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“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) Parasitic extraction PCB design IC Layout IC Characterization Donhee Ham RF IC Design Challenges – II: Physical Constraints * This slide best suits digital silicon CMOS technology. 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… Donhee Ham Noise in RF Receivers S • Shannon’s Theorem : C B log 2 (1 ) N Donhee Ham Signal Path Noise NF2 1 NF3 1 NFtot NF1 G1 G1G2 (Friis equation) • 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. Donhee Ham Frequency-Reference Noise (Phase Noise) Donhee Ham Noise in Front-End Circuits Mixers & Oscillators Front End 1. Nonlinear and/or time-varying systems Rich dynamics complicates the noise processes. LNA - LTI system Donhee Ham 2. Currently available noise models They 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. Chronology of Oscillator Phase Noise Study 1. Mathematical & physical ground work • • Kubo (1962), Stratonovich (1967) – Essential understanding. Lax (1967) – Comprehensive and general mathematical-physics analysis of phase noise (hard to beat!). Leeson (1966) – Phenomenological, yet insightful tuned-tank 2. electrical oscillator phase noise model. 3. CAD-oriented approaches – Kartner, Demir et al. 4. Recent circuit design-oriented approaches • • • • • Donhee Ham 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. Physics of Noise I – Einstein (1905) “Brownian Motion” x (t ) 2 Dt 2 Einstein Relation 1 kT D m (D: diffusion constant) 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), 1 2 1 mv kT 2 2 (energy equipartition) Donhee Ham v 2 kT m Physics of Noise II – Nyquist (1928) “4kTR Noise” 4kTR noise is a special case of the fluctuation-dissipation theorem. P kTf 4kTR noise 4kTR noise is analogous- nay, essentially equivalent to blackbody radiation following Planck radiation law in the classical regime. Donhee Ham energy equipartition (2 degrees of freedom – electric & magnetic) or, counting of the resonance modes for a given bandwidth Physics of Noise III “Brownian Motion in RC Circuits” Steady-state probability distribution function (PDF) of the voltage, v, across the capacitor “Fluctuation-dissipation balance” Donhee Ham “Energy equipartition” • Donhee Ham, Statistical Electronics: Noise Processes in Integrated Communication Systems, PhD dissertation, California Institute of Technology, 2002. Bridging the Gap … Design-Oriented Approaches Physics-Based Approaches Statistical physics CAD-Oriented Approaches Donhee Ham Electrical Circuits “Statistical Electronics” • Circuit engineering • Integrated circuits • Statistical physics • Thermodynamics Nonlinear Devices Quantum Devices Transistors Meso/nano scale devices Time-Varying Circuits Autonomous Circuits (Oscillators) Donhee Ham Driven Circuits (Mixers) Stochastic Resonance Noise-enhanced heterodyning, phase synchronization Distributed Circuits Lossy transmission lines, noise waives, etc. Communication Systems PLLs, Frequency Synthesizers CDRs 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 - I v ( t ) v 0 cos( w 0 t f ) Donhee Ham < f (t ) > 2 D t 2 Diffusion Constant Phase Diffusion - II v ( t ) v 0 cos( w 0 t f ) < f (t ) > 2 D t 2 Diffusion Constant most probable state • D (diffusion constant) : rate of entropy increase Donhee Ham • Donhee Ham and Ali Hajimiri, “Virtual damping and Einstein relation in oscillators,” IEEE JSSC, March 2003. Virtual Damping Phase Diffusion Constant < f 2 (t ) > 2 D t “ Virtual Damping Rate ” L{ w } D • 1 GHz, -121dBc/Hz at 600kHz offset : D = 5.6 Donhee Ham w0 2D (w ) 2 10 9 • Donhee Ham and Ali Hajimiri, “Virtual damping and Einstein relation in oscillators,” IEEE JSSC, March 2003. Experimental Virtual Damping – I Virtual Damping Measurement Setup Centre frequency : 5 MHz Donhee Ham Ensemble average on 512 Waveforms triggered at the same phase initially • Donhee Ham and Ali Hajimiri, “Virtual damping and Einstein relation in oscillators,” IEEE JSSC, March 2003. Experimental Virtual Damping – II Damping Rate : D Centre frequency : 5 MHz Ensemble average on 512 waveforms triggered at the same phase initially Donhee Ham • Donhee Ham and Ali Hajimiri, “Virtual damping and Einstein relation in oscillators,” IEEE JSSC, March 2003. Experimental Virtual Damping – III L{ w} Donhee Ham 2D 2 w ( ) 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 • Donhee Ham and Ali Hajimiri, “Virtual damping and Einstein relation in oscillators,” IEEE JSSC, March 2003. Linewidth Compression “Unified View of Resonators and Oscillators” Donhee Ham • Donhee Ham and Ali Hajimiri, “Virtual damping and Einstein relation in oscillators,” IEEE JSSC, March 2003. Brownian Motion & Einstein Relation < x (t ) > 2 D t 2 “ Einstein Relation ” 1 kBT D m Sensitivity (Energy equipartition) Friction (Energy loss) Donhee Ham Einstein Relation in Oscillator Phase Noise - Determination of Virtual Damping Rate, D - v02 C QL D~ B 0 1 k T w sensitivity Einstein relation friction (energy loss and/or noise) R g d 0 1 L Q ~ w 0C • 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. Donhee Ham Anatomy of Oscillator Phase Noise “Design Insight” (due to virtual damping) Einstein relation Donhee Ham • Donhee Ham and Ali Hajimiri, “Virtual damping and Einstein relation in oscillators,” IEEE JSSC, March 2003. LC Oscillator Design Example gate poly oxide source (p) drain (p) n-well p-substrate MOS varactor Spiral inductor I bias Donhee Ham Graphical Optimization With a decreasing inductance, L=Lmin= Lopt 4 start-up amplitude T.R.1 T.R.2 c (pF) c (pF) 3 T.R.1 2 T.R.2 amplitude 1 start-up 0 0 20 40 60 w (μ m) Donhee Ham 80 100 0 20 40 60 80 100 w (μ m) • Donhee Ham and Ali Hajimiri, “Concepts and methods in optimization of integrated LC VCOs,” IEEE JSSC, June 2001. Robust Design 6 start-up c (pF) 4 • Solid lines : fast corner • Broken lines : slow corner • Shaded region : unreliable design T.R.1 2 T.R.2 0 0 20 40 60 80 100 w (μ m) Donhee Ham • Donhee Ham and Ali Hajimiri, “Concepts and methods in optimization of integrated LC VCOs,” IEEE JSSC, June 2001. Phase Noise Measurement Bias Tee Vdd Bond Wires DUT Circuit Board Vdd Bias Tee Spectrum Analyzer 50 matching Probe Station 1.0 mm 1.1 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 • Donhee Ham and Ali Hajimiri, “Concepts and methods in optimization of integrated LC VCOs,” IEEE JSSC, June 2001. Performance Comparison Performance Metric : Power-Frequency-Tuning-Normalized (PFTN) Figure of Merit kT f 2 f 2 PFTN 10 log 0 tune L{ f off } Psup f off f 0 PFTN 0 CMOS 20 Bipolar CMOS/bondwire inductor CMOS distributed 40 CMOS/special metal layer This work Publications (Chronological Order) Donhee Ham • Donhee Ham and Ali Hajimiri, “Concepts and methods in optimization of integrated LC VCOs,” IEEE JSSC, June 2001. 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 • Two modes of mixer operation Hard-Switching Soft-Switching • C : IF port capacitance - Mixer parasitic capacitors - IF amplifier input capacitance - Important design parameter • Role of energy storing elements? Donhee Ham Characteristic of Mixers “Cyclostationary Noise” “Noise is shaped in time.” x(t ) n(t ) p(t ) stationary noise cyclostationary noise • Cyclostationary noise is periodically modulated noise. • It results when circuits have periodic operating points. • Its statistical averages are time-dependent. Donhee Ham periodic/deterministic function PSD of Cyclostationary Noise 1 2 S x ( f ) lim XT ( f ) Sx ( f ;t) T T T ( X T ( f ) x(t )e j 2ft dt ) 0 • operationally-defined, time-varying PSD. • F.T. of autocorrelation. “measurement = LTI bandpass filtering” Donhee Ham Cyclostationary Noise Flow in RF Systems S ( f ;t) S ( f ;t) Donhee Ham Importance of Cyclostationary Noise Donhee Ham • Donhee Ham and Ali Hajimiri, “Switching mixers: theory and measurement,” Submitted to IEEE JSSC. Theoretical Prediction of CG and NF new prediction Our approach conventional • fIF = 10 MHz • fLO = 300 MHz new prediction Utilization of stochastic calculus to evaluate the noise figure. • 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 conventional “Optimum design capacitance.” Thevenin Equivalent Circuit “time-varying filtering” hard switching soft switching IF component Non-IF components Donhee Ham • A. R. Shahani et al, ``A 12-mW wide dynamic range CMOS front-end for a portable GPS receiver," IEEE JSSC, Dec. 1997. Deterministic Dynamics - I • Donhee Ham et al, “Switching mixers: theory and measurement,” Submitted to IEEE JSSC. Donhee Ham Via Pseudo-beating (pattern generation) Deterministic Dynamics - II • Donhee Ham et al, “Switching mixers: theory and measurement,” Submitted to IEEE JSSC. “Conversion Gain Enhancement” Bump size ~ Harmonic Richness Donhee Ham Stochastic Dynamics dvnoise gT (t ) g (t ) vn (t ) T veff ,n (t ) dt C C synchronized Langevin Equation v(t )v(t ) Fourier Transform S ( f IF , t ) measurement (time-average) S ( f IF , t ) S ( f IF , t ) S0 ( f IF ) Donhee Ham • Donhee Ham and Ali Hajimiri, “Switching mixers: theory and measurement,” Submitted to IEEE JSSC. Mixer Test Chip and Board Test capacitors (to be laser-trimmed) MOS switching mixer core 0.7 mm Post amplifier 1.2 mm Conexant 0.35um BiCMOS Chip (MOS Only) Donhee Ham Assembled printed-circuit board for the chip test • Donhee Ham and Ali Hajimiri, “Switching mixers: theory and measurement,” Submitted to IEEE JSSC. Mixer Measurement Setup LODC LO RF RFDC • Test On-Chip Capacitors • Cut by Laser Trimming IF AMP Mixer NF Noise Diode (HP Noise Source) Donhee Ham • Donhee Ham and Ali Hajimiri, “Switching mixers: theory and measurement,” Submitted to IEEE JSSC. Measurement Results - I “First observation of cyclostationary noise effects” Measurement Result Theoretical Prediction NF(dB) NF(dB) Hard Switching Hard Switching Soft Switching Soft Switching IF capacitor (fF) Donhee Ham IF capacitor (fF) • Donhee Ham and Ali Hajimiri, “Switching mixers: theory and measurement,” Submitted to IEEE JSSC. Measurement Results - II “First observation of C.G. enhancement and NF degradation” Donhee Ham • Donhee Ham and Ali Hajimiri, “Switching mixers: theory and measurement,” Submitted to IEEE JSSC. 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 Electrical Brownian Motor T1 T1 T2 thermal noise Other Example T2 - Dithering in A/D converters Stochastic Resonance SNR U Escape rate ~ exp kT 1. Stochastic Resonance 2. 3. U Donhee Ham T Noise-enhanced heterodyning Noise-induced phase sync. Noise-enhanced linearization 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 time ? Pulse train generator “Soliton oscillator”: analogous to pulse lasers (e.g. femto-second lasers). Donhee Ham Harvard RF and High-Speed IC & Quantum Circuits Lab http://www.deas.harvard.edu/~donhee [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