PRACTICAL RF SYSTEM DESIGN

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PRACTICAL RF SYSTEM DESIGN PRACTICAL RF SYSTEM DESIGN WILLIAM F. EGAN, Ph.D. Lecturer in Electrical Engineering Santa Clara University The Institute of Electrical and Electronics Engineers, Inc., New York A JOHN WILEY & SONS, INC., PUBLICATION MATLAB is a registered trademark of The Math Works, Inc., 3 Apple Hill Drive, Natick, MA 01760-2098 USA; Tel: 508-647-7000, Fax 508-647-7101; WWW: http://www.mathworks.com; email: info@mathworks.com. Figures whose captions indicate they are reprinted from Frequency Synthesis by Phase Lock, 2nd ed., by William F. Egan, copyright  2000, John Wiley and Sons, Inc., are reprinted by permission. Copyright  2003 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. 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ISBN 0-471-20023-9 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 To those from whom I have learned: Teachers, Colleagues, and Students CONTENTS PREFACE xvii GETTING FILES FROM THE WILEY ftp AND INTERNET SITES xix SYMBOLS LIST AND GLOSSARY xxi 1 INTRODUCTION 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1 System Design Process / 1 Organization of the Book / 2 Appendixes / 3 Spreadsheets / 3 Test and Simulation / 3 Practical Skepticism / 4 References / 5 2 GAIN 7 2.1 Simple Cases / 8 2.2 General Case / 9 2.2.1 S Parameters / 9 2.2.2 Normalized Waves / 11 2.2.3 T Parameters / 12 vii viii CONTENTS 2.3 2.4 2.5 2.6 3 2.2.4 Relationships Between S and T Parameters / 13 2.2.5 Restrictions on T Parameters / 14 2.2.6 Cascade Response / 14 Simplification: Unilateral Modules / 15 2.3.1 Module Gain / 15 2.3.2 Transmission Line Interconnections / 16 2.3.3 Overall Response, Standard Cascade / 25 2.3.4 Combined with Bilateral Modules / 28 2.3.5 Lossy Interconnections / 32 2.3.6 Additional Considerations / 38 Nonstandard Impedances / 40 Use of Sensitivities to Find Variations / 40 Summary / 43 Endnotes / 45 NOISE FIGURE 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 Noise Factor and Noise Figure / 47 Modules in Cascade / 49 Applicable Gains and Noise Factors / 54 Noise Figure of an Attenuator / 55 Noise Figure of an Interconnect / 56 Cascade Noise Figure / 56 Expected Value and Variance of Noise Figure / 58 Impedance-Dependent Noise Factors / 59 3.8.1 Representation / 60 3.8.2 Constant-Noise Circles / 61 3.8.3 Relation to Standard Noise Factor / 62 3.8.4 Using the Theoretical Noise Factor / 64 3.8.5 Summary / 65 3.9 Image Noise, Mixers / 65 3.9.1 Effective Noise Figure of the Mixer / 66 3.9.2 Verification for Simple Cases / 69 3.9.3 Examples of Image Noise / 69 3.10 Extreme Mismatch, Voltage Amplifiers / 74 3.10.1 Module Noise Factor / 76 3.10.2 Cascade Noise Factor / 78 3.10.3 Combined with Unilateral Modules / 79 3.10.4 Equivalent Noise Factor / 79 47 CONTENTS ix 3.11 Using Noise Figure Sensitivities / 79 3.12 Mixed Cascade Example / 80 3.12.1 Effects of Some Resistor Changes / 81 3.12.2 Accounting for Other Reflections / 82 3.12.3 Using Sensitivities / 82 3.13 Gain Controls / 84 3.13.1 Automatic Gain Control / 84 3.13.2 Level Control / 86 3.14 Summary / 88 Endnotes / 90 4 NONLINEARITY IN THE SIGNAL PATH 4.1 Representing Nonlinear Responses / 91 4.2 Second-Order Terms / 92 4.2.1 Intercept Points / 93 4.2.2 Mathematical Representations / 95 4.2.3 Other Even-Order Terms / 97 4.3 Third-Order Terms / 97 4.3.1 Intercept Points / 99 4.3.2 Mathematical Representations / 100 4.3.3 Other Odd-Order Terms / 101 4.4 Frequency Dependence and Relationship Between Products / 102 4.5 Nonlinear Products in the Cascades / 103 4.5.1 Two-Module Cascade / 104 4.5.2 General Cascade / 105 4.5.3 IMs Adding Coherently / 106 4.5.4 IMs Adding Randomly / 108 4.5.5 IMs That Do Not Add / 109 4.5.6 Effect of Mismatch on IPs / 110 4.6 Examples: Spreadsheets for IMs in a Cascade / 111 4.7 Anomalous IMs / 115 4.8 Measuring IMs / 116 4.9 Compression in the Cascade / 119 4.10 Other Nonideal Effects / 121 4.11 Summary / 121 Endnote / 122 91 x 5 CONTENTS NOISE AND NONLINEARITY 123 5.1 Intermodulation of Noise / 123 5.1.1 Preview / 124 5.1.2 Flat Bandpass Noise / 125 5.1.3 Second-Order Products / 125 5.1.4 Third-Order Products / 130 5.2 Composite Distortion / 133 5.2.1 Second-Order IMs (CSO) / 134 5.2.2 Third-Order IMs (CTB) / 136 5.2.3 CSO and CTB Example / 136 5.3 Dynamic Range / 137 5.3.1 Spurious-Free Dynamic Range / 137 5.3.2 Other Range Limitations / 139 5.4 Optimizing Cascades / 139 5.4.1 Combining Parameters on One Spreadsheet / 139 5.4.2 Optimization Example / 143 5.5 Spreadsheet Enhancements / 146 5.5.1 Lookup Tables / 146 5.5.2 Using Controls / 147 5.6 Summary / 147 Endnotes / 147 6 ARCHITECTURES THAT IMPROVE LINEARITY 6.1 Parallel Combining / 149 6.1.1 90◦ Hybrid / 150 6.1.2 180◦ Hybrid / 152 6.1.3 Simple Push–Pull / 154 6.1.4 Gain / 155 6.1.5 Noise Figure / 156 6.1.6 Combiner Trees / 156 6.1.7 Cascade Analysis of a Combiner Tree / 157 6.2 Feedback / 158 6.3 Feedforward / 159 6.3.1 Intermods and Harmonics / 160 6.3.2 Bandwidth / 161 6.3.3 Noise Figure / 161 6.4 Nonideal Performance / 162 6.5 Summary / 163 Endnotes / 163 149 CONTENTS 7 FREQUENCY CONVERSION xi 165 7.1 Basics / 165 7.1.1 The Mixer / 165 7.1.2 Conversion in Receivers / 167 7.1.3 Spurs / 168 7.1.4 Conversion in Synthesizers and Exciters / 170 7.1.5 Calculators / 170 7.1.6 Design Methods / 170 7.1.7 Example / 171 7.2 Spurious Levels / 171 7.2.1 Dependence on Signal Strength / 171 7.2.2 Estimating Levels / 173 7.2.3 Strategy for Using Levels / 175 7.3 Two-Signal IMs / 176 7.4 Power Range for Predictable Levels / 177 7.5 Spur Plot, LO Reference / 180 7.5.1 Spreadsheet Plot Description / 180 7.5.2 Example of a Band Conversion / 182 7.5.3 Other Information on the Plot / 184 7.6 Spur Plot, IF Reference / 186 7.7 Shape Factors / 196 7.7.1 Definitions / 197 7.7.2 RF Filter Requirements / 197 7.7.3 IF Filter Requirements / 200 7.8 Double Conversion / 202 7.9 Operating Regions / 203 7.9.1 Advantageous Regions / 203 7.9.2 Limitation on Downconversion, Two-by-Twos / 206 7.9.3 Higher Values of m / 209 7.10 Examples / 211 7.11 Note on Spur Plots Used in This Chapter / 216 7.12 Summary / 216 Endnotes / 217 8 CONTAMINATING SIGNALS IN SEVERE NONLINEARITIES 8.1 Decomposition / 220 8.2 Hard Limiting / 223 8.3 Soft Limiting / 223 219
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