Sam Palermo Analog & Mixed-Signal Center

Texas A&M University

ECEN620: Network Theory Broadband Circuit Design

Fall 2012

Lecture 16: VCO Phase Noise

Agenda

• Phase Noise Definition and Impact

• Ideal Oscillator Phase Noise

• Leeson Model

• Hajimiri Model

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

3

( ) ( ) ( )dBc/Hz P

1Hz ,Plog10carrier

sideband

∆+=∆

ωωω oL

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

4

RX Reciprocal Mixing Strong Noisy TX Interfering with RX

Jitter Impact in HS Links

5

• 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

Ideal Oscillator Phase Noise

6

2tank

22

2

is voltagenoise squared-mean theofdensity spectral The

4

noise thermalintroduce willresistance tank The

Zf

if

v

RkT

fi

nn

n

∆=

∆

=∆

Tank Impedance Near Resonance

7

( )

( ) ( )

( )

( )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

Ideal Oscillator Phase Noise

8

{ } ( )

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

dBc/Hz 2

2log10

phase. and amplitudebetween 21evenly

split ispower noise thisTherefore, equal. arepower noise-phase and amplitude

m,equilibriuin that,states 2000] JSSC [Lee Theoremion Equipartit The

24

24

2

222

tank

22

∆

=∆

∆

=

∆

=

∆=

∆

ωωω

ωω

ωω

QPkTL

QkTR

QR

RkTZ

fi

fv

o

sig

oonn

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

9

[Perrott]

Leeson Phase Noise Model

10

• 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

11 ELEN620-IC Design of Broadband Communication circuit

A 3.5GHz LC tank VCO Phase Noise

Measure Phase noise

-30dB/decade -20dB/decade

-105dBc

12 ELEN620-IC Design of Broadband Communication circuit

VCO Output Spectrum Example

-85dBm

-20dBm RBW=10K

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

=-105dBc

dBc---in dB with respect to carrier

Leeson Model Issues

13

• 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

YCLO

AMSC-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

fin

∆

2

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

YCLO

AMSC-TAMU 16

ISF Model The phase variation due to injecting noise can be modeled as:

The function, Γ(x), is the time-varying proportionality factor and called the “impulse sensitivity function”. The phase shift is assumed linear to injection charge. ISF has the same oscillation period T of the oscillator itself. The unity phase impulse response can be written as:

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 Cadence Consider the effect on phase noise of each noise source

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 zero at peak.

Phase Noise Computation

19

( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) 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

ISF Decomposition w/ Fourier Series

20

( ) ( )

( ) ( ) ( ) ( )

ts.coefficien ISF the toaccording scaled and

bandsfrequency 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

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

nn

nnono

dnicdicq

nc

ncc

ττωτττφ

θ

θτωτω

Phase Noise Frequency Conversion

21

( ) ( )[ ]

( ) ( )

( ) ( )[ ]

( )

.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

Phase Noise Due to White & 1/f Sources

22

( )

.1by weightedand

teddownconver getscarrier theof multiplesinteger higher near noise White there.stayscarrier near the Noise

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

30

2

22max

0

22

f

ffc

ω

ωq

cf

i

P mm

n

SBC

∆

∆∆≈∆

∑∞

=ω

How to Minimize Phase Noise?

23

( )

( )

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

1/f Corner Frequency

24

( )

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

Cyclostationary Noise Treatment

25

( ) ( ) ( )

( )

( ) ( ) ( )xxx

x

i

ttiti

n

nn

α

α

ωα

Γ=Γ

=

eff

0

00

ISF effectivean formulate

can 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

Key Oscillator Design Points

26

• 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

Phasor-Based Phase Noise Analysis

27

• 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)

Phasor-Based LC Oscillator Analysis

28

• 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 Leeson model F parameter is obtained

{ } ( )dBc/Hz 2

2log102

∆

=∆ω

ωωQP

FkTL o

sig

LC Oscillator F Parameter

29

• 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

Tail Current Noise The switching differential pair can be modeled as a mixer for noise in the current source Only the noise located at even harmonics will produce phase noise.

YCLO AMSC-TAMU 30

Loading in Current-Biased Oscillator

YCLO AMSC-TAMU 31

• 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

Noise Filtering in Oscillator Only thermal noise in the current source transistor around 2nd harmonic of the oscillation causes phase noise. In 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.

YCLO AMSC-TAMU 32

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

YCLO AMSC-TAMU 33

Phase Noise w/ Tail Current Filtering

34

• Tail current noise filtering provides near 7dB improvement

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

YCLO AMSC-TAMU 35

Next Time

• Divider Circuits

36

37 ELEN620-IC Design of Broadband Communication circuit

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

38 ELEN620-IC Design of Broadband Communication circuit

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

If the input noise is represented as

∆ω

mω0 (m-1)ω0

mω0 ∆ω

Noise

Γ

39 ELEN620-IC Design of Broadband Communication circuit

If the input noise is represented by its power distribution function

For small noise level

( )( )( ) ( ) ( )( )( ) ( )( ) ( )ttsinVtcosVV

tsintsinVtcosVVttcosVV

o0o0out

o0o0out

o0out

φωωφωω

φω

−≅−≅

+=