Digital Frequency Synthesis Demystified DDS and Fractional-N PLLs Bar-Giora Goldberg a volume in the Demystified series LLH Technology Publishing Eagle Rock, VA www.LLH-Publishing.com Library of Congress Cataloging-in-Publication Data Goldberg, Bar-Giora. Digital frequency synthesis demystified / Bar-Giora Goldberg. p. cm. "A volume in the Demystified series." Includes bibliographical reference and index. ISBN 1-878707-47-7 (pbk. : alk. paper) 1. Frequency synthesizers-Design and construction. 2. Phase -locked loops. 3. Digital electronics. I. Title. TK7872.F73G55 1999 621.3815 486-dc21 99-34856 CIP Copyright © 1999 by LLH Technology Publishing. All rights reserved. No part of the book may be reproduced, in any form or means whatsoever, without written permission from the publisher. While every precaution has been taken in the preparation of this book, the publisher and author assume no responsibility for errors or omissions. Neither is any lia- bility assumed for damages resulting from the use of the information contained herein. Printed in the United States of America 10 987654321 Cover design: Sergio Villareal Developmental Editing: Carol Lewis Production: Kelly Johnson LLH Technology Publishing Eagle Rock, VA www.LLH-Publishing.com To Moshe, Shoshana, Pnina, Amit, and Dror This Page Intentionally Left Blank Contents Prefaces xi Symbols xv Chapter 1. Introduction to Frequency Synthesis 1 1-1 Introduction and Definitions 1 1-2 Synthesizer Parameters 5 1-2-1 Frequency Range 6 1-2-2 Frequency Resolution 6 1-2-3 Output Level 7 1-2-4 Control and Interface 7 1-2-5 Output Flatness 7 1-2-6 Output Impedance 7 1-2-7 Switching Speed 7 1-2-8 Phase Transient 8 1-2-9 Harmonics 9 1-2-10 Spurious Output 10 1-2-11 Phase Noise 10 1-2-12 Standard Reference 13 1-3 Auxiliary Specifications 13 1-4 Review of Synthesis Techniques 13 1-4-1 Phase-Locked Loop 14 1-4-2 Direct Analog Synthesis 21 1-4-3 Direct Digital Synthesis 26 1-5 Comparative Analysis 35 1-6 Conclusion 37 References 38 Chapter 2. Frequency Synthesizer System Analysis 39 2-1 Multiplying and Dividing 39 2-2 Phase Noise 42 2-3 Spurious and Phase Noise in PLL 49 2-4 Phase Noise Mechanism 51 2-4-1 Noise in Dividers 51 2-4-2 Noise in Oscillators 51 2-4-3 Noise in Phase Detectors 52 2-5 Mixing and Filtering 53 2-6 Frequency Planning 55 References 56 vi Contents Chapters. Measurement Techniques 57 3-1 Switching Speed 57 3-2 Phase Noise 61 3-2-1 Fl\/I Noise 62 3-2-2 Delay Line Discriminator 63 3-2-3 Integrated Phase Noise 66 3-2-4 Noise Density 66 3-3 Phase Continuity 66 3-4 Spurious Signals (Especially DDS) 67 3-5 Phase Memory 69 3-6 Step Size 69 3-7 Linear FM 70 3-8 Conclusion 70 References 71 Chapter 4. DDS General Architecture 73 4-1 Digital Modulators and Signal Reconstruction 75 4-2 Pulse Output DDS of the First Order 82 4-3 Pulse Output DDS of the Second Order 87 4-4 Standard DDS 89 4-4-1 Binary-Coded Decimal DDS 100 4-5 Randomization 105 4-5-1 Wheatley Procedure 106 4-5-2 Randomizing Sine Output 108 4-6 Quantization Errors 109 4-6-1 Digitized Model 109 4-7 Logic Speed Considerations 120 4-8 Modulation 120 4-9 State-of-the-Art Components and Systems 128 4-9-1 Very High-Speed Direct Digital Synthesizer 128 4-9-2 Medium-Speed Direct Digital Synthesizer 129 4-10 Performance Evaluation 133 4-10-1 Switching Speed 133 4-10-2 Phase Noise 133 4-10-3 Spurious Signals 134 4-10-4 Phase Continuity 134 4-10-5 Resolution 134 4-11 Sample-and-Hold Devices 134 4-12 Single-Bit DDS Revisited 135 4-13 Arbitrary Waveform Generators 138 4-14 Digital Chirp DDS 140 4-15 Conclusion 140 Appendix 4A DDS Applications 141 Appendix 4B DDS—Spectra and the Time Domain 143 Appendix 4C Sampling Theorem 157 Appendix 4D The Effect of Phase Noise on Data Conversion Devices 159 References 160 Contents vii Chapter 5. Phase-Locked Loop Synthesizers 163 5-1 Main Components of PLL Synthesis 164 5-1-1 Voltage Controlled Oscillators 165 5-1-2 Analog Phase Detector 168 5-1-3 Digital Phase Detector 1 172 5-1-4 Digital Phase Detector 2 175 5-1-5 Digital Phase Detector 3 176 5-1-6 Digital/Analog Phase Detector 4 177 5-1-7 Dividers 180 5-2 Performance Evaluation 184 5-2-1 Wireless PLL ASIC Configuration 198 5-3 Fractional-A/Synthesizers 201 5-3-1 Fractional-yv Synthesis of the First Order 204 5-3-2 Fractional-A/ Synthesis of the Second Order 216 5-4 Fractlonal-/V Synthesis of the Third Order 220 5-5 DDS-Based PLL 224 5-5-1 Speed Up 226 5-6 Single-Chip PLL Synthesis 227 5-7 Conclusion 230 References 235 Chapters. Accumulators 237 6-1 Binary Accumulators 237 6-2 Decimal Accumulators 245 6-3 Interface to ROM 246 6-4 Accumulator DDS 248 6-5 Phase Adder and Accumulator Segmentation 248 6-6 Conclusion 250 References 250 Chapter 7. Lookup Table and Sine ROM Compression 251 7-1 ROM Algorithm 252 7-2 Quadrant Compression 256 7-3 Compression Principles 259 7-4 Direct Taylor Approximation 260 7-5 Hutchison Algorithm 262 7-6 Sunderland Algorithm 266 7-7 Variations and Randomization 269 7-8 Auxiliary Function ROM Approximation 271 7-8-1 Spurious Signal Analysis 274 7-9 Coordinate Transformation (CORDIC) 275 7-10 Other Methods 278 7-11 Conclusion 279 References 280 viii Contents Chapter 8. Digital-to-Analog Converters 281 8-1 DAC Performance Evaluation 282 8-2 DAC Principles of Operation 285 8-3 DAC Parameters 292 8-3-1 Update Rate 292 8-3-2 Resolution 292 8-3-3 Logic Format 293 8-3-4 Setup-and-Hold Time 293 8-3-5 Rise, Fall, and Settling Times 293 8-3-6 Propagation Delay Time 294 8-3-7 Differential Linearity 294 8-3-8 Integral Nonlinearity 294 8-3-9 Monotonicity 295 8-3-10 IVIultiplying Bandwidth 295 8-3-11 Glitch Energy 295 8-3-12 Symmetry 296 8-4 State-of-the-Art DACs 296 8-4-1 Low-Speed Operation 296 8-4-2 Medium-Speed Operation 298 8-4-3 Very High-Speed Operation 298 8-4-4 Other Recommended DACs 299 8-5 Sine-Wave DAC 299 8-6 l\1ultiplexing 299 References 303 Chapter 9. Synthesizers in Use and Reference Generators 305 9-1 Synthesizers in Use 305 9-1-1 Hewlett-Packard 3325B 306 9-1-2 Hewlett-Packard 8662A 307 9-1-3 Program Test Sources 310 307 9-1-4 Comstron/Aeroflex FS-2000 309 9-1-5 Schomandl Models ND500 and ND1000 309 9-1-6 Stanford Research DS345 309 9-2 Reference Generators 313 9-2-1 General Review 314 9-2-2 Crystal Oscillators 316 9-3 Conclusion 319 References 319 Chapter 10. Original Paper and Software 321 10-1 Tierney, Rader, and Gold Article 321 10-2 Software Description 322 Index 333 ABOUT THIS BOOK AND CDROM This book—the latest volume in our popular Demystified series of technical references—is an updated version of an earlier text, Digital Techniques in Frequency Synthesis, published by McGraw- Hill. In addition to the updated text, a CDROM has been added that contains an assortment of design tools, including an informa- tive new reference in pdf format from Analog Devices called A Technical Tutorial on Digital Signal Synthesis. The CDROM also includes a fully searchable pdf file of the entire book contents. For a full list of the CDROM contents, see Chapter 10. ABOUT THE AUTHOR Bar-Giora Goldberg received his education at the Technion- Israel Institute of Technology in Haifa, and he worked there for 10 years in communication and spread-spectrum systems. In 1984 he cofounded Sciteq Electronics, a world leader in the field of digital frequency synthesis, and he now heads Vitacomm, a company dedicated to frequency and time engineering products for wireless and high-speed telecommunications. Giora has writ- ten extensively, has been awarded several patents, and has been a major contributor to the introduction and development of DDS and fractional-N technologies. He is also associated with Besser Associates in the US and Continuous Education International (CEI) in Europe, companies dedicated to continuous education via seminars and on-line courses.