highly linear low noise amplifier - texas a&m university linearized lna...amsc low noise...

1

AMSC

Highly Linear Low Noise Amplifier

Sivakumar GanesanTexas A&M Universitysivakumar@tamu.edu

Advisors: Dr. Edgar Sánchez-SinencioDr. Jose Silva-Martinez

Analog and Mixed Signal Center

Department of Electrical & Computer Engineering

2

AMSC Outline

• Motivation• Background• Proposed Solution• Testing Strategy• Experimental Results• Conclusion

3

AMSC Motivation

• Numerous co-existing wireless standards and wireless equipment

4

AMSC Frequency Spectrum

• Limited spectrum allotted to each user• Possible large interferers from other

channels in-band and out of band

5

AMSC Receiver Architecture

• Antenna receives the entire band of signals • Stringent requirements on the receiver front-end • BPF filters the out of band channels• LNA receives the entire in-band signals• In-band channel interference problems in LNA

– Blocking– Intermodulation

6

AMSC Blocking

– If , a large interferer results in signal being “blocked”

)()()()( 33

221 txtxtxty ααα ++=

tAtAtx 2211 coscos)( ωω +=

......cos23)( 11

2231 +⎟⎠⎞

⎜⎝⎛ +≅ tAAty ωαα

03 <α

7

AMSC Intermodulation

• Third order intermodulation (IM3) components corrupt the signal resulting in distortion

tAtAtx 2211 coscos)( ωω +=

)2cos(43)2cos(

43)( 121

223212

2133 ωωαωωα −+−= AAAAtyIM

DesiredChannel

Interferers

LNA

IM3

DesiredChannelInterferers

8

AMSC Linearity Measurement

• Third order Input Intercept Point (IIP3) is a measure of circuit non-linearity

• Fundamental = ,IM3 = 334

3 AαA1α

9

AMSC Low Noise Amplifier

• Low Noise Amplifier– First amplifying block in a receiver– High gain, Low Noise Figure– Presents amplified signals (desired + IM3) to

mixer• Highly linear LNA with high gain and low

NF required

10

AMSC Background

• Existing Linearization Techniques– Optimum Biasing– Negative Feedback– Input Impedance Frequency Termination– Feedforward Cancellation

11

AMSC Optimum Biasing

• Current =• IIP3= • gm3=0 results in very high IIP3

......33

221 +++= gsmgsmgsmd vgvgvgi

3

1

34

m

m

gg

12

AMSC Optimum Biasing

• Drawbacks– High IIP3 obtained over a narrow region– Process variations degrade IIP3– Limited voltage gain due to restricted input

transconductance (gm1)– Poor NF

13

AMSC Negative Feedback

• Popular in baseband circuits to improve linearity

• IIP3= ( ) β1

31

22

3

3

1 ,

121

134

mo

o

o

mm

m

o

m

m gT

TT

ggg

Tgg

=

⎟⎟⎠

⎞⎜⎜⎝

⎛+

−

+

14

AMSC Negative Feedback

• Linearity improvement at the expense of circuit gain

• Second order non-linearity effect on IIP3• gm3<0, leads to further deterioration• Feedback techniques not suitable at RF

frequencies

15

AMSC Negative Feedback

• Inductor LS acts as a feedback network

• Provides best gain and noise performance

• Poor linearity performance due to second order non-linearity feedback

Cascode LNA

16

AMSC

Input Impedance Termination• Feedback network is frequency dependent• Different effect on different harmonics

[ ] [ ] [ ]

)()()(,)(1)()()(

)(

2,2,)(

)2(212

)2()(1)(1)(14

)(3

1

211

3

1

sZsZsZsZgsZgsZgssZsC

gsA

fjsfjssssswhere

VsZsCg

sAsZsCg

sAsZsCVI

sAIIP

eb

emo

mmFje

m

bbaaba

sjem

jem

jeT

Q

+=++++

=

==<<−=∆

⎭⎬⎫

⎩⎨⎧

++∆∆+∆

+−+≈

βτ

ππ

17

AMSC

Input Impedance Termination• The input and output impedances selectively

tuned for second harmonic frequencies• Requires huge passive elements

18

AMSC Feedforward

• Scaled versions of the input signal are fed to two different amplifiers

Pre-scalar(β)

Amplifier(A)

Amplifier(A)

X(t) Y(t)

β

Ymain(t)

Yaux(t)

xA

tytyty

xxAtyxxAty

auxmain

auxmain

.11

)()()(

1*)1.(..)(),1.(.)(

2

322

22

2

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

−=

+=+=

β

ββαβα

19

AMSC Feedforward-1

• Drawbacks– Linearity improvement at the expense of gain– Reduced NF due to additional active

components– Mismatch and errors in signal scaling leads to

reduced improvement• Derivative Superposition (DS) method

addresses the above problems

20

AMSCDerivative Superposition (DS) Method

• DS method also addresses the problem of narrow range with optimum biasing technique.

• gm3 negative in strong inversion and positive in weak inversion

MAWA

MBWB

VGS VOFF

OUT

IN

L

ZS

StrongInversion

WeakInversion

21

AMSC DS-Method

• Wide range of bias values with very small gm3and hence IIP3 improvement obtained

• Drawbacks– Second order harmonics ( ) converted to

voltage at the source– Control parameter Vgs has both fundamental and

second harmonics

abba ωωωω ±±,2,2

LC

ZCjLj

g

gg

WhereLCg

IIP

gssgsm

mm

gsm

)2(22

132

,3

43

1

22

3

221

ωωω

ε

εω

+++−=

=

22

AMSC Modified DS-Method

• Addresses the effect of second order non-linearity feedback

• Magnitude and phase of second order non-linearity contribution to IM3 is tuned to cancel the third order non-linearity contribution to IM3

MB MA

VGS VOFF

OUT

IN

L2

L1

AuxiliaryTransistor

MainTransistor

23

AMSC Modified DS-Method

( )[ ]

( )

A

A

A

AA

ABA

AB

ABAA

gLjsngLLj

ggg

CLCCLCLsnsng

WhereCLCCLgIIP

12

121

1

22

321

223

2122

13

1)()(2

11

1321)()(

,3

4

ωω

ε

εω

+=+

+−+⎥

⎦

⎤⎢⎣

⎡++

+=

++=

24

AMSC Drawbacks

• Weak inversion transistor connected in parallel degrades NF

• Auxiliary transistor loads the input affecting the frequency of operation

• Auxiliary transistor affects both linearity and input match leading to increased design steps

0

222

02

54

4

d

gsng

dnd

gC

fkTi

gfkTi

ωδ

γ

∆=

∆=

tDsatd Ig φ=0

25

AMSC

Proposed Solution

26

AMSC Basic Idea

• An auxiliary circuit is unavoidable to achieve high linearity

• IM3 components in the drain current of the main transistor has the required information of its non-linearity

• 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

27

AMSC Basic Idea

(Magnitude and angle tuned)

Im

Reg3A g2A

g3B

28

AMSC Proposed LNA

29

AMSC Theoretical Analysis

• IIP3 derived using the harmonic input method of Volterra series analysis

33213

221211

33

33

221

*),,(*),(*)( xxxbaout

bbb

aaaaaaa

vsssCvssCvsCiii

vgi

vgvgvgi

++=+=

=

++=

LA

ZS

vx

va

vb CB ib

ia

LB

CA

ix ioutvout

30

AMSC Theoretical Analysis

( )

)(1)()(

)1(22)()(

3,

)()(Re613

1

2

22

31

22

3

12

1

BAB

AaA

BB

BBb

a

aa

a

s

sLsLsCsCgsLsn

CLsCLssnsng

gggwhere

gsAsZ

IIP

+++

=

++

+−=

⎭⎬⎫

⎩⎨⎧=

ε

ε

• The effect of second order non-linearity can be seen in the above equation

• The value of g3bcan be tuned to obtain high IIP3 by choosing appropriate values for the inductors LA and LB and the aspect ratios of the transistors.

31

AMSC Theoretical Analysis

• MATLAB plots for different values of LA and LB is plotted

• The result corroborates the idea of IIP3 improvement by cancellation of IM3 components

DesignedPoint

32

AMSC IIP3 Sensitivity

0

5

10

15

20

25

4 4.2 4.4 4.6 4.7 4.8 5 5.2 5.4

Main Transistor Inductor (nH)

IIP3

(dB

m)

0

5

10

15

20

25

0.5 0.75 0.9 1 1.05 1.1 1.25 1.5

Aux Transistor Inductor (nH)

IIP3

(dB

m)

Variation with La Variation with Lb

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AMSC Effect on Input Match

• If , the input impedance can be simplified to that of a cascode LNA

• The input matching is unaffected by the auxiliary transistor

12 <<BACLs

A

AaA

AGin C

LgsL

sCsLZ 11

+++=

34

AMSC Effect on Input Match

• Effect on input match (S11) with and without auxiliary transistor

202 MHz188 MHz

Without Auxiliary

With Auxiliary

35

AMSC Effect on NF

• The gate noise current of the auxiliary transistor gets added with the drain noise current of main transistor and is attenuated by the gain of LNA

36

AMSC Effect on NF

• 0.3dB degradation in NF observed• Lossy inductor in the auxiliary branch

contributes to increased NF

NF with auxiliary transistor

NF without auxiliary transistor

37

AMSC LNA Design

• Linear LNA was designed and fabricated in TSMC 0.35µm CMOS technology

• The inductors were designed using ASITIC and a Q of 2.5 was obtained

• The LNA was designed to have maximum gain at 900MHz

• The LNA fabricated was a stand alone LNA terminated by the 50Ω port impedance

38

AMSC Component Values

10 nHLD

1.05 nHLB

5 nHLA

30 nHLG

24 µm/0.4 µm, m=36MB

24 µm/0.4 µm, m=16MC

24 µm/0.4 µm, m=16MA

ValueComponent

39

AMSC Chip Photograph

40

AMSC Testing Strategy

• The gain obtained in LNA is less as it sees a 50Ω load impedance

• Gain can be improved by connecting a resistor in series with the port

•LNA Gain= 5050* +

=R

VV

VV

in

out

in

x

41

AMSC Advantages

• Increased gain results in larger signal swings

• LNA subject to large signal swings is an ideal test for linearity

• Linearity of LNA unaffected due to linear resistive element

42

AMSC Experimental Results

• R=0Ω, S11=-15.85 dB, S21=4.4 dB, Gain= 4.4 dB

S21 (Power Gain)S11 (Input Match)

43

AMSC Experimental Results

• R=75 Ω, S11=-11.7 dB, S21=1.5 dB, Gain= 9.5 dB

S21 (Power Gain)S11 (Input Match)

44

AMSC IIP3 Test Setup

45

AMSC IIP3 Measurement

• Pin=-10dBm, Pf= -13.2dBm PIM3= -75.07dBm

• IIP3 = +20.93 dBm

PowerOutputtoneIMTotalP

PowerOutputSignalTotalPPowerInputSignalTotalPwhere

PPPdBmIIP

IM

f

in

IMfin

3

2)(3

3

3

=

==

−+=

• R=75 Ω

46

AMSC IIP3 MeasurementO

utpu

t Pow

er p

er to

ne (d

Bm

)

47

AMSC Experimental Results

• R=100 Ω, S11=-10.7 dB, S21=1.1 dB, Gain= 10.6 dBS21 (Power Gain)S11 (Input Match)

48

AMSC IIP3 MeasurementO

utpu

t Pow

er p

er to

ne (d

Bm

)

49

AMSC Summary of Results

20.511.5-0.5-9.5150

2110.61.1-10.7100

20.99.51.5-11.775

204.44.4-15.850

IIP3 (dBm)LNA Gain (dB)S21 (dB)S11 (dB)R (Ω)

50

AMSC De-embedding Results

• 6dB increment in gain when ‘R’ is changed from 0Ω to 100Ω and hence on-chip load resistance can be computed to be 150Ω

• Gain of LNA with Zext=∞ is 6dB more than gain with R=100Ω• Gain of LNA adding other losses is estimated to be 18.5dB• The NF of the LNA after de-embedding the noise contribution of

termination resistors (R=100Ω and 50Ω port) is calculated to be

1.76dB

51

AMSC Comparison of Results

23.5

8.9

11.7

5.4

24.2

45

21.1

22.5

Pdc

(mW)

54

29

124

117

503

3

19

793

FOM

221.6515.50.90.25µm CMOSMTT ‘05

10.51.814.60.90.25µm CMOSISCAS ‘04

11.71.415.70.880.5µm SiGe BiCMOSESSCC ‘05

15.62.8100.90.35µm CMOSJSSC ‘04

182.82.50.90.35µm CMOSISSCC ‘01

16.1314.92.20.25µm CMOSISSCC ‘03

151.96.530.18µm CMOSISCAS ‘04

211.7618.50.950.35µm CMOSThis Work

IIP3 (dBm)

NF (dB)

Gain (dB)

Freq (GHz)TechnologyWork

52

AMSC

Fig 1 shows the simplified small signal model of LNA. RL is the load impedance of LNA presented by the LC resonant circuit at the output, R is the external resistor connected to improve the gain and 50Ω is the resistance of the port.

Fig 1: Small Signal Model

De-Embedding the NF of LNA

53

AMSC

For numerical analysis a value of RL=150Ω and R=75Ω are used below.

From Table 3 in the paper, the measured gain at the point VLNA shown in Fig 1 is 10.5dB for R=75Ω and NF is 2.95dB. Hence

(1)972.1101 1095.2

250

2==+=

Ω

−

VV

NF inmeasured

54

AMSC Noise Analysis at output:

Fig 2: Noise Analysis

Fig 2 shows the model used for noise analysis. 2LNAi and

2RLi

are the noise currents due to input transistor and the load resistance (RL) respectively. 22RLLNA ii + is reflected to the output port to generate

2_ outLNAv

.

55

AMSC

The resistors R and 50Ω generate an output noise voltage at the node ‘OUT’ given by

( )( )72.0*50*4

5050*

5050*4

505050

505014

2

2

22

22

KT

RRR

RRRR

KT

RRR

RRRR

KTV

LL

L

LL

Ladd

=

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

+++⎟⎟

⎠

⎞⎜⎜⎝

⎛++

+=

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛++

+⎟⎟⎠

⎞⎜⎜⎝

⎛++

+=

(2)

The output noise measured at the node ‘OUT’ is the sum of noise contributed by the LNA and the output resistive network formed by R and 50Ω and is given as follows.

56

AMSC

))2((72.0*50*450

50*

5050*

22

_

22

2_

2

fromKTR

V

VR

VV

outLNA

addoutLNAoutmeasured

+⎟⎠⎞

⎜⎝⎛

+=

+⎟⎠⎞

⎜⎝⎛

+=− (3)

The overall gain of LNA for R=75Ω is given as follows.

34.14.0*35.3)(

4.07550

50

35.35.10

*

_

_

_

_

==

=+

=

==

==

v

outLNA

out

in

outLNA

outLNA

out

in

outLNA

in

out

AGainOverall

VV

dBV

V

VV

VV

VV

GainOverall

57

AMSC

Total input measured noise is given as follows.

))3((72.0*50*42

2

2

22

fromA

KTV

AV

V

vinLNA

v

outmeasuredinmeasured

+=

=

−

−−

Where 2inLNAV − is the total input referred noise contribution of LNA and RL alone.

50*4250 KTVLet n =

. Hence total input referred noise contribution of LNA and the load resistor alone is given by

( )( )5.0

4.09.0

))1((72.0*

110

250

250

2

25010

95.2250

2

n

n

v

nninLNA

V

V

fromA

VVV

=

−=

−⎥⎦⎤

⎢⎣⎡ −=−

De-embedded NF = 1+0.5=1.76dB

58

AMSC Conclusion

• A highly Linear LNA using a non-linearity cancellation technique has been proposed

• Theoretical analysis using Volterra series has been done to corroborate the idea

• The LNA has been designed and fabricated in TSMC 0.35µm technology

• An IIP3 of +21dBm has been experimentally achieved