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Sam Palermo

Analog & Mixed-Signal Center

Texas A&M University

ECEN620: Network Theory

Broadband Circuit DesignFall 2012

Lecture 16: VCO Phase Noise

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Agenda

Phase Noise Definition and Impact

Ideal Oscillator Phase Noise

Leeson Model

Hajimiri Model

2

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Phase Noise Definition

An ideal oscillator has an impulse shape in the frequency domain

A real oscillator has phase noise skirts centered at the carrier frequency

Phase noise is quantified as the normalized noise power in a 1Hzbandwidth at a frequency offset from the carrier

3

( )( )

( )dBc/HzP

1Hz,Plog10

carrier

sideband

+=

oL

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Phase Noise Impact in RF Communication

At the RX, a large interferer can degrade theSNR of the wanted signal due to reciprocalmixing caused by the LO phase noise

Having large phase noise at the TX can degrade

the performance of a nearby RX 4

RX Reciprocal Mixing Strong Noisy TX Interfering with RX

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Jitter Impact in HS Links

5

RX sample clock jitter reduces the timing marginof the system for a given bit-error-rate

TX jitter also reduces timing margin, and can be

amplified by low-pass channels

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6

2

tank

22

2

isvoltagenoisesquared-meantheofdensityspectralThe

4

noisethermalintroducewillresistancetankThe

Zf

i

f

v

R

kT

f

i

nn

n

=

=

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Tank Impedance Near Resonance

7

( )

( )( )

( )

( )2

2

tank

tank

22tank

2tank

2

2

1Tank

1

2221

resonancetoclosesfrequencieConsider

1:FrequencyResonance

11

=

==

=

+=

+=

=

==

Q

RZ

Q

RjZ

Q

R

CCRQ

C

j

LC

Lj

LCLCLC

LjZ

LC

LCLjLj

CjZ

o

o

o

o

o

oo

o

oo

o

o

o

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8

{ } ( )

carrierthefromawayslope20dB/dec-adisplaywillnoisethermaltoduenoisePhase

dBc/Hz2

2log10

phase.andamplitudebetween2

1evenly

splitispowernoisethisTherefore,equal.arepowernoise-phaseandamplitude

m,equilibriuinthat,states2000]JSSC[LeeTheoremionEquipartitThe

242

4

2

22

2

tank

22

=

=

==

QP

kTL

QkTRQ

R

R

kT

Zf

i

f

v

o

sig

oonn

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Other Phase Noise Sources

Tank thermal noise is only one piece of thephase noise puzzle

Oscillator transistors introduce their own thermal

noise and also flicker (1/f) noise 9

[Perrott]

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Leeson Phase Noise Model

10

Leesons model modifies thepreviously derived expression toaccount for the high frequencynoise floor and 1/f noiseupconversion

A empirical fitting parameter F isintroduced to account forincreased thermal noise

Model predicts that the (1/)3region boundary is equal to the1/f corner of device noise andthe oscillator noise flattens athalf the resonator bandwidth

{ } ( )dBc/Hz1212log10

3

1

2

+

+=

fo

sigQP

FkTL

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11 ELEN620-IC Design of Broadband Communication circuit

A 3.5GHz LC tank VCO PhaseNoise

MeasurePhase

noise

-30dB/decade -20dB/decade

-105dBc

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VCO Output Spectrum Example

-85dBm

-20dBm

RBW=10K

PN=-85dBm-(-20dBm)-10log10(10e3)

=-105dBc

dBc---in dBwith respect to

carrier

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Leeson Model Issues

13

The empirical fittingparameter F is not knownin advance and can varywith different processtechnologies and

oscillator topologies

The actual transitionfrequencies predicted bythe Leeson model doesnot always matchmeasured data

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YCLO

AMSC-TAMU 14

Harjimiris Model (T. H. Lee) Injection at Peak (amplitude noise only)

Injection at Zero Crossing (maximum phase noise)

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A time-Varying Phase Noise model: Hajimiri-Lee model

Impulse applied to the tank to measure its sensitivity

function

The impulse response for the phase variation can be represented as

f

in

2

is the impulse sensitivity function ISFqmax, the maximum charge displacement across the capacitor, is a normalizing factor

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YCLO

AMSC-TAMU 16

ISF Model

The phase variation due to injecting noise can be

modeled as:

The function, (x), is the time-varying proportionalityfactor and called the impulse sensitivity function.

The phase shift is assumed linear to injection charge.

ISF has the same oscillation period T of the oscillatoritself.

The unity phase impulse response can be written as:

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How to obtain the Impulse sensitivi ty function

for a LC oscillator

() can be obtained using CadenceConsider the effect on phase noise of each noise source

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YCLO

AMSC-TAMU 18

Typical ISF Example

The ISF can be estimated analytically or calculated

from simulation. The ISF reaches peak during zero crossing and zeroat peak.

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Phase Noise Computation

19

( )( )

( )

( ) ( ) ( ) ( ) ( )

diq

dith

tuq

th

t

o

o

==

=

max

max

1,t

functionimpulsenoisephaseth thecurrent winoisearbitraryany

theofintegralon)(convolutiionsuperpositby thecomputedbecan thennoisephaseThe

,

functionimpulsenoisephaseobtain thetousedisfunctionysensitivitimpulseThe

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ISF Decomposition w/ Fourier Series

20

( ) ( )

( ) ( ) ( ) ( )

ts.coefficienISFthetoaccordingscaledand

bandsfrequencydifferentfromdownmixedisnoisecurrentthey,Essentialld.detereminearetscoefficien

FourierISFtheoncecomputedbetosourcenoisearbitraryanfromphaseexcesstheallowsThis

cos2

1t

bycomputedbecan thennoisephaseThe

harmonic.ISFththeofphasetheisandrealaretscoefficienthewhere

cos2

seriesFourieraasexpressedbemayitperiodic,isISFthebecauseandinsight,furthergainorder toIn

1

0

max

1

0

+=

++=

=

=

n

o

t

n

t

nn

n

nono

dnicdicq

nc

ncc

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Phase Noise Frequency Conversion

21

( ) ( )[ ]

( )( )

( ) ( )[ ]

( )

.1

toalproportionispowerthat thisNote

4log10

powerthcarrier wiabout thesymmetricsidebandsightedequally wetwobewillthere,cos

waveformsinusoidalaAssuming.atsidebandsequaltwoshowwillspectrumfrequencyresultingThe

2

sin

other than

termsallfromoncontributinegligibleabewillthereintegral,ncomputationoisephasetheperformingWhen

cos

frequencynoscillatiotheofmultipleinteger

annearisfrequencyosecurrent whnoisesinusoidalahavewewherecasesimpleaconsiderFirst

2

2

max

max

+=

=

+=

q

cIP

tttv

q

tcIt

mn

tmIti

m

mmSBC

oout

mm

om

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Phase Noise Due to White & 1/f Sources

22

( )

.1byweightedand

teddownconvergetscarriertheofmultiplesintegerhighernearnoiseWhitethere.stayscarriernear theNoise

carrier.near thenoise1becomesnoise1so,tcoefficienbyweightedd,upconvertegetsdcnearNoise

.1

byweightedareanditself

carriernear thefoldallfrequencycarriertheofmultiplesintegernearcomponentsnoiseHere

4log10

inresultssourcenoisewhiteaofcasegeneralthetoanalysisprevioustheExtending

2

3

0

2

22

max

0

22

f

ffc

q

cf

i

P mm

n

SBC

=

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How to Minimize Phase Noise?

23

( )

( )

s.frequencieallatnoisephasethereducewillreducingThus,

2log10

asexpressedbecanregion1in thespectrumThe

21

theoremsParseval'Usingminimized.beshouldtscoefficienISFthenoise,phaseminimizeorder toIn

22

max

2

2

2

2

0

22

0

2

rms

rmsn

rms

m

m

n

q

fi

L

f

dxxc

c

=

==

=

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1/f Corner Frequency

24

( )

noise.1inreductionsdramaticforpotentialtheisethen thersymmetry,time-falland-risethrough

minimizedisIfcorner.noisecuitdevice/cir1thelower thangenerallyisThis

4

isfrequencycorner1theThus,

8log10

slideprevioustheFrom

frequencycorner1theiswhere

content1includeswhichnoisecurrentConsider

2

12

2

011

3

1

22

max

2

0

2

1

122

1,

3

f

f

c

f

q

cf

i

L

f

ii

f

dc

rms

dcf

rms

ff

f

n

f

f

nfn

=

=

=

=

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Cyclostationary Noise Treatment

25

( ) ( ) ( )

( )

( ) ( ) ( )xxx

x

i

ttiti

n

nn

=

=

eff

0

00

ISFeffectiveanformulate

canwethis,Usingunity.ofpeak valueaithfunction wunitlessperiodicaisandsource,noise

onarycyclostatitheofthattoequalispeak valuewhosesourcenoisewhitestationaryaisHere

function.periodicaand

noisewhitestationaryofproducttheasitgby treatinthishandleeasilycanmodelLTVThe

cycle.oscillatoranoverlydramaticalchangecannoise,thusandcurrent,drainTransistor

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Key Oscillator Design Points

26

As the LTI model predicts, oscillator signal powerand Q should be maximized

Ideally, the energy returned to the tank should bedelivered all at once when the ISF is minimum

Oscillators with symmetry properties that have smalldc will provide minimum 1/f noise upconversion

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Phasor-Based Phase Noise Analysis

27

Models noise at 2 sideband frequencieswith modulation terms

The 1 and 2 terms sum co-linear with

the carrier phasor and produceamplitude modulation (AM)

The 1 and 2 terms sum orthogonalwith the carrier phasor and producephase modulation (PM)

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Phasor-Based LC Oscillator Analysis

28

This phasor-based approachcan be used to find closed-form expressions for LCoscillator phase noise that

provide design insight

In particular, an accurate

expression for the Leesonmodel F parameter is obtained

{ } ( )dBc/Hz2

2log10

2

=

QP

FkTL o

sig

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LC Oscillator F Parameter

29

1st Term = Tank Resistance Noise

2nd Term = Cross-Coupled Pair Noise

3rd Term = Tail Current Source Noise

{ } ( )dBc/Hz22log10

2

= QP

FkTL osig

The above expression gives us insight on how to optimizethe oscillator to reduce phase noise

The tail current source is often a significant contributor to

total noise

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Tail Current Noise

The switching differential pair can be modeled as a

mixer for noise in the current sourceOnly the noise located at even harmonics willproduce phase noise.

YCLO

AMSC-TAMU 30

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Loading in Current-Biased Oscillator

YCLO

AMSC-TAMU 31

The current sourceplays 2 roles It sets the oscillator bias

current Provides a high impedance

in series with theswitching transistors toprevent resonator loading

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Noise Filtering in Oscillator

Only thermal noise in the current source transistor around 2ndharmonic of the oscillation causes phase noise.

In balanced circuits, odd harmonics circulate in a differentialpath, while even harmonics flow in a common-mode path

A high impedance at the tail is only required at the 2nd harmonicto stop the differential pair FETs in triode from loading the

resonator.

YCLO

AMSC-TAMU 32

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Tail-biased VCO with noise filtering.

YCLO

AMSC-TAMU 33

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Phase Noise w/ Tail Current Filtering

34

Tail current noise filtering provides near 7dB improvement

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A top-biased VCO often provides improved substrate

noise rejection and reduced flicker noise

YCLO

AMSC-TAMU 35

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Next Time

Divider Circuits

36

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The input sensitivity function can be characterized as a Fourier Series:

An the phase noise is then

Therefore:

In general the impulse sensitivity function is periodic with a

fundamental frequency equal to the oscillating frequency

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Due to the periodicity of the terms, the series converge to (n=m term only):

Phase noise

If the input noise is represented as

m0(m-1)0

m0

Noise

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39 ELEN620 IC D i f B db dC i ti i it

If the input noise is represented by its power distribution function

For small noise level

( )( )

( ) ( ) ( )( )

( ) ( )( ) ( )ttsinVtcosVV

tsintsinVtcosVV

ttcosVV

o0o0out

o0o0out

o0out

+=

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