donhee ham “statistical electronics” noise processes in rf integrated circuits (oscillators and...

Donhee Ham

“Statistical Electronics” Noise Processes in RF Integrated Circuits

(Oscillators and Mixers)

Donhee Ham

Harvard RF and High-Speed IC & Quantum Circuits Laboratory

copyright © 2003 by Donhee Ham

Donhee Ham

Outline

1. Introduction – “Statistical Electronics”

2. Phase Noise in Oscillators

“Virtual Damping and Einstein Relation in Oscillators”

3. Noise in Mixers

“Cyclostationary Noise in CMOS Switching Mixers”

4. Stochastic Resonance and RF Circuits

5. Soliton Electronics

Donhee Ham

RF IC Design Challenges – I: Design Constraints

Circuit idea

Circuit analysis – hand calculation

Simulation(Circuits and EM)

IC Layout

IC Characterization

Parasiticextraction PCB design

Donhee Ham

RF IC Design Challenges – II: Physical Constraints

1. Active devices– Trade-offs among speed, overhead, gain, & breakdown voltage– Poor noise performance

2. Passive devices– Skin effect loss & noise – Conductive substrate loss & noise

3. Cross talk– e.g. “unintentional” injection

locking through conductive substrate

4. Poor ground reference

5. and more…

* This slide best suits digital silicon CMOS technology.

Donhee Ham

Noise in RF Receivers

• Shannon’s Theorem : )1(log2 N

SBC

Donhee Ham

Signal Path Noise

• NF quantifies the degradation in SNR in the receiver.

• NF sets the lower end of receiver dynamic range.

• NF of a receiver is practically always dominated by NF of its front-end.

21

3

1

21

11

GG

NF

G

NFNFNFtot (Friis equation)

Donhee Ham

Frequency-Reference Noise (Phase Noise)

Donhee Ham

Noise in Front-End Circuits

LNA - LTI system

Front End1. Nonlinear and/or time-varying systems

Rich dynamics complicates the noise processes.

2. Currently available noise modelsThey have greatly helped designers better understand noise processes in oscillators and mixers. However, they assume rather phenomenological standpoints and a more fundamental yet intuitive understanding is still needed. Proper physical understanding could lead to deeper design insight. (e.g.) Trade-off between voltage swing and

phase noise in oscillators is often not best understood.

Mixers & Oscillators

Donhee Ham

Chronology of Oscillator Phase Noise Study1. Mathematical & physical ground work

• Kubo (1962), Stratonovich (1967) – Essential understanding.• Lax (1967) – Comprehensive and general mathematical-physics

analysis of phase noise (hard to beat!).

2. Leeson (1966) – Phenomenological, yet insightful tuned-tank electrical oscillator phase noise model.

3. CAD-oriented approaches – Kartner, Demir et al.

4. Recent circuit design-oriented approaches • McNeill – Jitter study in ring oscillators.• Razavi – Q-based phase noise modeling.• Rael & Abidi – Phase noise factor calculation.• Hajimiri & Lee – General study of time-varying effects; first account

for the interaction between cyclostationary noise and impulse sensitivity and its impact on phase noise.

• and many more…(omitted here not due to technical insignificance but due to space limitation.).

* Many important other works on phase noise are omitted in this slide due only to space limitation.

Donhee Ham

Physics of Noise I – Einstein (1905)“Brownian Motion”

Fluctuation-Dissipation Theorem

• Fluctuation: microscopic description of thermal motions of liquid molecules• Dissipation: macroscopic average of thermal motions of liquid molecules• Fluctuation and dissipation are of the same physical origin, and in thermal equilibrium, they balance each other out. • When the fluctuation-dissipation balance is reached (equilibrium),

Einstein Relation

Dttx 2)(2

m

kTD

1

kTmv2

1

2

1 2 m

kTv 2

(energy equipartition)

(D: diffusion constant)

Donhee Ham

Physics of Noise II – Nyquist (1928)“4kTR Noise”

4kTR noise is analogous- nay, essentially equivalent to black-body radiation following Planck radiation law in the classical regime.

fkTP kTR4 noise

energy equipartition(2 degrees of freedom – electric & magnetic)

counting of the resonance modes for a given bandwidth

or,

4kTR noise is a special case of the fluctuation-dissipation theorem.

Donhee Ham

Physics of Noise III“Brownian Motion in RC Circuits”

“Fluctuation-dissipation balance” “Energy equipartition”

Steady-state probability distribution function (PDF) of the voltage, v, across the capacitor

• Donhee Ham, Statistical Electronics: Noise Processes in Integrated Communication Systems, PhD dissertation, California Institute of Technology, 2002.

Donhee Ham

Bridging the Gap …

CAD-Oriented Approaches

Design-Oriented Approaches

Physics-Based Approaches

Statistical

physicsElectrical

Circuits

Donhee Ham

• Statistical physics• Thermodynamics

• Circuit engineering

AutonomousCircuits (Oscillators)

Time-Varying Circuits

DrivenCircuits(Mixers)

• Integrated circuits

Transistors

Nonlinear DevicesQuantum Devices

PLLs, FrequencySynthesizers

Communication Systems

CDRs

Noise-enhancedheterodyning, phase

synchronization

Stochastic Resonance

“Statistical Electronics”

Lossy transmission lines, noise waives, etc.

DistributedCircuits

Meso/nano scaledevices

Donhee Ham

Outline




3. Noise in Mixers




Donhee Ham

Self-Sustained Oscillator

Equivalent model for tuned-tank oscillators

Donhee Ham

Oscillator Phase Noise

Donhee Ham

Ensemble of Identical Oscillators

Same

initial

phase

Donhee Ham

Phase Diffusion - IDiffusion Constant)cos()( 00

tvtv D tt 2)(2

Donhee Ham

Phase Diffusion - IIDiffusion Constant)cos()( 00

tvtv D tt 2)(2

most probable state

• D (diffusion constant) : rate of entropy increase

• Donhee Ham and Ali Hajimiri, “Virtual damping and Einstein relation in oscillators,” IEEE JSSC, March 2003.

Donhee Ham

Virtual Damping

Phase Diffusion Constant

“ Virtual Damping Rate ”

D tt 2)(2

2)(

2}{

D

L

• 1 GHz, -121dBc/Hz at 600kHz offset : D = 5.69

0

10

D


Donhee Ham

Experimental Virtual Damping – I

Ensemble average on 512 Waveforms triggered at the same phase initially

Virtual Damping Measurement Setup

Centre frequency :5 MHz


Donhee Ham

Experimental Virtual Damping – II

Ensemble average on 512 waveforms triggered at the same phase initially

Damping Rate : D

Centre frequency: 5 MHz


Donhee Ham

Experimental Virtual Damping – III

Injected current noise PSD (A2/Hz)

Measured D

(sec-1)

PN from measured D

(dBc/Hz)

PN from spec. analyzer

(dBc/Hz)

2.60 x 10-15 1.02 x 104 -92.9 -93.0

4.84 x 10-15 1.56 x 104 -91.0 -90.0

9.66 x 10-15 3.53 x 104 -87.4 -86.5

2.12 x 10-14 9.30 x 104 -83.3 -81.7

6.04 x 10-14 1.90 x 105 -80.0 -79.5

2)(

2}{

D

L


Donhee Ham

Linewidth Compression“Unified View of Resonators and Oscillators”


Donhee Ham

Brownian Motion & Einstein Relation

D ttx 2)(2

m

TkD B

1

“ Einstein Relation ”

Sensitivity

(Energyequipartition)

Friction

(Energy loss)

Donhee Ham

Einstein Relation in Oscillator Phase Noise- Determination of Virtual Damping Rate, D -

sensitivity

friction (energy loss and/or noise)

L

B

Q C

T k

vD

020

1~

• The virtual damping rate, D, can be also mathematically derived by solving a time-varying diffusion equation for the phase diffusion. It’s a simple kind of math, which can be found in Donhee Ham et al, “Virtual damping and Einstein relation in oscillators,” IEEE JSSC, March 2003. The result of the mathematical derivation perfectly agrees with the virtual damping rate jotted down above, obtained resorting only to Einstein relation.

0

0

1~

d

L

gR

CQ

Einstein relation

Donhee Ham

Anatomy of Oscillator Phase Noise“Design Insight”

(due to virtual damping)

Einstein relation


Donhee Ham

LC Oscillator Design Example

drain (p)

source (p)

oxide

gate poly

n-well

p-substrate

biasI

MOS varactor

Spiral inductor

Donhee Ham

Graphical Optimization With a decreasing inductance,

0 20 40 60 80 100

4

3

2

1

0

w (μ m)

c (p

F)

T.R.1

start-up

amplitude

0 20 40 60 80 100

L=Lmin= Lopt

c (p

F)

w (μ m)

T.R.2

amplitude

start-up

T.R.1

T.R.2

• Donhee Ham and Ali Hajimiri, “Concepts and methods in optimization of integrated LC VCOs,” IEEE JSSC, June 2001.

Donhee Ham

0 20 40 60 80 100

6

4

2

0

• Solid lines : fast corner• Broken lines : slow corner• Shaded region : unreliable design

Robust Design

start-up

w (μ m)

T.R.1

T.R.2

c (p

F)


Donhee Ham

Phase Noise Measurement

Bias Tee

50 matching

Probe Station

Bond Wires DUT

Circuit Board

ddV

Spectrum Analyzer

Bias Tee ddV

1.1 mm

1.0

mm

Supply voltage 2.5 V

Current (Core) 4 mA

Center frequency 2.33 GHz

Tuning range 26 %

Output power 0 dBm

Phase noise

@ 600kHz

-121dBc/Hz

Conexant 0.35um BiCMOS(MOS Only)


Donhee Ham

Performance Comparison

}{log10 off

2

0

tune

2

off

0

sup

fLf

f

f

f

P

kTPFTN

Performance Metric : Power-Frequency-Tuning-Normalized (PFTN) Figure of Merit

CMOS

Bipolar

CMOS/bondwire inductor

CMOS distributed

CMOS/special metal layer

This work

40

20

0

Publications (Chronological Order)

PFTN


Donhee Ham

Outline




3. Noise in Mixers




Donhee Ham

MOS Switching Mixer

Hard-Switching

Soft-Switching

• C : IF port capacitance

- Mixer parasitic capacitors

- IF amplifier input capacitance

- Important design parameter

• Two modes of mixer operation

• Role of energy storing elements?

Donhee Ham

Characteristic of Mixers “Cyclostationary Noise”

• Cyclostationary noise is periodically modulated noise.

• It results when circuits have periodic operating points.

• Its statistical averages are time-dependent.

“Noise is shaped in time.”

)()()( tptntx

cyclostationary noise

stationary noise

periodic/deterministicfunction

Donhee Ham

PSD of Cyclostationary Noise

);()(1

lim)(2

tfSfXT

fS xTT

x

))()((0

2T ftj

T dtetxfX

• operationally-defined, time-varying PSD.• F.T. of autocorrelation.

“measurement = LTI bandpass filtering”

Donhee Ham

Cyclostationary Noise Flow in RF Systems

);( tfS);( tfS

Donhee Ham

Importance of Cyclostationary Noise

• Donhee Ham and Ali Hajimiri, “Switching mixers: theory and measurement,” Submitted to IEEE JSSC.

Donhee Ham

Theoretical Prediction of CG and NF

“Optimum design capacitance.”

Utilization of stochastic calculusto evaluate the noise figure.

• fIF = 10 MHz

• fLO = 300 MHz

Our approach

conventional

new prediction

conventional

new prediction

• The next 4 slides sketch the theoretical analysis which resulted in the new predictions presented in this slide. Further details of this theoretical analysis can be found in Donhee Ham et al, “Switching mixers: theory and measurement,” Submitted to IEEE JSSC.

Donhee Ham

Thevenin Equivalent Circuit

“time-varying filtering”

hard switching soft switching

IF component

Non-IF components

• A. R. Shahani et al, ``A 12-mW wide dynamic range CMOS front-end for a portable GPS receiver," IEEE JSSC, Dec. 1997.

Donhee Ham

Deterministic Dynamics - I

Via Pseudo-beating (pattern generation)

• Donhee Ham et al, “Switching mixers: theory and measurement,” Submitted to IEEE JSSC.

Donhee Ham

Deterministic Dynamics - II

“Conversion Gain Enhancement”Bump size ~ Harmonic Richness

• Donhee Ham et al, “Switching mixers: theory and measurement,” Submitted to IEEE JSSC.

Donhee Ham

Stochastic Dynamics

)()(

)()(

, tvC

tgtv

C

tg

dt

dvneff

Tn

Tnoise )()( tvtv

),( tfS IF

)( ),( 0 IFIF fStfS

),( tfS IF

LangevinEquation

FourierTransform

measurement (time-average)

synchronized


Donhee Ham

Mixer Test Chip and Board

1.2 mm

0.7

mm

Post amplifier

Test capacitors(to be laser-trimmed)

MOS switching mixer core

Conexant 0.35um BiCMOS Chip(MOS Only)

Assembled printed-circuit board for the chip test


Donhee Ham

Mixer Measurement Setup

Mixer

AMPRF

LO

RFDC

LODC

IF

NFNoise Diode(HP Noise Source)

• Test On-Chip Capacitors• Cut by Laser Trimming


Donhee Ham

IF capacitor (fF)

NF(dB)

Hard Switching

Measurement Results - I

NF(dB)

Soft Switching

IF capacitor (fF)

Hard Switching

Soft Switching

Theoretical Prediction Measurement Result

“First observation of cyclostationary noise effects”


Donhee Ham

Measurement Results - II“First observation of C.G. enhancement and NF degradation”


Donhee Ham

Outline




3. Noise in Mixers




Donhee Ham

When Noise Plays a Creative Role…Brownian Motor

Other Example

- Dithering in A/D converters

Electrical Brownian Motor

thermal noise

T1

T2

T1 T2

U

Escape rate ~

kT

Uexp


SNR

T


1. Noise-enhanced heterodyning

2. Noise-induced phase sync.

3. Noise-enhanced linearization

Donhee Ham

Outline




3. Noise in Mixers




Donhee Ham

Ultra-Fast Nonlinear Electronics“Soliton Electronics”

NLTL

Positive active feedback

?

“Soliton oscillator”: analogous to pulse lasers (e.g. femto-second lasers).

time

Pulse train generator

Donhee Ham

Harvard RF and High-Speed IC & Quantum Circuits Lab

http://www.deas.harvard.edu/[email protected]

• Wireless communication circuits (RF IC)• Wireline communication circuits (high-speed IC)• Statistical & soliton electronics• Quantum devices and circuits• UWB communication circuits

Donhee Ham

Acknowledgement

• Caltech (Ali Hajimiri, Michael Cross, Chris White, Ichiro Aoki, Hui Wu, Behnam Analui, Hossein Hashemi, Yu-Chong Tai, P. P. Vaidyanathan, and David Rutledge.),

• IBM T. J. Watson (Mehmet Soyuer, Dan Friedman, Modest Oprysko, and Mark Ritter),

• Analog Devices (Larry DeVito),

• IBM Fishkill (J.O. Plouchart and Noah Zamdmer),

• Conexant Systems (Currently, Skyworks Inc. and Jazz Semiconductor.),

• Lee Center, ONR, and NSF,

• Paul Horowitz (Harvard).

donhee ham “statistical electronics” noise processes in rf integrated circuits (oscillators and...

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