dB -20dbm
S11 -17 dB
Power supply 1.8 V 1.8 V