PHASE-LOCK BASICS Second Edition WILLIAM F. EGAN, Ph.D. Lecturer in Electrical Engineering Santa Clara University <<>>IEEE The Institute of Electrical and Electronics Engineers, Inc., New York BICINTINNI AU JI in ; 1 807 jj \ ®WILEY \ I2007 \ WILEY-INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION
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PHASE-LOCK BASICS
Second Edition
WILLIAM F. EGAN, Ph.D. Lecturer in Electrical Engineering Santa Clara University
<<>>IEEE The Institute of Electrical and Electronics Engineers, Inc., New York
B I C I N T I N N I AU J I in
; 1 8 0 7 jj
\ ®WILEY \ I 2 0 0 7 \
WILEY-INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION
CONTENTS
PREFACE TO THE SECOND EDITION xix
PREFACE TO THE FIRST EDITION xxi
SYMBOLS LIST AND GLOSSARY xxv
PART 1 PHASE LOCK WITHOUT NOISE
1 INTRODUCTION 3
1.1 What is a Phase-Locked Loop (PLL)? / 3 1.2 Why Use a Phase-Locked Loop? / 3
7.4.4 Phase or Frequency at Inputs and Outputs / 119 7.5 Transient Responses Between Various Points / 120 7.6 Magnitude and Phase of the Transfer Functions / 120
10.A.5 Modulation Response / 224 ilO.B Appendix: Costas Loop forNPhases / 227 ilO.C Appendix: Symbol Clock Recovery / 227 ilO.D Appendix: ADPLL by Pulse Addition and Removal,
Additional Material / 228
10.F Appendix: Fractional-/V and Sigma-Delta / 228
ilO.M Appendix: MATLAB® Simulations / 228
ilO.T Appendix: Combined PLL and DLL / 229
PART 2 PHASE LOCK IN NOISE
11 PHASE MODULATION BY NOISE 233
11.1 Representation of Noise Modulation / 233 11.2 Processing of Noise Modulation by the
Phase-Locked Loop / 236 11.3 Phase and Frequency Variance / 237 11.4 Typical Oscillator Spectrums / 238 11.5 Limits on the Noise Spectrum—Infinite Variances / 240 11.6 Power Spectrum / 242
11.6.1 Spectrum for Small m I 242
11.6.2 Single-Sideband Density / 243 11.6.3 When is the Modulation Small? / 245 11.6.4 Modification of Spectral Shape at Higher Modulation
Index / 246 11.6.5 Scr ip ta / 247
XJV CONTENTS
11.7 Frequency Multiplication and Division / 247 11.8 Other Representations / 248 ill.H Shape of Output Spectrum / 249 1 l.S Appendix: Spreadsheets for Integrating Densities / 249
12 RESPONSE TO PHASE NOISE 251
12.1 Processing of Reference Phase Noise / 251 12.2 Processing ofVCO Phase Noise / 254 12.3 Harmful Effect of Phase Noise in Radio Receivers / 255 12.4 Superposition / 256
12.5 Optimum Loop With Both Input and VCO Noise / 257 12.6 Multiple Loops / 260 12.7 Effects of Noise Injected Elsewhere / 260 12.8 Measuring Phase Noise / 261
12.8.1 Using a Phase Detector / 263 12.8.1.1 Calibration / 263
12.8.1.2 Obtaining a Measurement Reference / 265
12.8.2 Using a Frequency Discriminator / 269 12.8.3 Using a Spectrum Analyzer or Receiver / 270
13 REPRESENTATION OF ADDITIVE NOISE 271
13.1 General / 271
13.2 Phase Modulation on the Signal / 273 13.3 Multiplicative Modulation on Quadrature Carriers / 275 13.4 Noise at the Phase Detector Output / 276 13.5 Restrictions on the Noise Models / 277 13.6 Does the Loop Lock to the Additive Noise? / 280
13.7 Other Types of Phase Detectors in the Presence of Noise / 281 13.7.1 Triangulär Characteristic / 282 13.7.2 Sawtooth Characteristic / 283
13.8 Modified Phase Detector Characteristic with Phase Noise / 283 il3.A Appendix: Decomposition of a Single Sideband / 286
14 LOOP RESPONSE TO ADDITIVE NOISE 287
14.1 Noise Bandwidth / 287 14.2 Signal-to-Noise Ratio in the Loop Bandwidth / 290 14.3 Loop Optimization in the Presence of Noise / 291
14.3.1 The Problem / 292
CONTENTS XV
14.3.2 Measures to be Used / 292 14.3.3 Optimum Loop for a Phase Step Input / 293 14.3.4 Optimum Loop for a Frequency Step Input / 294 14.3.5 Optimum Loop for a Frequency Ramp Input / 294 il4.A Appendix: Integration of Eq. (6.4a) / 296 il4.B Appendix: Loop Optimization in the
Presence of Noise / 296
15 PHASE-LOCKED LOOP AS A DEMODULATOR 297
15.1 Phase Demodulation / 297 15.1.1 Noise / 297
15.1.2 DistortionoftheDemodulated Signal / 299 15.1.3 Demodulation with a Linear Phase Detector
Characteristic / 300 15.2 Frequency Demodulation, Bandwidth Set by a Filter / 301 15.3 Frequency Discriminator, First-Order Loop / 305 15.4 Frequency Discriminator, Second-Order Loop / 306 15.5 Expected Phase Error / 307
15.6 Summary of Frequency Discriminator S/N I 308 15.7 Standard Discriminator and Click Noise / 310 15.8 Clicks with a PLL / 313 15.9 Noise in a Carrier Recovery Loop / 314 15.C Appendix: Spectrum of Clicks / 316 15.E Appendix: erfc / 317
16 PARAMETER VARIATION DUE TO NOISE 319
16.1 Preview / 319 16.1.1 Automatic Gain Control (AGC) / 319 16.1.2 Limiter / 320 16.1.3 Driving the Phase Detector Hard from
the Signal / 321 16.1.4 Effects of Variations / 322
20.3 Extension to Other Types of Interference / 411 i20.M Appendix: MATLAB® Scripts / 413
i20.O Appendix: Off set Interference Data Correlation / 413 i20.S Appendix: Band Limited Simulation Data / 413
21 FURTHER INFORMATION 415
21.1 Sources for Additional Studies in Phase Lock / 415 21.2 Sources Covering Phase-Locked Frequency Synthesis / 416 2 LA Appendix: Modulations and Spectrums / 416 21.B Appendix: Getting Files from the Wiley Internet Site / 421