1

Low-Noise Amplifier

2

RF Receiver

BPF1 BPF2LNA

LO

Mixer BPF3 IF Amp

Demodulator

Antenna

RF front end

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

4

LNA Design Consideration

• Noise performance• Power transfer• Impedance matching• Power consumption• Bandwidth• Stability• Linearity

5

Noise Figure• Definition

• As a function of device

G: Power gain of the device

outout

inin

out

in

NSNS

SNRSNRNF

source

sourcedevice

NGNGNNF

6

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

...GGGNF...

GGNF

GNFNFNF

7

Simple Model of Noise in MOSFET

fWLCkfV

oxg )(2

• Flicker noise– Dominant at low frequency

• Thermal noise– : empirical constant

2/3 for long channelmuch larger for short channel

– PMOS has less thermal noise

• Input-inferred noise

md gkTfI 4)(2

Vg

Id

Vi

fWLCk

gkTfV

oxmi

4)(2

8

Noise Approximation

Thermal noise

1/f noise

Band of interest Frequency

Noise spectral density

Thermal noise dominant

9

Power Transfer and Impedance Matching

LLLss

sdel R

jXRjXRVP

2

s

ssXXRRL R

VVPPLsLs 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

10

Available Power

Equal power on load and source resistors

11

Reflection Coefficient

***

max 4))((

4aa

RIZVIZV

RVVP

s

ss

s

ss

s

s

RIZVa

2

****

max 4))(( bb

RZIVIZVPPP

s

ssdelref

Rs

Vs

jXs jXL

RLI V

s

s

RIZVb

2

*

sL

sL

ZZZZ

ab

*

2)( **

LLdel

ZZIIP

LIZV

12

Reflection Coefficient

No reflectionMaximum power transfer

13

S-Parameters• Parameters for two-port system analysis• Suitable for distributive elements• Inputs and outputs expressed in powers

– Transmission coefficients– Reflection coefficients

14

S-Parameters

2221212

2121111

aSaSbaSaSb

a1

b1

b2

a2

S11

S12

S22

S21

15

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

abS

abS

abS

abS

16

S-Parameters

SZ1 Z2

Vs1 Vs2

I1

V1

I2

V2

0222

*222

22

01

2

222

*111

12

02

1

111

*222

210111

*111

11

11

22

)Re()Re(

)Re()Re(

ss

ss

VV

VV

ZIVZIVS

ZZ

ZIVZIVS

ZZ

ZIVZIVS

ZIVZIVS

17

Stability Condition

• Necessary condition

where• Stable iff

where

1||2

||||||1

2112

2211

222

SSSSK S

21122211 SSSSS

1|| 2 LLS

2||||||2

222

112112

SSSSL

18

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

ZgViG

io

19

Power Gain• Voltage input• Current output

2

22

2

22

22

*

*

1)(1

1)(1)(1

||

s

T

gss

m

gss

m

gss

gsm

ins

inmmeff

ss

oo

RCRg

CRjg

CjRCjg

ZRZgG

VViiG

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

CRgkTR

gkTNG

NGNNF

gs

mT C

g

21

Unity Current Gain Frequency

Device ioutiin

1ωω

Tin

Touti

in

outi

iiA

iiA

T

0dB

fT

Ai

ffrequency

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

23

T Calculation

gdgsiggsiggdgs

gdgsigdgs

VCCrRsCsrRCCs

CCrsCCsVIY 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

CCrssCCsrgVIY 2

2

01

221 )(1

)1(

2

24

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

CCg

1)()(

21

11 T

T

jYjY

Set:

Solve for T

25

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

26

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

27

Impedance Matching for LNA• Resistive termination• Series-shunt feedback• Common-gate connection• Inductor degeneration

28

Resistive Termination

2

/1/1 gsIs

m

CjRRgG

• Current-current power gain

• Noise figure

Rs

Vs Is Rs

4kT/Rs

Vgs gmVgs

io

RI RI

4kT/RI4kTgm

2

22111

Tsm

Ism

s

I

s RgRRg

RRRNF

29

Comparison with Previous Example• Previous example

• Resistive-termination

2

22

11T

smI

s

smI

s RgRR

RgRRNF

2

2

1T

msms

gRgR

NF

Introduced by input resistance Signal attenuated

30

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

31

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

RRsCgRRRRRRsC

RRsCgRRRgR

32

Common-Gate Structure

RsRL

Vs

Rs 4kTRs

VgsgmVgs

RL

4kTgm

Vs

Rs 4kTRs

Vgs gmVgs

RL

4kTgm

gm

gsssm

m

s

outeff

CsRRgg

VIG

1

33

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

34

Noise Performance of CG Structure

2

2

2222

222

2

41

)1(1

)()1(4

41

T

gsssmms

gsssm

ms

m

in

indevice

CRRggR

CRRggkTR

gkTNG

NGNNF

222

22

)()1( gsssm

meff CRRg

gGG

Signal attenuated

35

Power Transfer of CG Structure• Rs = RL = R = 50 ohm

• S11=0, S21=1 @ Low frequency

gss

gss

gsssm

gsssm

sin

sin

CsRCsR

CsRRgCsRRg

ZZZZS

2

11*

11

gs

gsssm

mLeffL

sC

CsRRggRGRS

22

12221

36

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

37

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

CLg

sCLLsI

sLsC

IgIsC

IsLI

sLVgIsC

IsLIV

1)(

)1(1

)(1

Zin

38

Input Matching for ID Structure

• Zin=Rs

– IM{Zin}=0

– RE{Zin}=Rs

gs

sm

gssgin C

LgsC

LLsZ 1)(

gssg CLL )(12

0

sgs

sm RC

Lg

Vgs gmVgs

iout

Cgs

Rs

Vs

LgLs

Zin

gmLs/Cgs

39

Effective Transconductance

Vgs gmVgs

iout

Cgs

Rs

Vs

LgLs

Zin

gmLs/Cgs

)()(1

)(

2sggssmgss

m

ins

gsm

s

outeff

LLCsLgCRsgZR

sCgVIG

40

Noise Factor of ID Structure

• Calculate NF at 0

22

22

2

)(1

)(4

410

smgssms

smgss

ms

m

in

indevice

LgCRgR

LgCRgkTR

gkTNG

NGNNF

2222

22

)()](1[ smgsssggs

meff LgCRLLC

gGG

= 0 @ 0

41

Input Quality Factor of ID Structure

CRRIICII

powerLostpowerStoredQ

1*

*

Cgs

Rs

Vs

LgLs

gmLs/Cgs

C

R

V

L

gsssmgss

gssmsgsin

CRLgCR

CLgRCCRQ

21

)(1

)/(11

I

42

Noise Factor of ID Structure

2

22

11

)(1

0

inms

smgssms

QgR

LgCRgR

NF

)(1

smgssin LgCR

Q

• Increase power transfergmLs/Cgs = Rs

• Decrease NFgmLs/Cgs = 0

• Conflict between– Power transfer– Noise performance

43

Further Discussion on NF

sg

s

sggsms

sm

smgssms

LLL

LLCgRLg

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

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

LLCsCRLgsLLCs

CsRLsgLLCsCsRLsgLLCs

ZZZZS

)()(122 221

sggssmgss

LmLeff LLCsLgCRs

RgRGS

)(1

smgssin LgCR

Q

gssg CLL )(

120

s

LTinLm

smgss

Lm

RRjQRgj

LgCRjRgSS

002111 2

)(2 ;0

45

Computing Av without S-ParaRs

Vs

Ls

Lg

)(2/1

22

;2 :matchimput and resonanceAt

0

00

0

oos

T

s

ov

sTssgssmo

gsinmgsmossin

sin

YYRj

VVA

RjVRCjVgI

CjIgVgIRVIRZ

46

Power Consumption

DDTgsox

DDD VVVLWCVIP 2)(

2

WLCC oxgs 32

)( Tgsoxm VVLWCg

222

23

Tgsoxgs

m VVLWC

CLg

gs

sms C

LgR s

gssm L

CRg

)/1(31

)(31

3

)(333

320

2222

0

22

20

2

22

2

2222

sgs

DDs

sg

DDTDDgs

T

sg

DD

s

sDDgs

s

sDD

gs

m

LLLVRL

LLVLVCLP

LLV

LRLVC

LRLV

CLgP

47

Power Consumption

)/1(1

320

22

sgs

s

LLLRLP

• 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

LLLNF

410

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

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

50

Rs

Vs

Ls

Lg

LL

M1

Vo

Vgs gmVgsCgs

Rs

Vs

Lg

Ls LL

Vo

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

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

53

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

54

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

56

Simplified view

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

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

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

60

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

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

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.

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

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

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.

67

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.

68

Simulation Results - S21• The overall gain of

the LNA is 12 dB

S21 at 1.4025 GHz

69

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

70

From an earlier slide:

fWLCkfV

oxg )(2

• Flicker noise– Dominant at low frequency

• Thermal noise– : empirical constant

2/3 for long channelmuch larger for short channel

– PMOS has less thermal noise• Input-inferred noise

md gkTfI 4)(2

Vg

Id

Vi

fWLCk

gkTfV

oxmi

4)(2

Not accurate for low voltage short channel devices

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

dodgkTgkTfI 44)(2

Thermonoise

72

gdo vs gm in short channel

73

gdo vs gm in short channel

74

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)

fK

fK

fI

fWLCkfV

fnf

d

oxg

)(

)(

2

2

75

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

Tdong gkTi

76

Input impedance

Set to be real and equal to source resistance:

real

gs

m

gsgin C

LgsC

LLssZ degdeg

1)()(

gsg CLL )(1

deg

20

sgs

m RCLg

deg

77

Output noise current

)14(21)( 222 QcgkTfI dddod

Noise scaling factor:

)14(2141 22 Qc dd

Where for 0.18 processc=-j0.55, =3, =6, gdo=2gm,

d = 0.32

5do

md g

g

s

g

gss RLL

CRQ

2)(

21 deg0

0

78

Noise factor

Noise factor scaling coefficient:

22 )14(212 dd

m

donf Qc

gg

QK

22 )14(212

1 ddm

do

T

o Qcgg

QF

42

1)(41 0220

0 QCR

gRNGNGNNF

Tgss

msin

indevice

Compare:

79

Noise factor scaling coefficient versus Q

80

Example • Assume Rs = 50 Ohms, Q = 2, fo = 1.8 GHz, ft = 47.8

GHz• From

gss CRQ

021

fFeQR

Cs

gs 442)2(98.12)50(2

12

1

0

nHe

RgCR

LT

s

m

gss 17.098.472

50deg

nHLC

LCLL gs

ggsg

5.171)(

1deg2

0deg

20

81

Have We Chosen the Correct Bias Point?

IIP3 is also a function of Q

82

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

83

Lower current density to 100

Need to verify that IIP3 still OK (once we know Q)

84

We now need to re-plot the Noise Factor scaling coefficient - Also plot over a wider range of Q

Lower current density to 100

43.05268.0

568.0

15.178.0

do

md

do

m

gg

gg

GHz 8.4229.2

78.0

fFmS

Cg

gs

mT

22 )14(21211 dd

m

do

T

o QcQg

gF

85

86

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

mmW 913

274

87

• 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

88

Other architectures of LNAs

•Add output load to achieve voltage gain•In practice, use cascode to boost gain

•Added benefit of removing Cgd effect

89

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

90

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?

91

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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bao

bmb

amamama

iiivgi

vgvgvgi

3

3

33

221

•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 ?

95

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(21211 dd

m

do

T

o QcQg

gF

22 )14(2121

ddm

donf Qc

QggK

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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

103

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 plotsLinearity 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 SimulatedNoise Figure 1.6 dB 0.8 dBDrain Current < 10mA 8 mAVoltage gain 20 dB 21 dBIIP3 -8 dBm -6.4 dBmP1dB -20dbmS11 -17 dBPower supply 1.8 V 1.8 V