Amplitude and Phase Noise Amplitude and Phase Noise in Nano-scale RF Circuitsin Nano-scale RF Circuits

Reza Navid Reza Navid

May 14, 2007May 14, 2007

CMOS Scaling Since Early 70sCMOS Scaling Since Early 70s

100

1,000

10,000

100,000

1,000,000

10,000,000

100,000,000

1,000,000,000

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

0.01

0.1

1

10

100

Today, 45nm technology node is available for commercial production design.Today, 45nm technology node is available for commercial production design.Several other nano-scale devices are also becoming available.Several other nano-scale devices are also becoming available.

4004 Intel Processor2,250 10-MOSFETs

386 Intel Processor275,000 1-MOSFETs

Pentium IV Intel Processor169,000,000 90n-MOSFETs

Ch

ann

el L

eng

th (

Mic

ron

)

Nu

mb

er o

f M

OS

FE

Ts

Scaling Problem at Nanometer ScalesScaling Problem at Nanometer Scales

Reliability: Mismatch:

Intrinsic Gain:

Small output resistance Low intrinsic gain

Noise:

Short-channel MOSFETs are noisier that Long-channel ones

Physical lengthPhysical length

Ro Long-channel prediction

1986 Year19991994 1996

Dra

in N

oise

leve

l

Phase Noise

ffo f

of

LNA Noise

f

Noise in RF ReceiversNoise in RF Receivers

Electrical noise strongly impacts the overall performance.Electrical noise strongly impacts the overall performance.

LNA

LO

Mixer

Input Noise Output Noise

TransmissionTransmission No SignalNo Signal

ff s sf

f f

so ff

IF Filter

OutlineOutline

• Amplitude Noise in MOSFETNoise in MOSFETsPhysical and Compact ModelsNoise Performance of Ballistic MOSFETs

• Jitter and Phase Noise in OscillatorsIndirect Noise Characterization Using Phase NoiseTime-Domain Formulation of Phase NoiseExperimental Results

• Directions for Further Research

• Conclusions

OutlineOutline

• Amplitude Noise in MOSFETNoise in MOSFETsPhysical and Compact ModelsNoise Performance of Ballistic MOSFETs

• Jitter and Phase Noise in OscillatorsIndirect Noise Characterization Using Phase NoiseTime-Domain Formulation of Phase NoiseExperimental Results

• Directions for Further Research

• Conclusions

Noise Sources in MOSFETsNoise Sources in MOSFETs

• There are two noise sources in a MOSFET:Drain current noise (ind)Induced gate noise (ing)

Drain

Source

Gate

1/f noise

White noise

We study the white noise part of the drain noise in saturation.We study the white noise part of the drain noise in saturation.

ing Cgsgg gmvgs go ind

• 1/f Noise: Unknown origin, believed to be due to traps

Gate

Source

Drain

• Gate Noise: Carrier fluctuations

coupled to gate through Cgs

2ngi 2gsC

2ndi

f f

dR

RkTvn d4d 2

dx

Classical MOSFET Noise FormulationClassical MOSFET Noise Formulation

• Classical long-channel formulationImpedance Field Method [Van Der Ziel, 1970]:

Divide the channel into small piecesCalculate noise of each piece (assuming equilibrium noise)Integrate (assuming independence)

It accurately predicts noise in long-channel MOSFETs.It accurately predicts noise in long-channel MOSFETs.

N+ N+

GS D

Noise transfer Noise transfer function (Impedance)function (Impedance)

2

22 d

dxZ

vi nnd

L

x

ndnd ii0

22 d

3/2,42 dond gkTi

dR

Deficiency of the Long-Channel ModelDeficiency of the Long-Channel Model

Several methods are proposed to study this excess noise.Several methods are proposed to study this excess noise.

Long-channel prediction

1986 Year

2.9

7.9

Jindal (0.75m)

Abidi (0.7m)

1999

Scholten (0.35m)1.1

1994

Triantis (0.7m)

1996

3.3

0.67

Tedja (1m)

• Excess noise has been reported for 20 years now:

Excess Noise in Short-Channel FETsExcess Noise in Short-Channel FETs

• Researchers have tried to explain excess noise:Local heating effects [Traintis, 1996]Hydrodynamic simulations [Goo, 1999, Jungemann 2002] Montecarlo analysis [Jungemann, 2002]…

We present a model based on ballistic MOSFET model.We present a model based on ballistic MOSFET model.

Usual approach

Model revision

Long-Channel FETsLong-Channel FETsToday’s FETs, 50% Today’s FETs, 50%

BallisticBallistic Ballistic FETsBallistic FETs

Long-Channel Model:Long-Channel Model:IIndnd=4=4kTkTggdodo

Short-Channel Short-Channel Model: Model: IIndnd=4=4kTkTshshggdodo

Model revision

Our approach

Ballistic Mode:Ind=2qId

• MOSFETs are moving towards ballistic limit.

Short-Channel Model: Ind=ks(2qId)

OutlineOutline

• Amplitude Noise in MOSFETNoise in MOSFETsPhysical and Compact ModelsNoise Performance of Ballistic MOSFETs

• Jitter and Phase Noise in OscillatorsJitter and Phase Noise in OscillatorsIndirect Noise Characterization Using Phase NoiseTime-Domain Formulation of Phase NoiseExperimental Results

• Directions for Further Research

• Conclusions

-4

-2

0

2

4

Phase Noise in OscillatorsPhase Noise in Oscillators

• Device noise leads to frequency fluctuations.Example: Ring Oscillators

Phase noise characterizes the frequency fluctuations.Phase noise characterizes the frequency fluctuations.

Ou

tpu

t

t

ffo

I

t

Time Domain

Ph

ase

No

ise

Frequency Domain

Phase Noise: Phase Noise: Formulation and MeasurementFormulation and Measurement

• Phase noise definition: PSD of signal divided by power

Hard to formulate

Easy to measure PN

(d

Bc/

Hz)

fo ffo+f

• Phase noise measurement helps estimate device noise:

This method is most suitable for formulation of phase noise in This method is most suitable for formulation of phase noise in switching-base oscillators.switching-base oscillators.

• Need accurate formulation for specific oscillators.Time-domain phase noise analysis method

Time-Domain Phase Noise AnalysisTime-Domain Phase Noise Analysis

• Formulation of phase noise:1) Calculate jitter2) Calculate phase noise using jitter-phase-noise relationships

TTiiTTjj has necessary andhas necessary and sufficient sufficient

information for phase noise calculation.information for phase noise calculation.

• Jitter characterization:

T2Ti

T1

With white noise(presented here)

i-j0

2oT

ji TT

With colored noise(presented elsewhere)

i-j0

2oTji TT

Without low-frequency poles

Jitter in Switching-Based Oscillators (1)Jitter in Switching-Based Oscillators (1)

• Switching-based oscillators: Energy-injecting elements act like ideal switches.

Calculate jitter during each switching; Add them up to find total jitter.Calculate jitter during each switching; Add them up to find total jitter.

vC

in C R

vref

Ideal noise-free switch

Passive noisy network

vout

vC voutin in

Jitter in Switching-Based Oscillators (2)Jitter in Switching-Based Oscillators (2)

• Calculation procedure:Calculate voltage variance at the switching time.Divide by the square of voltage slope to get jitter.

This is suitable for switching-based oscillators.This is suitable for switching-based oscillators.

2

222

0 0

)(

2

)2

(

2 )( ,d d )()()(

)2

(

S

tvTeiie

C

etv C

o

t t

nnRC

RC

t

CRC

t

vC

in C R

vrefvc

t

2vc

2vc2T

Slope=Svref

-120

-100

-80

-60

-40

-20

0

-1.E+06 -5.E+05 0.E+00 5.E+05 1.E+06

Jitter-Phase-Noise Relationships (1)Jitter-Phase-Noise Relationships (1)

• If all covariance terms are zero [Navid, 2005],

Phase noise has peaks around odd harmonics, as expected.Phase noise has peaks around odd harmonics, as expected.

The 1st harmonic

PN

(dB

c/H

z)

f (Hz)

The 3rd harmonic

f (Hz)

-120

-100

-80

-60

-40

-20

0

-1.E+06 -5.E+05 0.E+00 5.E+05 1.E+06

0

222

21

2220

22

22

cos2

cosh

24cosh

2cos

4cosh

4sinh)(

TT

Tf

TTT

TfPN

oo

oo

o

Variance of one period

-180

-160

-140

-120

-100

-80

-60

-40

-20

0

1.E+00 1.E+02 1.E+04 1.E+06 1.E+08 1.E+10

Jitter-Phase-Noise Relationships (2)Jitter-Phase-Noise Relationships (2)

• It can be approximated by a Lorentzian Function.Consistent with the results for sinusoidal signals [Herzel, 1999]

Jitter-phase-noise relationship for nonzero jitter covariance is Jitter-phase-noise relationship for nonzero jitter covariance is presented elsewhere [Navid, 2004].presented elsewhere [Navid, 2004].

Lorentzian

Exact phase noise• Usually:

PN

(dB

c/H

z)

f (Hz)

2

223

23

)(

ooo

oo

ffTf

TffPN

23ooo Tfff

2

23

)( f

TffPN oo

off

Phase Noise in Ring OscillatorsPhase Noise in Ring Oscillators

• Time-domain phase noise analysis:Treat invertors as ideal switches.Use long-channel noise formulation.

On State:

Off State:

I og/1

dog/1dokTg4

dokTg3

8

A B

Use time-domain jitter analysis for switching-based oscillators.Use time-domain jitter analysis for switching-based oscillators.

A B

Phase Noise in Ring Oscillators (cont.)Phase Noise in Ring Oscillators (cont.)

• Using jitter-phase-noise relationships [Navid, 2005]:

oddo

o fP

kT

vNCf

kTT

min22

2 33.733.7

2

min22

33.733.7

f

f

P

kT

fNCv

kTffPN o

dd

o

Very simple equations, but how accurate?Very simple equations, but how accurate?

Dynamic Power2

min ddovNCfP

Phase Noise in Ring OscillatorsPhase Noise in Ring Oscillators

Lmin m

fosc MHz

PNmeas. dBc/Hz

PNmin.

dBc/HzPN dB

2.00 232 -118.5 -119.7 1.2 2.00 115 -126.0 -128.0 2.0 0.53 751 -114.0 -115.4 1.4 0.39 850 -112.6 -114.6 2.0 0.36 931 -111.7 -113.8 2.1 0.32 932 -112.5 -114.2 1.7 0.32 869 -112.2 -114.6 2.4 0.28 929 -112.3 -114.3 2.0 0.25 898 -112.0 -115.9 3.9 0.25 959 -110.9 -115.5 4.6 0.25 1330 -111.5 -116.7 5.2

The difference is only a few dB; it increases in short-channel devices.The difference is only a few dB; it increases in short-channel devices.

• Measured results form Hajimiri, JSSC 1999 compared to our formulation:

ff=1MHz=1MHz

Lmin (m)

PN

(dB

)

2

min

33.7

f

f

P

kTfPN o

0

1

2

3

4

5

6

0 0.5 1 1.5 2 2.5

Oscillators for Noise CharacterizationOscillators for Noise Characterization

The unsymmetrical ring oscillator is only one of many possibilities.The unsymmetrical ring oscillator is only one of many possibilities.

• Need an oscillator with predictable phase noise, not necessarily low phase noise: an unsymmetrical ring oscillator.

The Unsymmetrical Ring OscillatorThe Unsymmetrical Ring Oscillator

Fabricated in National Semiconductor’s 0.18Fabricated in National Semiconductor’s 0.18m CMOS process.m CMOS process.

• Chip photo:

OSC3, L=.54m

OSC2, L=.38m

OSC1, L=.18m

Ring oscillators for Ring oscillators for functionality testfunctionality testMIM MIM

CapacitorsCapacitors

MOSFET Noise CharacterizationMOSFET Noise Characterization

The oscillator with longer transistors has better spectral purity.The oscillator with longer transistors has better spectral purity.

• Frequency spectrum of the oscillators:

MOSFET Noise Characterization (Cont.)MOSFET Noise Characterization (Cont.)

Oscillator with Longer transistors has 7dB smaller phase noise.Oscillator with Longer transistors has 7dB smaller phase noise.

• Phase noise of the oscillators:

Device Noise ParametersDevice Noise Parameters

Extracted device noise parameters are consistent with our prediction.Extracted device noise parameters are consistent with our prediction.

• Device noise parameters can be extracted from phase noise data.

Long-channel Long-channel predictionprediction

OSC3OSC3OSC1OSC1

Full shot Full shot noisenoise

Further Research on Phase NoiseFurther Research on Phase Noise

• Time-domain phase noise analysis:

Jitter/phase noise calculation for various oscillators/PLL systems.

Vb

PFD Charge Pump

:N

VCOLoopFilter

Fref

• Indirect device noise characterization for Nanotubes and Nanowires:

Ring oscillators built with these devices are already available (Z. Chen et al, Science 24 March 2006).

Noise for Device EngineeringNoise for Device Engineering

• Non-equilibrium noise carries unique device informationDevice engineering based on noise characterization

Examples:Examine carrier transport using noise data

Nano-tubes, Nano-wires, MOSFETs, …

Design new devices based on noise measurement Bio-analytical devices

Use noise data to improve existing devices and build new ones.Use noise data to improve existing devices and build new ones.

Other Scaling ProblemsOther Scaling Problems

Reliability: Mismatch:

Intrinsic Gain:

Small output resistance Low intrinsic gain

Noise:

Short-channel MOSFET are noisier that Long-channel ones

Ro Long-channel prediction

1986 Year19991994 1996

Dra

in N

oise

leve

l

Physical lengthPhysical length

ConclusionsConclusions

• Efficient CMOS analog design calls for a careful study of noise in MOSFETs, which has been a mystery for two decades.

• Time domain phase noise analysis method accurately predicts the phase noise in switching-based oscillators.

• Device noise can be characterized through phase noise measurement, facilitating process characterization.

• Noise can be useful.

AcknowledgmentAcknowledgment

This work is supported under an SRC customized research project from Texas Instruments and

MARCO MSD center.

We would like to thank National Semiconductor Inc. for the fabrication of test chips.