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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
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
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 and Ali Hajimiri, “Virtual damping and Einstein relation in oscillators,” IEEE JSSC, March 2003.
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 and Ali Hajimiri, “Virtual damping and Einstein relation in oscillators,” IEEE JSSC, March 2003.
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 and Ali Hajimiri, “Virtual damping and Einstein relation in oscillators,” IEEE JSSC, March 2003.
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 and Ali Hajimiri, “Virtual damping and Einstein relation in oscillators,” IEEE JSSC, March 2003.
Donhee Ham
Linewidth Compression“Unified View of Resonators and Oscillators”
• Donhee Ham and Ali Hajimiri, “Virtual damping and Einstein relation in oscillators,” IEEE JSSC, March 2003.
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 and Ali Hajimiri, “Virtual damping and Einstein relation in oscillators,” IEEE JSSC, March 2003.
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 and Ali Hajimiri, “Concepts and methods in optimization of integrated LC VCOs,” IEEE JSSC, June 2001.
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 and Ali Hajimiri, “Concepts and methods in optimization of integrated LC VCOs,” IEEE JSSC, June 2001.
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 and Ali Hajimiri, “Concepts and methods in optimization of integrated LC VCOs,” IEEE JSSC, June 2001.
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
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 and Ali Hajimiri, “Switching mixers: theory and measurement,” Submitted to IEEE JSSC.
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 and Ali Hajimiri, “Switching mixers: theory and measurement,” Submitted to IEEE JSSC.
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 and Ali Hajimiri, “Switching mixers: theory and measurement,” Submitted to IEEE JSSC.
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 and Ali Hajimiri, “Switching mixers: theory and measurement,” Submitted to IEEE JSSC.
Donhee Ham
Measurement Results - II“First observation of C.G. enhancement and NF degradation”
• Donhee Ham and Ali Hajimiri, “Switching mixers: theory and measurement,” Submitted to IEEE JSSC.
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
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
Stochastic Resonance
SNR
T
Stochastic Resonance
1. Noise-enhanced heterodyning
2. Noise-induced phase sync.
3. Noise-enhanced linearization
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
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).