PowerPoint Presentationrfic.eecs.berkeley.edu/.../pdf/eecs242_lect23_phasenoise.pdf · 2009. 8....

A. Tasic © 20091

On the Phase Noise

and Noise Factor in

Circuits and Systems -New Thoughts on an Old

SubjectAleksandar Tasic

QCT - Analog/RF Group

Qualcomm Incorporated, San Diego

A. Tasic © 2009 2

Outline

• Spectral Analysis of Noise in LC-Oscillators

• LC-tank, gm-cell, bias current source noise

• (Phase-) Noise factor

• Bipolar vs. CMOS LC-Oscillators

• LC-Oscillators Noise Reduction Methods

• Mixer Noise Factor from VCO Noise Factor

• Oscillator Phase Noise in Receiver’s SNR

• LNA and Mixer Noise Factors in a Receiver

• BBFilter Noise Transfer vs. LO/Mix Duty

A. Tasic © 20093

Phase Noise Model

of Bipolar and

CMOS

LC-Oscillators

A. Tasic © 20094

Outline

• Oscillation Condition

• LC-Tank Noise Folding

• gm-Cell Noise Folding

• Bias-Current Source Noise Folding

• Phase-Noise Model of Bipolar LC-Oscillators

• Phase-Noise Model of CMOS LC-Oscillators


A. Tasic © 20095

LC-Oscillator Noise Sources

LC-tank noise

transconductor noise

bias current source noise

L/2

Q1 Q

2

QCS

~ ~

vB1

vB2

iC1 iC2

iB2iB1

iGTK

iBCS

2C

ITAIL

RTK/2 RTK/2

L/2

2C

2 ( ) 2 / 2N C C mi I qI KTg

2 ( ) 2N TK TKi G KTG

2 ( ) 2N B Bv r KTr

2

, , ,( ) (1 2 )N BCS m CS B CS m CSi I KTg r g

A. Tasic © 20096

Oscillator and Phase-Noise Model

• phase-modulating noise component (double-sided)

*0 , 0 , 0

1( ) ( ) ( )

2PM N O N Oi f i f i f

*0 , 0 , 0

1( ) ( ) ( )

2PM N O N Oi f i f i f

• phase-related noise power (single-sided)2

2 2 ,2, 0 0 0 2

1( ) ( ) ( )

2 4

PM TOTPM TOT PM PM

TOT

iv i f i f Z f

C

iAM

iS

iPM

*, 0( )N Oi f

, 0( )N Oi f‘

‘

LC-tank

gm-cell

+Nv

,NOv

,NOi

A. Tasic © 20097

gm-Cell Transfer Function

• Fourier domain – (magnitude) complex harmonic components

2f0f0-f0f0-2

g0 g2g-2

f0-4

g-4 g4

4f03f0-3f0

2

2

sin( )i

i dg gd

i d

00

0

/ 42

2/4

0

2( )

Tj i t

iT

g g t e dtT

1

2d

k

• small-signal gain in the presence of a large signal

1 / f 0

1 / 2 f 0

- g = g m / 2 d / 2 f 0

t

i OUT

v S

= d i d v S g IN OUT

A. Tasic © 20098

Oscillation Condition• harmonics: gm-cell and oscillation signal

• convolution:

• oscillation signal:

• oscillation condition:

g0

2f0f0-f0f0-2

g2g-2

vS/2 vS/2

g0

2f0f0-f0f0-2

g-2

g0

g2vS/2 vS/2vS/2 vS/2

0 0 0 00 0 2 2 0 2

( ) ( ) ( ) ( )( )

2 2 2 2

S S S SS TK S TK

v f v f v f v fv g g g g R g g v R

0 2 TKg g Gsmall-signal loop gain:

k=RTKgm/2

duty cycle:

d=1/(2k)

A. Tasic © 20099

0( )Nv f

2f0f0-f0f0-2

g0

0( )Nv f0( )Nv f

0( )Nv f

g2g-2

0( )Nv f

2f0f0-f0f0-2

g0 0( )Nv f0( )Nv f

0( )Nv f g0g0g0

LC-Tank Noise Folding• convolution: g0 and g 2 harmonics and LC-tank noise

0( )Nv f

2f0f0-f0f0-2

g0

0( )Nv f0( )Nv f

0( )Nv f

g2g-2

0( )Nv f

2f0f0-f0f0-2

0( )Nv f 0( )Nv f0( )Nv fg-2 g2g2g-2

A. Tasic © 200910

• LC-tank noise contribution:

LC-Tank Noise Folding

, 0 0 0 2 0( ) ( ) ( )N O N Ni f g v f g v f

, 0 0 0 2 0( ) ( ) ( )N O N Ni f g v f g v f

, 0 0 0 2 0( ) ( ) ( )N O N Ni f g v f g v f

, 0 0 0 2 0( ) ( ) ( )N O N Ni f g v f g v f

0( )

Nv f

2f0f0-f0f0-2

g0 0( )

Nv f

0( )

Nv f

0( )

Nv f g0g0g0

0( )

Nv f

2f0f0-f0f0-2

0( )

Nv f 0

( )N

v f0

( )N

v fg-2 g2g2g-2

A. Tasic © 200911

LC-Tank Noise Contribution• phase-modulating noise component:

• LC-tank noise transfer function:

2 2 2 220 22( ) ( ) 2 ( )2 ( ) 4

( ) 14 4 4 4

N NPM TK TK TKTK TKTK

TK TK TK TK

g g v R G v Ri R KTGF R

KTG KTG KTG KTG

• LC-tank noise factor:

, 0 , 0 , 0 , 0

1( ) ( ) ( ) ( )

2PM N O N O N O N Oi i f i f i f i f

0 2 0 0 2 0( ) ( ) ( ) ( )PM N Ni g g v f g g v f

• phase-related noise power (k>>1, g=g0=g 2):

2 2 20 2( ) ( )TK TKg R g g G

2 2 20 2( ) ( ) ( )

PM NTK TKi R g g v R

A. Tasic © 200912

0( )

Nv f

2f0f0-f0f0-2

g0

0( )

Nv f

0( 3 )

Nv f

0( 3 )

Nv f

g2g-2

0( )

Nv f

2f0f0-f0f0-2

g0 0( )

Nv f

0( )

Nv f

0( )

Nv f g0g0g0

0( )

Nv f

2f0f0-f0f0-2

0( )

Nv f 0

( )N

v f0

( )N

v fg-2 g2g2g-2

f0-4

g-4

0(3 )

Nv f

0(3 )

Nv f

g4

0( )

Nv f

0( )

Nv f

4f03f0-3f0

gm-Cell Noise Folding• convolution: g0 and g 2 harmonics and f0 gm-cell noise

• gm-cell noise around odd multiples of the oscillation frequency is

folded to the LC-tank noise around the oscillation frequency

A. Tasic © 2007 13

gm-Cell Noise Contribution

• phase-modulating noise component:

• number of (g2i-2+g2i) folding pairs:

• phase-related noise power (k>>1, g=g0=g 2=…):

0 2 0 0 2 0

2 4 0 2 4 0

2 2 2 0 2 2 2 0

( ) ( ) ( ) ( )

+( ) (3 ) ( ) (3 ) ...

+( ) ((2 1) ) ( ) ((2 1) )

PM N N

N N

i i N i i N

i g g v f g g v f

g g v f g g v f

g g v i f g g v i f

2 2 2 2 20 2 2 4 2 2 2( ) ( ) ( ) ... ( ) ( )

PM Nm IN i i m INi g g g g g g g v g

• number of g2i harmonic components:

0

0

2 1 1

2

f

d f d

1 2

2 2

kk

d

-g=gm/2d/2f0

t

fd/2f0

A. Tasic © 200914

gm-Cell Noise Contributions

2 22 (2 ) 2 4(2 ) 2

4 4

PM B TK BB B TK

TK TK

i r kG KTrF r kr G kc

KTG KTG

• gm-cell noise factors:

• phase-related noise power:2

2 2 2 2 2 222 2 2

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

2PM N N N

im IN i i m IN m IN m IN

gi g g g v g v g dg v g

d d

• gm-cell noise transfer function:

2 2 2 2 21( ) 2 2 ( ) 2 ( )

2 2

mm IN TK TK

gg g dg d kG kG

k

2 22 (2 ) 2 2 / 1(2 ) /

24 4

PM C TK mC TK m

TK TK

i I kG KT gF I kG g

KTG KTG

A. Tasic © 2007 15

2 2 2 2 2 20 2 4 2 2( ) 2 4 4 ... 4 ( )

PM NB i Bi r g g g g v r

2

0

2

/ 2

22 2 2 2 2 22

2 21 / 2 0

2 4 4( ) 2 2 ( ) (1 )

3

T

B i

i T

tg r g g g t dt g dt g d

T T

22 ( ) 2(2 ) 2

34

PM B

B

TK

i rF r kc

KTG

rB Noise Contribution – Be Precise

• phase-related noise power (k>>1):

• Paseval’s Theorem:

• rB noise factor:

A. Tasic © 200916

Bias Current-Source Noise

Transfer Function• gm-cell large-signal V-to-I transfer function

I

VIN

1/f0

OUT

1 / f

1

-1

IOUT

0

• Fourier domain – (magnitude) complex harmonic components

2f0f0-f0f0-2

c1c-1

f0-4

c-3 c3

4f03f0-3f0

2 1

sin((2 1) / 2)

(2 1) / 2i

ic

i

A. Tasic © 200917

• BCS noise factor:

• phase-related noise power:

• BCS noise transfer function:

22 ( ) (1 2 ) 2 (1 2 )( )

4 4 4

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

2 2

PM BCS m B m TKBCS

TK TK TK

C B

i I KTg r g KT kG kcF I

KTG KTG KTG

k kc k kc k F I F r

BCS Noise Contribution

2,2 2( ) 1

( ) ( )4 4

PM DIFF BCSPM BCS N BCS

i Ii I i I

2 1( )

4BCSg I

BCS noise around even multiples of the oscillation frequency is

folded to the LC-tank noise around the oscillation frequency

A. Tasic © 200918

Phase-Noise Model of

Bipolar Switching LC-Oscillators

• Noise factor:

( ) (2 ) (2 ) ( )

1 2 1 1 21 ( ) 1 (1 ) ( )

2 3 2 2 3

TK C B BCSF F R F I F r F I

F kc k kc k kc k

2 2 2

( ) (2 ) (2 ) ( ) 4

(4 ) (4 )S

TK C B BCS TK

TOT TOT

R I r I KTG F

C v C

L L L LL

• Phase noise:

2

2 2

1 21 (1 ) ( )

4 2 3( )8(4 )

TK

TTOT

k kc kKTG

VC kL

8S Tv kV

A. Tasic © 200919

• Constant phase-noise contributions

• LC-tank noise contribution ~ 1

• gm-cell current shot noise contribution ~ ½

• Small-signal loop-gain related contributions

• gm-cell base-resistance noise contribution ~ 0.66ck

• phase-noise contribution of the bias current source is

k-times larger then the noise contribution of the gm-cell ~

k(½+ck)!

Phase Noise Model of

Bipolar Switching LC-Oscillators

1 2 11 ( )

2 3 2F kc k kc

A. Tasic © 200920

• high ss loop-gain, high quality LC-tank, BCS noise present:

2

1 1( )

3 1 12 2~ ~5 10

k kc kc

kk kL

e.g., k>>1(=10), c<<1(~0.01)

2

7 3(1 )

56 2~ ~ 14

k

kL

e.g., k~1(=2), c~1(~0.5)

Low/High-Performance VCO Designs

• low ss loop-gain, low quality LC-tank, BCS noise present:

• high ss loop-gain, high quality LC-tank, BCS noise eliminated:

e.g., k>>1(=10), c<<1(~0.01)

2 2

1 21

7.8 1 1 12 3~ ~5 10 10

kc

k kL

A. Tasic © 200921

Single/Double-Switch CMOS LC-VCOs

2

,( ) 2N BCS m CSi I KT g

2 ( ) 2N D mi I KT g

2 ( ) 2N TK TKi G KTG

TKN

m

Gd

g

Q1 Q

2

Q3 Q

4

Q2

QCS

iD1 iD2

iBCS

Q1

iD1 iD2

iBCSQCS

iD3 iD4

L/2

iGTK

2C

RTK/2 RTK/2

L/2

2C

VDD

L/2

iGTK

2C

RTK/2 RTK/2

L/2

2C

2

TKC

m

Gd

g

2

, ,( ) 2N D P P m Pi I KT g

2

, ,( ) 2N D N N m Ni I KT g

A. Tasic © 200922


CMOS LC-Oscillators

,

( ) (2 ) ( )

1 /(4 )

SS TK D BCS

SS m CS TK

F F R F I F I

F g G

2 2 2

( ) (2 ) ( ) 4

(4 ) (4 )S

TK D BCS TK

TOT TOT

R I I KTG F

C v C

L L LL

• Phase noise:

,

22

1 /(4 )4

2(4 ) ( )

m CS TKTKSS

TAIL TK

g GKTG

C I R

L

• Noise factor ( N= P, gm,N=gm,P):

,

( ) (4 ) ( )

1 /

DS TK D BCS

DS m CS TK

F F R F I F I

F g G

,

22

1 /4

4(4 ) ( )

m CS TKTKDS

TAIL TK

g GKTG

C I R

L

A. Tasic © 200923


CMOS LC-Oscillators

• Constant phase-noise contributions

• LC-tank noise contribution ~ 1

• gm-cell drain-current thermal noise contribution ~

• Small-signal loop-gain related contributions (?)

• bias current source noise contribution ~ gm,CS/GTK (k )

,1 /m CS TKF g G

A. Tasic © 200924

CMOS vs. Bipolar LC-Oscillators

1 21

2 3BIPF kc

1CMOSF

• noise factors (for removed BCS noise):

• bipolar VCO better for the same power consumption (vs,BIP=vs,CMOS)

3 2 5

2 3 3kc

8

TKB

Rkr

• e.g., k=10, RTK=800

80010

80Br

• e.g., k=10, RTK=80

801

80Br

A. Tasic © 200925

CMOS vs. Bipolar LC-Oscillators

• power consumption figure of merit:

• VCC=1.8V, vs,BIP=0.4V, vs,SS-CMOS=1.2V, (3ICC,BIP=ICC,SS-CMOS)

2

0

10log ( ) CC CCFOM V IL

4.8BIP SS CMOSFOM FOM dB

• VCC=1.8V, vs,BIP=0.4V, vs,DS-CMOS=1.2V, (1.5ICC,BIP=ICC,DS-CMOS)

7.8BIP DS CMOSFOM FOM dB

A. Tasic © 200926

Phase-Noise Model Conclusions

Parametric Phase-Noise Model

electrical circuit parameters (ss loop gain)

worst-case phase noise (bandwidth unlimited)

Bipolar vs. CMOS LC-Oscillators

bipolar ss loop-gain related contributions

vS,BIP~k (<<VCC), vS,CMOS~VCC

bipolar capacitive tapping for larger vS,BIP, but

also larger k-related noise contributions and

power consumption

A. Tasic © 2007 27

Verification of the Phase-Noise Model

A. Tasic © 2007 28

VCO Noise Contributions

LC-tank

noise ~ 1

transconductor

noise ~

n(0.5+0.66c•k)

bias current-source

noise ~ n(0.5+c•k)•k

Q1 Q

2

QCS

vB1

vB2

iC1 iC2

iB2iB1

iBCS

CA

CB

CA

CB

ITAIL

C C

L

V V

iGTK

VCC

VTUNE

~ ~

• f0~5.74GHz, RTK~340 , n~1.65, c~0.25, VCC=2.2V

A. Tasic © 2007 29

gm-Cell Noise Contributions

0,7

0,75

0,8

0,85

0,9

0,95

1

4 6 8 9,6

calculations

simulations

F (2IC)

k

0

0,5

1

1,5

2

2,5

4 6 8 9,6

calculations

simulations

F (2r B)

k

( ) 0.872

C

nF I

2 2(2 ) 1.65 0.25 0.27

3 3BF r nkc k k

• k=0.5gmRTK<0.5gm,actualRTK=0.5gmRTK/(1+gmrE)=kactual

A. Tasic © 2007 30

Bias Noise Contributions

,

1( ) 0.82

2C CSF I nk k

0

1

2

3

4

5

6

7

4 6 8 9,6

calculation

s

simulations

F (I C,CS)

k

0

2

4

6

8

10

12

14

16

18

20

4 6 8 9.6

calculation

simulation

s

F (r B,CS )

k

2 2,( ) 1.65 0.25 0.41B CSF r knkc k k

A. Tasic © 200931

Suppression of Bias Current-Source Noise

in

LC-Oscillators

A. Tasic © 2009

Outline

• Contribution of Bias Current-Source Noise to Phase Noise of LC-Oscillators

• Techniques for Reduction of Bias Current-Source Noise

• Noise Analysis of Degenerated Bias Current Source

• Bias Noise Suppression - Design Example

32

A. Tasic © 200933


LC-tank

noise ~ 1

transconductor

noise ~ 0.5+c•k

bias current-source

noise ~ (0.5+c•k)•k

Q1 Q

2

QCS

vB1

vB2

iC1 iC2

iB2iB1

iBCS

CA

CB

CA

CB

ITAIL

C C

L

V V

iGTK

VCC

VTUNE

~~

A. Tasic © 200934


0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

4 6 8 9.6

r B,CS

I C,CS

r B

I C

R TK

BCS:

~85%

g m :

~15%

k

• f0~5.74GHz, RTK~340 , n~1.65, c~0.25, VCC=2.2V

A. Tasic © 2007 35

Phase-Noise Ratio

0

1

2

3

4

5

6

7

8

9

10

4 6 8 9.6

PNR [dB]

k

( )( ) (2 ) (2 ) ( ) 21

2( ) (2 ) (2 ) 12 3

TK C B BCS

TK C B

nk nkc

R I r IPNR

nR I r nkc

L L L L

L L L

PNR=8.2dB

A. Tasic © 200936

Bias Noise Reduction Techniques

resonant inductive degeneration (RID) resistive degeneration (RD) common emitter (CE)

high supply

required large area if

integrated

noise injection if

discrete

transconductor

noise always ON

reduced output

impedance

resistive

degenerationinductive

degenerationfiltering?

VIN

ITAIL

VIN

ITAIL

RD

LD

VIN

ITAIL

+-

CD

A. Tasic © 200937

Capacitive Filtering

AC short

AC open

2

0

1

d/ 0f2

1/ f0

1/ f0

0

d’/ 0f2

1

1' (1 )

2d d

'(2 ) ~2

C

nF I k

1

2d

k

(2 ) ~2

C

nF I

• for k=10, d=5%, d’=52.5%, and F’>F

A. Tasic © 200938

Bias Current Source with

Resonant-Inductive Degeneration

LRID matched to C at 2f0

rB,CS noise contribution reduced

transconductance gain small at resonance

series resonance

IB,CS noise contribution small

common-base like configuration (gain of 1)

IC,CS noise contribution removed

parallel resonance

emitter open at resonance (IC,CS floats)

LRID

VIN

ITAIL

C

A. Tasic © 2007 39

Circuit Diagram for Noise

Transfer Functions

• iC,CS to iOUT: vB,CS short, iB,CS open

• iB,CS to iOUT: vB,CS short, iC,CS open

• vB, CS to iOUT: iC,CS open, iB,CS open

~(vB

- vE)g

C

E

B

LRID

rB C

iOUT,CS

~vB

iB i

C

m,CS

,CS

,CS

,CS

,CS,CS

A. Tasic © 2007 40

Bias Current-Source Noise

Contributions

,

2,,,

1( ) 1

1( )1 ( )

m CSOUT

B CSN B CSB mm CS

TRID RID

gif

C r fi Ir gg j C

fL j L

,

2,,,

,

1( ) 1 1 0

1( )1 ( )

m CSOUT

B CSN C CSB mm CS

T CSRID RID

gif

C r fi Ir gg j C

fL j L

,

, ,

1( ) ( )

1( )

T CSOUTm

N B CS T CST RID RID

i ff g

v r fL j L

j C

series resonance

parallel resonance

parallel resonance

A. Tasic © 2007 41

BCS w/ RID vs. BCS w/o RID

• more than a factor (fT,CS/2f0)2 noise reduction after RID

2

, ,2 2 0, , ,

0 ,

1 24 0 ( ) 2

2 2

m CS T CS

CS RID B CS m CS

T CS

g f fi kT r g

f f

, ,2 2

, ,

0

14 1 0 ( ) 2

2 2

m CS T CS

CS B CS m CS

g fi kT r g

f

• BCS noise without degeneration

• BCS noise with degeneration

• for (fT,CS/2f0)=5, a factor of 25 reduction

2

2 2 0,

,

2CS RID CS

T CS

fi i

f

A. Tasic © 200942


after RID applied to BCS• f0~5.74GHz, LRID~1.3nH, RTK~340 , n~1.65, c~0.25, VCC=2.2V

0%

20%

40%

60%

80%

100%

4 6 8 9.6

r B,CSI C,CS

r B

I C

R TK

BCS:

~6%

g m:

~94%

k

A. Tasic © 2007 43

LC-tankRID

buffer-g-cell

m

buffer

5.7GHz–band VCO

5 metals

active area 0.1mm2

LRID=2.6nH, 7-turns, 0.01mm2

A. Tasic © 200945

with RID

without RID

Phase Noise (w/ RID vs. w/o RID)

• 6dB phase-noise improvement with RID

• -112dBc/Hz @1MHz from 5.7GHz @ 4.8mA&2.2V

A. Tasic © 200946

RID Conclusions

BCS noise >> gm-cell and LC-tank noise

Resonant inductive degeneration good suppression of high frequency BCS noise

low voltage operation

small chip area (vs. discrete solutions)

BCS DC noise upconversion

large area (vs. resistive degeneration)

poorer noise suppression at high supplies (vs.

resistive degeneration)

A. Tasic © 200947

Oscillator Conclusions


• Phase-Noise Model

• LC-tank, gm-cell, bias current source

contributions


• Oscillator Noise Reduction Methods

• Resonant-Inductive Degeneration

A. Tasic © 200948

Future Worries

• Low-(Supply and Swing)-Voltage Operation

• Linear and Quasi-Linear Phase-Noise Model

• Low-Performance Oscillators

• Noise-Reduction Methods

A. Tasic © 200950

Conclusions


• LC-tank, gm-cell, bias current source noise

contributions

• Bipolar and CMOS VCO Noise Factors

• LC-Oscillators Noise Reduction Methods

• Mixer Noise Factor from VCO Noise Factor

• Oscillator Phase Noise in Receiver’s SNR

• Mixer Noise Factor in a Receiver

• LNA Noise Factor in a Receiver

• BBFilter Noise Transfer vs. LO/Mix Duty

PowerPoint Presentationrfic.eecs.berkeley.edu/.../pdf/eecs242_lect23_phasenoise.pdf · 2009. 8....

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Transcript of PowerPoint Presentationrfic.eecs.berkeley.edu/.../pdf/eecs242_lect23_phasenoise.pdf · 2009. 8....