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Phaselock Techniques_3rd.Edition.F.M.Gardner.pdf

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    PHASELOCK TECHNIQUES
    PHASELOCK TECHNIQUES Third Edition FLOYD M. GARDNER Consulting Engineer Palo Alto, California A JOHN WILEY & SONS, INC., PUBLICATION
    Copyright  2005 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com. Library of Congress Cataloging-in-Publication Data: Gardner, Floyd Martin, 1929– Phaselock techniques / Floyd M. Gardner.—3rd ed. p. cm. Includes bibliographical references and index. ISBN-13 978-0-471-43063-6 (cloth) ISBN-10 0-471-43063-3 (cloth) 1. Phase-locked loops. I. Title. TK7872.P38G37 2005 621.3815 364—dc22 2004065041 Printed in the United States of America. 10 9 8 7 6 5 4 3 2 1
    To Benjamin
    CONTENTS PREFACE NOTATION 1 INTRODUCTION 1.1 Salient Properties of PLLs / 2 1.1.1 Bandwidth / 2 1.1.2 Linearity / 3 1.2 Organization of the Book / 3 1.3 Annotated Bibliography / 3 1.3.1 Books / 3 1.3.2 Reprint Volumes / 4 1.3.3 Journal Special Issues / 5 2 TRANSFER FUNCTIONS OF ANALOG PLLs 2.1 Basic Transfer Functions / 6 2.1.1 Transfer Functions of Individual Elements / 7 2.1.2 Combined Transfer Functions / 8 2.1.3 Characteristic Equation / 9 2.1.4 Nomenclature, Coefficients, and Units / 9 2.2 Second-Order PLLs / 10 2.2.1 Loop Filters / 10 2.2.2 Order and Type / 12 xvii xix 1 6 vii
    viii CONTENTS 2.2.3 Loop Parameters / 12 2.2.4 Frequency Response / 15 2.3 Other Loop Types and Orders / 20 2.3.1 General Definition of Loop Gain K / 20 2.3.2 Examples of Type 1 PLLs / 22 2.3.3 Examples of Type 2 PLLs / 24 2.3.4 Higher-Type PLLs / 28 Reference / 28 3 GRAPHICAL AIDS 3.1 Root-Locus Plots / 30 29 3.1.1 Description of Root-Locus Plots / 30 3.1.2 Stability Criterion / 33 3.1.3 Root Loci of Type 1 PLLs / 33 3.1.4 Root Loci of Type 2 PLLs / 33 3.1.5 Root Loci of Type 3 PLLs / 34 3.1.6 Root Loci of Higher-Order PLLs / 35 3.1.7 Effect of Loop Delay on Root Locus / 38 3.2 Bode Plots / 38 3.2.1 Presentation Options / 38 3.2.2 Stability / 39 3.2.3 Bode Plots of Type 1 PLLs / 40 3.2.4 Bode Plots of Type 2 PLLs / 43 3.2.5 Bode Plots of Type 3 PLLs / 48 3.3 Nyquist Diagrams / 49 3.4 Nichols Charts / 49 3.4.1 Stability Criterion / 49 3.4.2 M-Contours / 50 3.4.3 Examples of Nichols Charts / 50 3.5 Closed-Loop Frequency-Response Curves / 52 Appendix 3A: Salient Features of Root Loci / 52 3A.1 Branches of Root Loci / 53 3A.2 Locus on the Real Axis / 53 3A.3 Locus Intersections with Axes / 54 Appendix 3B: Formats of the Open-Loop Transfer Function G(s) / 56 3B.1 Proportional-Plus-Integral Section / 56 3B.2 High-Frequency Section / 60 3B.3 Calculations / 60
    ix 65 CONTENTS Appendix 3C: Closed-Loop Frequency Responses / 61 3C.1 Frequency-Response Formulas / 61 3C.2 Example Frequency-Response Graphs / 61 References / 64 4 DIGITAL PLLs: TRANSFER FUNCTIONS AND RELATED TOOLS 4.1 Distinctive Properties of Digital PLLs / 65 4.2 Digital Transfer Function / 66 4.2.1 Configuration of a Digital PLL / 66 4.2.2 Difference Equations / 67 4.2.3 z-Transforms of the Loop Elements / 69 4.2.4 Loop Filter / 70 4.2.5 Loop Transfer Functions / 71 4.2.6 Poles and Zeros / 71 4.3 Loop Stability / 73 4.3.1 Type 1 DPLLs / 73 4.3.2 Type 2 DPLLs / 73 4.3.3 Type 3 DPLLs / 74 4.4 Root-Locus Plots / 74 4.4.1 Root Loci of Type 1 DPLLs / 75 4.4.2 Root Loci of Type 2 DPLLs / 75 4.4.3 Root Loci of Type 3 DPLLs / 78 4.5 DPLL Frequency Responses: Formulation / 79 4.6 Bode Plots and Nichols Charts / 80 4.6.1 Basis of Bode Plots / 80 4.6.2 Bode Stability Criteria / 81 4.6.3 Bode Plots of Example DPLLs / 81 4.6.4 Nichols Chart Example / 83 4.7 Time-Continuous Approximation for a DPLL / 85 4.8 Frequency-Response Examples / 86 4.8.1 Effect of Delay / 86 4.8.2 Effect of Bandwidth / 87 4.9 Lowpass Filters in the Loop / 88 4.9.1 Infinite Impulse Response Lowpass Filter / 88 4.9.2 Finite Impulse Response Lowpass Filter / 90 Appendix 4A: Stability of Digital Phaselock Loops / 91 4A.1 Type 1 DPLL / 92 4A.2 Type 2 DPLL / 93 Reference / 96
    x 5 TRACKING 5.1 Linear Tracking / 97 CONTENTS 97 5.1.1 Steady-State Phase Errors / 98 5.1.2 Transient Response / 100 5.1.3 Response to Sinusoidal Angle Modulation / 109 5.2 Nonlinear Tracking: Lock Limits / 112 5.2.1 Phase-Detector Nonlinearity / 112 5.2.2 Steady-State Limits / 112 5.2.3 Transient Limits / 114 5.2.4 Modulation Limits / 118 References / 121 6 EFFECTS OF ADDITIVE NOISE 6.1 Linear Operation / 123 123 6.1.1 Noise Model of a Phase Detector / 123 6.1.2 Noise Transfer Function / 129 6.1.3 Noise Bandwidth / 129 6.1.4 Signal-to-Noise Ratio in a PLL / 131 6.1.5 Optimality / 132 6.2 Nonlinear Operation / 132 6.2.1 Observed Behavior / 133 6.2.2 Nonlinear Analysis of Phase Error / 135 6.2.3 Probability Density and Variance / 136 6.2.4 Cycle Slips / 137 6.2.5 Experimental and Simulation Results / 138 6.2.6 Approximate Analyses / 138 6.2.7 Miscellaneous Features / 139 References / 141 7 EFFECTS OF PHASE NOISE 143 7.1 Properties of Phase Noise / 144 7.1.1 Oscillator Model / 144 7.1.2 Neglect of Amplitude Noise / 144 7.1.3 Variance / 144 7.1.4 Nonstationarity / 144 7.2 Spectra of Phase Noise / 146 7.2.1 Theoretical Spectrum Wvo(f ) / 146 7.2.2 Normalized Spectrum L(f ) / 147 7.2.3 RF Spectra WRF(f ) and PRF(f ) / 147 7.2.4 Phase-Noise Spectrum Wφ(f ) / 149
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