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Analog Integrated Circuit Design
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CHAPTER 1 INTEGRATED-CIRCUIT DEVICES AND MODELLING 1 1.1 Semiconductors and pn Junctions 1 1.1.1 Diodes 2 1.1.2 Reverse-Biased Diodes 4 1.1.3 Graded Junctions 7 1.1.4 Large-Signal Junction Capacitance 9 1.1.5 Forward-Biased Junctions 10 1.1.6 Junction Capacitance of Forward-Biased Diode 11 1.1.7 Small-Signal Model of a Forward-Biased Diode 12 1.1.8 Schottky Diodes 13 1.2 MOS Transistors 14 1.2.1 Symbols for MOS Transistors 15 1.2.2 Basic Operation 16 1.2.3 Large-Signal Modelling 21 1.2.4 Body Effect 24 1.2.5 p-Channel Transistors 24 1.2.6 Low-Frequency Small-Signal Modelling in the Active Region 25 1.2.7 High-Frequency Small-Signal Modelling in the Active Region 30 1.2.8 Small-Signal Modelling in the Triode and Cutoff Regions 33 1.2.9 Analog Figures of Merit and Trade-offs 36 1.3 Device Model Summary 38 1.3.1 Constants 38 1.3.2 Diode Equations 39 1.3.3 MOS Transistor Equations 40 1.4 Advanced MOS Modelling 42 1.4.1 Subthreshold Operation 42 1.4.2 Mobility Degradation 44 1.4.3 Summary of Subthreshold and Mobility Degradation Equations 47 1.4.4 Parasitic Resistances 47 1.4.5 Short-Channel Effects 48 1.4.6 Leakage Currents 49 1.5 SPICE Modelling Parameters 50 1.5.1 Diode Model 50 1.5.2 MOS Transistors 51 1.5.3 Advanced SPICE Models of MOS Transistors 51 1.6 Passive Devices 54 1.6.1 Resistors 54 1.6.2 Capacitors 58 1.7 Appendix 60 1.7.1 Diode Exponential Relationship 60 1.7.2 Diode-Diffusion Capacitance 62 1.7.3 MOS Threshold Voltage and the Body Effect 64 1.7.4 MOS Triode Relationship 66 1.8 Key Points 68 1.9 References 69 1.10 Problems 69 CHAPTER 2 PROCESSING AND LAYOUT 73 2.1 CMOS Processing 73 2.1.1 The Silicon Wafer 73 2.1.2 Photolithography and Well Definition 74 2.1.3 Diffusion and Ion Implantation 76 2.1.4 Chemical Vapor Deposition and Defining the Active Regions 78 2.1.5 Transistor Isolation 78 2.1.6 Gate-Oxide and Threshold-Voltage Adjustments 81 2.1.7 Polysilicon Gate Formation 82 2.1.8 Implanting the Junctions, Depositing SiO2, and Opening Contact Holes 82 2.1.9 Annealing, Depositing and Patterning Metal, and Overglass Deposition 84 2.1.10 Additional Processing Steps 84 2.2 CMOS Layout and Design Rules 86 2.2.1 Spacing Rules 86 2.2.2 Planarity and Fill Requirements 94 2.2.3 Antenna Rules 94 2.2.4 Latch-Up 95 2.3 Variability and Mismatch 96 2.3.1 Systematic Variations Including Proximity Effects 96 2.3.2 Process Variations 98 2.3.3 Random Variations and Mismatch 99 2.4 Analog Layout Considerations 103 2.4.1 Transistor Layouts 103 2.4.2 Capacitor Matching 104 2.4.3 Resistor Layout 107 2.4.4 Noise Considerations 109 2.5 Key Points 113 2.6 References 114 2.7 Problems 114 CHAPTER 3 BASIC CURRENT MIRRORS AND SINGLE-STAGE AMPLIFIERS 117 3.1 Simple CMOS Current Mirror 118 3.2 Common-Source Amplifier 120 3.3 Source-Follower or Common-Drain Amplifier 122 3.4 Common-Gate Amplifier 124 3.5 Source-Degenerated Current Mirrors 127 3.6 Cascode Current Mirrors 129 3.7 Cascode Gain Stage 131 3.8 MOS Differential Pair and Gain Stage 135 3.9 Key Points 138 3.10 References 139 3.11 Problems 139 CHAPTER 4 FREQUENCY RESPONSE OF ELECTRONIC CIRCUITS 144 4.1 Frequency Response of Linear Systems 144 4.1.1 Magnitude and Phase Response 145 4.1.2 First-Order Circuits 147 4.1.3 Second-Order Low-Pass Transfer Functions with Real Poles 154 4.1.4 Bode Plots 157 4.1.5 Second-Order Low-Pass Transfer Functions with Complex Poles 163 4.2 Frequency Response of Elementary Transistor Circuits 165 4.2.1 High-Frequency MOS Small-Signal Model 165 4.2.2 Common-Source Amplifier 166 4.2.3 Miller Theorem and Miller Effect 169 4.2.4 Zero-Value Time-Constant Analysis 173 4.2.5 Common-Source Design Examples 176 4.2.6 Common-Gate Amplifier 179 4.3 Cascode Gain Stage 181 4.4 Source-Follower Amplifier 187 4.5 Differential Pair 193 4.5.1 High-Frequency T-Model 193 4.5.2 Symmetric Differential Amplifier 194 4.5.3 Single-Ended Differential Amplifier 195 4.5.4 Differential Pair with Active Load 196 4.6 Key Points 197 4.7 References 198 4.8 Problems 199 CHAPTER 5 FEEDBACK AMPLIFIERS 204 5.1 Ideal Model of Negative Feedback 204 5.1.1 Basic Definitions 204 5.1.2 Gain Sensitivity 205 5.1.3 Bandwidth 207 5.1.4 Linearity 207 5.1.5 Summary 208 5.2 Dynamic Response of Feedback Amplifiers 208 5.2.1 Stability Criteria 209 5.2.2 Phase Margin 211 5.3 First- and Second-Order Feedback Systems 213 5.3.1 First-Order Feedback Systems 213 5.3.2 Second-Order Feedback Systems 217 5.3.3 Higher-Order Feedback Systems 220 5.4 Common Feedback Amplifiers 220 5.4.1 Obtaining the Loop Gain, L(s) 222 5.4.2 Non-Inverting Amplifier 226 5.4.3 Transimpedance (Inverting) Amplifiers 231 5.5 Summary of Key Points 235 5.6 References 235 5.7 Problems 236 CHAPTER 6 BASIC OPAMP DESIGN AND COMPENSATION 242 6.1 Two-Stage CMOS Opamp 242 6.1.1 Opamp Gain 243 6.1.2 Frequency Response 245 6.1.3 Slew Rate 249 6.1.4 n-Channel or p-Channel Input Stage 252 6.1.5 Systematic Offset Voltage 252 6.2 Opamp Compensation 254 6.2.1 Dominant-Pole Compensation and Lead Compensation 254 6.2.2 Compensating the Two-Stage Opamp 255 6.2.3 Making Compensation Independent of Process and Temperature 259 6.3 Advanced Current Mirrors 261 6.3.1 Wide-Swing Current Mirrors 261 6.3.2 Enhanced Output-Impedance Current Mirrors and Gain Boosting 263 6.3.3 Wide-Swing Current Mirror with Enhanced Output Impedance 266 6.3.4 Current-Mirror Symbol 267 6.4 Folded-Cascode Opamp 268 6.4.1 Small-Signal Analysis 270 6.4.2 Slew Rate 272 6.5 Current Mirror Opamp 275 6.6 Linear Settling Time Revisited 279 6.7 Fully Differential Opamps 281 6.7.1 Fully Differential Folded-Cascode Opamp 283 6.7.2 Alternative Fully Differential Opamps 284 6.7.3 Low Supply Voltage Opamps 286 6.8 Common-Mode Feedback Circuits 288 6.9 Summary of Key Points 292 6.10 References 293 6.11 Problems 294 CHAPTER 7 BIASING, REFERENCES, AND REGULATORS 302 7.1 Analog Integrated Circuit Biasing 302 7.1.1 Bias Circuits 303 7.1.2 Reference Circuits 305 7.1.3 Regulator Circuits 306 7.2 Establishing Constant Transconductance 307 7.2.1 Basic Constant-Transconductance Circuit 307 7.2.2 Improved Constant-Transconductance Circuits 309 7.3 Establishing Constant Voltages and Currents 310 7.3.1 Bandgap Voltage Reference Basics 310 7.3.2 Circuits for Bandgap References 314 7.3.3 Low-Voltage Bandgap Reference 319 7.3.4 Current Reference 320 7.4 Voltage Regulation 321 7.4.1 Regulator Specifications 322 7.4.2 Feedback Analysis 322 7.4.3 Low Dropout Regulators 324 7.5 Summary of Key Points 327 7.6 References 327 7.7 Problems 328 CHAPTER 8 BIPOLAR DEVICES AND CIRCUITS 331 8.1 Bipolar-Junction Transistors 331 8.1.1 Basic Operation 331 8.1.2 Analog Figures of Merit 341 8.2 Bipolar Device Model Summary 344 8.3 SPICE Modeling 345 8.4 Bipolar and BICMOS Processing 346 8.4.1 Bipolar Processing 346 8.4.2 Modern SiGe BiCMOS HBT Processing 347 8.4.3 Mismatch in Bipolar Devices 348 8.5 Bipolar Current Mirrors and Gain Stages 349 8.5.1 Current Mirrors 349 8.5.2 Emitter Follower 350 8.5.3 Bipolar Differential Pair 353 8.6 Appendix 356 8.6.1 Bipolar Transistor Exponential Relationship 356 8.6.2 Base Charge Storage of an Active BJT 359 8.7 Summary of Key Points 359 8.8 References 360 8.9 Problems 360 CHAPTER 9 NOISE AND LINEARITY ANALYSIS AND MODELLING 363 9.1 Time-Domain Analysis 363 9.1.1 Root Mean Square (rms) Value 364 9.1.2 SNR 365 9.1.3 Units of dBm 365 9.1.4 Noise Summation 366 9.2 Frequency-Domain Analysis 367 9.2.1 Noise Spectral Density 367 9.2.2 White Noise 369 9.2.3 1/f, or Flicker, Noise 370 9.2.4 Filtered Noise 371 9.2.5 Noise Bandwidth 373 9.2.6 Piecewise Integration of Noise 375 9.2.7 1/f Noise Tangent Principle 377 9.3 Noise Models for Circuit Elements 377 9.3.1 Resistors 378 9.3.2 Diodes 378 9.3.3 Bipolar Transistors 380 9.3.4 MOSFETS 380 9.3.5 Opamps 382 9.3.6 Capacitors and Inductors 382 9.3.7 Sampled Signal Noise 384 9.3.8 Input-Referred Noise 384 9.4 Noise Analysis Examples 387 9.4.1 Opamp Example 387 9.4.2 Bipolar Common-Emitter Example 390 9.4.3 CMOS Differential Pair Example 392 9.4.4 Fiber-Optic Transimpedance Amplifier Example 395 9.5 Dynamic Range Performance 397 9.5.1 Total Harmonic Distortion (THD) 398 9.5.2 Third-Order Intercept Point (IP3) 400 9.5.3 Spurious-Free Dynamic Range (SFDR) 402 9.5.4 Signal-to-Noise and Distortion Ratio (SNDR) 404 9.6 Key Points 405 9.7 References 406 9.8 Problems 406 CHAPTER 10 COMPARATORS 413 10.1 Comparator Specifications 413 10.1.1 Input Offset and Noise 413 10.1.2 Hysteresis 414 10.2 Using an Opamp for a Comparator 415 10.2.1 Input-Offset Voltage Errors 417 10.3 Charge-Injection Errors 418 10.3.1 Making Charge-Injection Signal Independent 421 10.3.2 Minimizing Errors Due to Charge-Injection 421 10.3.3 Speed of Multi-Stage Comparators 424 10.4 Latched Comparators 426 10.4.1 Latch-Mode Time Constant 427 10.4.2 Latch Offset 430 10.5 Examples of CMOS and BiCMOS Comparators 431 10.5.1 Input-Transistor Charge Trapping 435 10.6 Examples of Bipolar Comparators 437 10.7 Key Points 439 10.8 References 440 10.9 Problems 440 CHAPTER 11 SAMPLE-AND-HOLD AND TRANSLINEAR CIRCUITS 444 11.1 Performance of Sample-and-Hold Circuits 444 11.1.1 Testing Sample and Holds 445 11.2 MOS Sample-and-Hold Basics 446 11.3 Examples of CMOS S/H Circuits 452 11.4 Bipolar and BiCMOS Sample-and-Holds 456 11.5 Translinear Gain Cell 460 11.6 Translinear Multiplier 462 11.7 Key Points 464 11.8 References 465 11.9 Problems 466 CHAPTER 12 CONTINUOUS-TIME FILTERS 469 12.1 Introduction to Continuous-Time Filters 469 12.1.1 First-Order Filters 470 12.1.2 Second-Order Filters 470 12.2 Introduction to Gm-C Filters 471 12.2.1 Integrators and Summers 472 12.2.2 Fully Differential Integrators 474 12.2.3 First-Order Filter 475 12.2.4 Biquad Filter 477 12.3 Transconductors Using Fixed Resistors 479 12.4 CMOS Transconductors Using Triode Transistors 484 12.4.1 Transconductors Using a Fixed-Bias Triode Transistor 484 12.4.2 Transconductors Using Varying Bias-Triode Transistors 486 12.4.3 Transconductors Using Constant Drain-Source Voltages 491 12.5 CMOS Transconductors Using Active Transistors 493 12.5.1 CMOS Pair 493 12.5.2 Constant Sum of Gate-Source Voltages 494 12.5.3 Source-Connected Differential Pair 495 12.5.4 Inverter-Based 495 12.5.5 Differential-Pair with Floating Voltage Sources 497 12.5.6 Bias-Offset Cross-Coupled Differential Pairs 499 12.6 Bipolar Transconductors 500 12.6.1 Gain-Cell Transconductors 500 12.6.2 Transconductors Using Multiple Differential Pairs 501 12.7 BiCMOS Transconductors 506 12.7.1 Tunable MOS in Triode 506 12.7.2 Fixed-Resistor Transconductor with a Translinear Multiplier 507 12.7.3 Fixed Active MOS Transconductor with a Translinear Multiplier 508 12.8 Active RC and MOSFET-C Filters 509 12.8.1 Active RC Filters 510 12.8.2 MOSFET-C Two-Transistor Integrators 512 12.8.3 Four-Transistor Integrators 515 12.8.4 R-MOSFET-C Filters 521 12.9 Tuning Circuitry 516 12.9.1 Tuning Overview 517 12.9.2 Constant Transconductance 519 12.9.3 Frequency Tuning 520 12.9.4 Q-Factor Tuning 522 12.9.5 Tuning Methods Based on Adaptive Filtering 523 12.10 Introduction to Complex Filters 525 12.10.1 Complex Signal Processing 525 12.10.2 Complex Operations 526 12.10.3 Complex Filters 527 12.10.4 Frequency-Translated Analog Filters 528 12.11 Key Points 531 12.12 References 532 12.13 Problems 534 CHAPTER 13 DISCRETE-TIME SIGNALS 537 13.1 Overview of Some Signal Spectra 537 13.2 Laplace Transforms of Discrete-Time Signals 537 13.2.1 Spectra of Discrete-Time Signals 540 13.3 z-Transform 541 13.4 Downsampling and Upsampling 543 13.5 Discrete-Time Filters 545 13.5.1 Frequency Response of Discrete-Time Filters 545 13.5.2 Stability of Discrete-Time Filters 548 13.5.3 IIR and FIR Filters 550 13.5.4 Bilinear Transform 550 13.6 Sample-and-Hold Response 552 13.7 Key Points 554 13.8 References 555 13.9 Problems 555 CHAPTER 14 SWITCHED-CAPACITOR CIRCUITS 557 14.1 Basic Building Blocks 557 14.1.1 Opamps 557 14.1.2 Capacitors 558 14.1.3 Switches 558 14.1.4 Nonoverlapping Clocks 559 14.2 Basic Operation and Analysis 560 14.2.1 Resistor Equivalence of a Switched Capacitor 560 14.2.2 Parasitic-Sensitive Integrator 560 14.2.3 Parasitic-Insensitive Integrators 565 14.2.4 Signal-Flow-Graph Analysis 569 14.3 Noise in Switched-Capacitor Circuits 570 14.4 First-Order Filters 572 14.4.1 Switch Sharing 575 14.4.2 Fully Differential Filters 575 14.5 Biquad Filters 577 14.5.1 Low-Q Biquad Filter 577 14.5.2 High-Q Biquad Filter 581 14.6 Charge Injection 585 14.7 Switched-Capacitor Gain Circuits 588 14.7.1 Parallel Resistor-Capacitor Circuit 588 14.7.2 Resettable Gain Circuit 588 14.7.3 Capacitive-Reset Gain Circuit 591 14.8 Correlated Double-Sampling Techniques 593 14.9 Other Switched-Capacitor Circuits 594 14.9.1 Amplitude Modulator 594 14.9.2 Full-Wave Rectifier 595 14.9.3 Peak Detectors 596 14.9.4 Voltage-Controlled Oscillator 596 14.9.5 Sinusoidal Oscillator 598 14.10 Key Points 600 14.11 References 601 14.12 Problems 602 CHAPTER 15 DATA CONVERTER FUNDAMENTALS 606 15.1 Ideal D/A Converter 606 15.2 Ideal A/D Converter 608 15.3 Quantization Noise 609 15.3.1 Deterministic Approach 609 15.3.2 Stochastic Approach 610 15.4 Signed Codes 612 15.5 Performance Limitations 614 15.5.1 Resolution 614 15.5.2 Offset and Gain Error 615 15.5.3 Accuracy and Linearity 615 15.6 Key Points 620 15.7 References 620 15.8 Problems 620 CHAPTER 16 NYQUIST-RATE D/A CONVERTERS 623 16.1 Decoder-Based Converters 623 16.1.1 Resistor String Converters 623 16.1.2 Folded Resistor-String Converters 625 16.1.3 Multiple Resistor-String Converters 625 16.1.4 Signed Outputs 627 16.2 Binary-Scaled Converters 628 16.2.1 Binary-Weighted Resistor Converters 629 16.2.2 Reduced-Resistance-Ratio Ladders 630 16.2.3 R-2R-Based Converters 630 16.2.4 Charge-Redistribution Switched-Capacitor Converters 632 16.2.5 Current-Mode Converters 633 16.2.6 Glitches 633 16.3 Thermometer-Code Converters 634 16.3.1 Thermometer-Code Current-Mode D/A Converters 636 16.3.2 Single-Supply Positive-Output Converters 637 16.3.3 Dynamically Matched Current Sources 638 16.4 Hybrid Converters 640 16.4.1 Resistor-Capacitor Hybrid Converters 640 16.4.2 Segmented Converters 640 16.5 Key Points 642 16.6 References 643 16.7 Problems 643 CHAPTER 17 NYQUIST-RATE A/D CONVERTERS 646 17.1 Integrating Converters 646 17.2 Successive-Approximation Converters 650 17.2.1 DAC-Based Successive Approximation 652 17.2.2 Charge-Redistribution A/D 653 17.2.3 Resistor-Capacitor Hybrid 658 17.2.4 Speed Estimate for Charge-Redistribution Converters 658 17.2.5 Error Correction in Successive-Approximation Converters 659 17.2.6 Multi-Bit Successive-Approximation 662 17.3 Algorithmic (or Cyclic) A/D Converter 662 17.3.1 Ratio-Independent Algorithmic Converter 662 17.4 Pipelined A/D Converters 665 17.4.1 One-Bit-Per-Stage Pipelined Converter 667 17.4.2 1.5 Bit Per Stage Pipelined Converter 669 17.4.3 Pipelined Converter Circuits 672 17.4.4 Generalized k-Bit-Per-Stage Pipelined Converters 673 17.5 Flash Converters 673 17.5.1 Issues in Designing Flash A/D Converters 675 17.6 Two-Step A/D Converters 677 17.6.1 Two-Step Converter with Digital Error Correction 679 17.7 Interpolating A/D Converters 680 17.8 Folding A/D Converters 683 17.9 Time-Interleaved A/D Converters 687 17.10 Key Points 690 17.11 References 691 17.12 Problems 692 CHAPTER 18 OVERSAMPLING CONVERTERS 696 18.1 Oversampling without Noise Shaping 696 18.1.1 Quantization Noise Modelling 697 18.1.2 White Noise Assumption 697 18.1.3 Oversampling Advantage 699 18.1.4 The Advantage of 1-Bit D/A Converters 701 18.2 Oversampling with Noise Shaping 702 18.2.1 Noise-Shaped Delta-Sigma Modulator 703 18.2.2 First-Order Noise Shaping 704 18.2.3 Switched-Capacitor Realization of a First-Order A/D Converter 706 18.2.4 Second-Order Noise Shaping 706 18.2.5 Noise Transfer-Function Curves 708 18.2.6 Quantization Noise Power of 1-Bit Modulators 709 18.2.7 Error-Feedback Structure 709 18.3 System Architectures 711 18.3.1 System Architecture of Delta-Sigma A/D Converters 711 18.3.2 System Architecture of Delta-Sigma D/A Converters 713 18.4 Digital Decimation Filters 714 18.4.1 Multi-Stage 715 18.4.2 Single Stage 717 18.5 Higher-Order Modulators 718 18.5.1 Interpolative Architecture 718 18.5.2 Multi-Stage Noise Shaping (MASH) Architecture 719 18.6 Bandpass Oversampling Converters 721 18.7 Practical Considerations 722 18.7.1 Stability 722 18.7.2 Linearity of Two-Level Converters 723 18.7.3 Idle Tones 725 18.7.4 Dithering 726 18.7.5 Opamp Gain 726 18.8 Multi-Bit Oversampling Converters 727 18.8.1 Dynamic Element Matching 727 18.8.2 Dynamically Matched Current Source D/S Converters 728 18.8.3 Digital Calibration A/D Converter 728 18.8.4 A/D with Both Multi-Bit and Single-Bit Feedback 729 18.9 Third-Order A/D Design Example 730 18.10 Key Points 732 18.11 References 734 18.12 Problems 735 CHAPTER 19 PHASE-LOCKED LOOPS 738 19.1 Basic Phase-Locked Loop Architecture 738 19.1.1 Voltage Controlled Oscillator 739 19.1.2 Divider 740 19.1.3 Phase Detector 741 19.1.4 Loop Filer 746 19.1.5 The PLL in Lock 747 19.2 Linearized Small-Signal Analysis 748 19.2.1 Second-Order PLL Model 749 19.2.2 Limitations of the Second-Order Small-Signal Model 751 19.2.3 PLL Design Example 754 19.3 Jitter and Phase Noise 756 19.3.1 Period Jitter 760 19.3.2 P-Cycle Jitter 761 19.3.3 Adjacent Period Jitter 761 19.3.4 Other Spectral Representations of Jitter 762 19.3.5 Probability Density Function of Jitter 764 19.4 Electronic Oscillators 765 19.4.1 Ring Oscillators 766 19.4.2 LC Oscillators 771 19.4.3 Phase Noise of Oscillators 772 19.5 Jitter and Phase Noise in PLLS 777 19.5.1 Input Phase Noise and Divider Phase Noise 777 19.5.2 VCO Phase Noise 778 19.5.3 Loop Filter Noise 779 19.6 Key Points 781 19.7 References 782 19.8 Problems 782 INDEX 787

About the Author

Tony Chan Carusone completed the B.A.Sc. and Ph.D. degrees at the University of Toronto in 1997 and 2002 respectvely, during which tme he received the Governor-General's Silver Medal. Since 2001, he has been with the Department of Electrical and Computer Engineering at the University of Toronto where he is currently an Associate Professor. From 2002 to 2007 he held the Canada Research Chair in Integrated Systems and in 2008 was a visitng researcher at the University of Pavia. He is also an occasional consultant to industry, having worked for Snowbush Inc., Gennum Corp., and Intel Corp., all in the area of high-speed links. Tony was a co-author of the best student papers at both the 2007 and 2008 Custom Integrated Circuits Conference and the best paper at the 2005 Compound Semiconductor Integrated Circuits Symposium. He is an appointed member of the Administratve Commitee of the IEEE Solid-State Circuits Society, a member and past chair of the Analog Signal Processing Technical Commitee for the IEEE Circuits and Systems Society, and a past member and chair of the Wireline Communicatons subcommitee of the Custom Integrated Circuits Conference. He has served as a guest editor for both the IEEE Journal of Solid-State Circuits and the IEEE Transactons on Circuits and Systems I: Regular Papers, and served on the editorial board of the IEEE Transactons on Circuits and Systems II: Express Briefs from 2006 untl 2009 when he was Editor-in-Chief.

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