Sam PalermoAnalog & Mixed-Signal Center

Texas A&M University

ECEN620: Network TheoryBroadband Circuit Design

Fall 2014

Lecture 11: VCO Phase Noise

Announcements & Agenda

• HW3 is due today at 5PM

• Phase Noise Definition and Impact• Ideal Oscillator Phase Noise• Leeson Model• Hajimiri Model• Phasor-Based Phase Noise Analysis

• VCO phase noise and jitter papers are posted on the website

2

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 1Hz

bandwidth at a frequency offset ∆ω from the carrier

( ) ( ) ( )dBc/Hz P

1Hz ,Plog10carrier

sideband

∆+=∆

ωωω oL

3

Phase Noise Impact in RF Communication

• At the RX, a large interferer can degrade the SNR of the wanted signal due to “reciprocal mixing” caused by the LO phase noise

• Having large phase noise at the TX can degrade the performance of a nearby RX

RX Reciprocal Mixing Strong Noisy TX Interfering with RX

4

Jitter Impact in HS Links

• RX sample clock jitter reduces the timing margin of the system for a given bit-error-rate

• TX jitter also reduces timing margin, and can be amplified by low-pass channels

5

Ideal Oscillator Phase Noise

2tank

22

2

is voltagenoise squared-mean theofdensity spectral The

4

noise thermalintroduce willresistance tank The

Zf

if

v

RkT

fi

nn

n

∆=

∆

=∆

6

Tank Impedance Near Resonance

( )

( ) ( )

( )

( )2

2tank

tank

22tank

2tank

2

2

1 Tank

12221

resonance toclose sfrequencieConsider

1 :Frequency Resonance

11

∆

=∆

∆

−≈∆

=⇒=

∆

−=∆−

−≈∆−∆−−

∆+=∆

∆+=

=

−==

ωωω

ωωω

ωω

ωω

ωωωω

ωωωωωωω

ωωω

ω

ωωω

ωω

QRZ

QRjZ

QR

CCRQ

Cj

LCLj

LCLCLCLjZ

LC

LCLjLj

CjZ

o

o

oo

o

oo

o

oo

o

o

o

7

Ideal Oscillator Phase Noise

{ } ( )

carrier thefromaway slope 20dB/dec- adisplay willnoise thermal todue noise Phase

dBc/Hz 2

2log102

421

log1021

log10

phase. and amplitudebetween 21evenly

split ispower noise thisTherefore, equal. arepower noise-phase and amplitudem,equilibriuin that,states 2000] JSSC [Lee Theoremion Equipartit The

24

24

22

22

2

222

tank

22

∆

=

∆

=

∆

=∆

∆

=

∆

=

∆=

∆

ωω

ωωω

ωω

ωω

QPkT

Qv

kTR

vf

v

L

QkTR

QR

RkTZ

fi

fv

o

sig

o

sigsig

n

oonn

• Phase noise improves as both the carrier power and Q increase8

Other Phase Noise Sources

• Tank thermal noise is only one piece of the phase noise puzzle

• Oscillator transistors introduce their own thermal noise and also flicker (1/f) noise

[Perrott]

9

Leeson Phase Noise Model

• Leeson’s model modifies the previously derived expression to account for the high frequency noise floor and 1/f noise upconversion

• A empirical fitting parameter F is introduced to account for increased thermal noise

• Model predicts that the (1/∆ω)3

region boundary is equal to the 1/f corner of device noise and the oscillator noise flattens at half the resonator bandwidth

{ } ( )dBc/Hz 12

12log1031

2

∆

∆+

∆

+=∆ω

ω

ωωω fo

sig QPFkTL

Noise Floor

1/f Noise

10

11 ELEN620-IC Design of Broadband Communication circuit

A 3.5GHz LC tank VCO Phase Noise

MeasurePhasenoise

-30dB/decade-20dB/decade

-105dBc

12 ELEN620-IC Design of Broadband Communication circuit

RBW=10K

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

=-105dBc

VCO Output Spectrum Example

-85dBm

-20dBm

dBc---in dB with respect to carrier

Make sure to account for the spectrum analyzer resolution bandwidth

Leeson Model Issues

• The empirical fitting parameter F is not known in advance and can vary with different process technologies and oscillator topologies

• The actual transition frequencies predicted by the Leeson model does not always match measured data

13

YCLOAMSC-TAMU 14

Harjimiri’s Model (T. H. Lee) Injection at Peak (amplitude noise only)

Injection at Zero Crossing (maximum phase noise)

15 ELEN620-IC Design of Broadband Communication circuit

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

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

Impulse Sensitivity Function (ISF) Model

• The phase variation due to injected noise can be modeled as

• The function Γ(ωοτ) is a time-varying proportionality factor called the “impulse sensitivity function”• Encodes information about the sensitivity of the oscillator

to an impulse injected at phase ωοτ• Phase shift is assumed linear to charge injection• ISF has the same oscillation period as the oscillator

• The phase impulse response can be written as

16

17 ELEN620-IC Design of Broadband Communication circuit

How to obtain the Impulse sensitivity function for a LC oscillator

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

YCLOAMSC-TAMU 18

Typical ISF Example The ISF can be estimated analytically or calculated from simulation. The ISF reaches peak during zero crossing and zero at peak for typical LC and ring oscillators.

Phase Noise Computation

( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) τττωτττφ

ττωτ

φ

φ

diq

dith

tuq

th

t

o

o

∫∫∞−

∞

∞−

Γ==

−Γ

=

max

max

1,t

function impulse noise phase th thecurrent wi noisearbitrary any

theof integral on)(convolutiion superposit by the computed becan then noise phase The

,

function impulse noise phase obtain the toused isfunction y sensitivit impulse The

19

ISF Decomposition w/ Fourier Series

( ) ( )

( ) ( ) ( ) ( )

ts.coefficien ISF the toaccording scaled andbandsfrequency different fromdown mixed is noisecurrent they,Essentiall d.deteremine are tscoefficien

Fourier ISF theonce computed be tosource noisearbitrary an from phase excess theallows This

cos2

1t

by computed becan then noise phase The.irrelevant is phase relative their and ed,uncorrelat are components noise that theassumed isit as

ignored, typicallyis Note, harmonic. ISFth theof phase theis and real are tscoefficien thewhere

cos2

seriesFourier a as expressed bemay it periodic, is ISF thebecause and insight,further gain order toIn

1

0

max

1

0

+=

++=Γ

∑ ∫∫

∑

∞

= ∞−∞−

∞

=

no

t

n

t

nnn

nnono

dnicdicq

nc

ncc

ττωτττφ

θθ

θτωτω

20

Phase Noise Frequency Conversion

( ) ( )[ ]

( ) ( )

( ) ( )[ ]

( )

.1 toalproportion ispower that thisNote

4log10

powerth carrier wi about the symmetric sidebands ightedequally we twobe will there,cos

waveformsinusoidal a Assuming .at sidebands equal twoshow willspectrumfrequency resulting The

2sin

other than

termsall fromon contributi negligible a be will thereintegral,n computatio noise phase theperformingWhen

cos

frequencyn oscillatio theof multipleinteger

an near isfrequency osecurrent wh noise sinusoidal a have we wherecase simple aconsider First

2

2

max

max

∆

∆

≈∆

+=

∆±

∆∆

≈

=

∆+=

ω

ωqcIP

tttv

ωqωtcItφ

mn

tmIti

m

mmSBC

oout

mm

om

ω

φω

ω

ωω

21

Phase Noise Due to White & 1/f Sources

( )

.1 and by weightedand teddownconver getscarrier theof multiplesinteger higher near noise White

carrier. near the stays and 1 and by weightediscarrier near the noise White

carrier. near the noise 1 becomes noise 1 so ,t coefficienby weightedd,upconverte gets dcnear Noise

.1by weightedare and itself

carrier near the fold allfrequency carrier theof multiplesinteger near components noise Here

4log10

in results source noise whitea of case general the toanalysis previous theExtending

2

21

30

2

22max

0

22

fc

fc

ffc

ω

ωq

cf

i

P

m

mm

n

SBC

∆

∆∆

≈∆∑∞

=ω

22

How to Minimize Phase Noise?

( )

( )

s.frequencie allat noise phase thereduce will reducing Thus,

2log10

as expressed becan region 1 in the spectrum The

21

theoremsParseval' Usingminimized. be should tscoefficien ISF thenoise, phase minimize order toIn

22max

22

2

2

0

22

0

2

rms

rmsn

rmsm

m

n

ωqf

i

L

f

dxxc

c

Γ

∆

Γ∆=∆

Γ=Γ= ∫∑∞

=

ω

π

π

23

1/f Corner Frequency

( )

noise. 1in reductions dramaticfor potential theis e then thersymmetry, time-fall and -risethrough

minimized is If corner. noisecuit device/cir 1 thelower thangenerally is This

4

isfrequency corner 1 theThus,

8log10

slide previous theFrom

frequencycorner 1 theis where

content 1 includes which noisecurrent Consider

2

12

20

11

3

122

max

20

2

1

1221,

3

f

f

c

f

ωq

cf

i

L

f

ii

f

dc

rms

dcf

rmsff

f

n

f

fnfn

Γ

ΓΓ

=Γ

=∆

∆∆∆=∆

∆=

ωωω

ωω

ω

ω

ωω

24

Cyclostationary Noise Treatment

( ) ( ) ( )

( )

( ) ( ) ( )xxx

xi

ttiti

n

nn

α

α

ωα

Γ=Γ

=

NMF

0

00

ISF effectivean formulatecan we this, Usingunity. of peak value aith function w unitless periodic a is and source, noise

onarycyclostati theof that toequal is peak value whosesource noise whitestationary a is Here

function. periodic a and noise whitestationary ofproduct theasit gby treatin thishandleeasily can model LTV The

cycle. oscillatoran over ly dramatical changecan noise, thusand current,drain Transistor

25

Key Oscillator Design Points from Hajimiri Model

• As the LTI model predicts, oscillator signal power and Q should be maximized

• Ideally, the energy returned to the tank should be delivered all at once when the ISF is minimum

• Oscillators with symmetry properties that have small Γdc will provide minimum 1/f noise upconversion

26

Phasor-Based Phase Noise Analysis

• Models noise at 2 sideband frequencies with modulation terms

• The α1 and α2 terms sum co-linear with the carrier phasor and produce amplitude modulation (AM)

• The φ1 and φ2 terms sum orthogonal with the carrier phasor and produce phase modulation (PM)

27

Phasor-Based LC Oscillator Analysis

• This phasor-based approach can be used to find closed-form expressions for LC oscillator phase noise that provide design insight

• In particular, an accurate expression for the Leesonmodel F parameter is obtained

{ } ( )dBc/Hz 2

2log102

∆

=∆ω

ωωQP

FkTL o

sig

28

LC Oscillator F Parameter

• 1st Term = Tank Resistance Noise• 2nd Term = Cross-Coupled Pair Noise• 3rd Term = Tail Current Source Noise

{ } ( )dBc/Hz 2

2log102

∆

=∆ω

ωωQP

FkTL o

sig

• The above expression gives us insight on how to optimize the oscillator to reduce phase noise

• The tail current source is often a significant contributor to total noise

29

Loading in Current-Biased Oscillator

YCLOAMSC-TAMU 30

• The current source plays 2 roles• It sets the oscillator bias

current• Provides a high impedance

in series with the switching transistors to prevent resonator loading

Tail Current NoiseThe switching differential pair can be modeled as a mixer for noise in the current sourceLow frequency noise only produces amplitude noise, not phase noiseOnly the noise located at even harmonics will produce phase noise

YCLOAMSC-TAMU 31

Noise Filtering in Oscillator Only thermal noise in the current source transistor around 2nd

harmonic of the oscillation causes phase noiseIn balanced circuits, odd harmonics circulate in a differential path, while even harmonics flow in a common-mode path A high impedance at the tail is only required at the 2nd harmonic to stop the differential pair FETs in triode from loading the resonator

YCLOAMSC-TAMU 32

How can we present a low-impedance for the 2nd

harmonic noise current to filter it and a high-impedance to the tank at the 2nd

harmonic to avoid loading the tank?

Noise Filtering in Oscillator Tail-biased VCO with noise filtering.

YCLOAMSC-TAMU 33

Phase Noise w/ Tail Current Filtering

• Tail current noise filtering provides near 7dB improvement 34

Noise Filtering in OscillatorA top-biased VCO often provides improved substrate noise rejection and reduced flicker noise

YCLOAMSC-TAMU 35

Next Time

• Divider Circuits

36