PRACTICAL RF SYSTEM

yuyingdugu

CONTENTS
PREFACE xvii
GETTING FILES FROM THE WILEY ftp AND INTERNET SITES xix
SYMBOLS LIST AND GLOSSARY xxi
1 INTRODUCTION 1
1.1 System Design Process / 1
1.2 Organization of the Book / 2
1.3 Appendixes / 3
1.4 Spreadsheets / 3
1.5 Test and Simulation / 3
1.6 Practical Skepticism / 4
1.7 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
2.2.4 Relationships Between S and T Parameters / 13
2.2.5 Restrictions on T Parameters / 14
2.2.6 Cascade Response / 14
2.3 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
2.4 Nonstandard Impedances / 40
2.5 Use of Sensitivities to Find Variations / 40
2.6 Summary / 43
Endnotes / 45
3 NOISE FIGURE 47
3.1 Noise Factor and Noise Figure / 47
3.2 Modules in Cascade / 49
3.3 Applicable Gains and Noise Factors / 54
3.4 Noise Figure of an Attenuator / 55
3.5 Noise Figure of an Interconnect / 56
3.6 Cascade Noise Figure / 56
3.7 Expected Value and Variance of Noise Figure / 58
3.8 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
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 91
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
x CONTENTS
5 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 149
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
CONTENTS xi
7 FREQUENCY CONVERSION 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 219
8.1 Decomposition / 220
8.2 Hard Limiting / 223
8.3 Soft Limiting / 223
xii CONTENTS
8.4 Mixers, Through the LO Port / 225
8.4.1 AM Suppression / 225
8.4.2 FM Transfer / 226
8.4.3 Single-Sideband Transfer / 226
8.4.4 Mixing Between LO Components / 228
8.4.5 Troublesome Frequency Ranges in the LO / 228
8.4.6 Summary of Ranges / 235
8.4.7 Effect on Noise Figure / 236
8.5 Frequency Dividers / 240
8.5.1 Sideband Reduction / 240
8.5.2 Sampling / 241
8.5.3 Internal Noise / 242
8.6 Frequency Multipliers / 242
8.7 Summary / 243
Endnotes / 244
9 PHASE NOISE 245
9.1 Describing Phase Noise / 245
9.2 Adverse Effects of Phase Noise / 247
9.2.1 Data Errors / 247
9.2.2 Jitter / 248
9.2.3 Receiver Desensitization / 249
9.3 Sources of Phase Noise / 250
9.3.1 Oscillator Phase Noise Spectrums / 250
9.3.2 Integration Limits / 252
9.3.3 Relationship Between Oscillator Sϕ and Lϕ / 252
9.4 Processing Phase Noise in a Cascade / 252
9.4.1 Filtering by Phase-Locked Loops / 253
9.4.2 Filtering by Ordinary Filters / 254
9.4.3 Implication of Noise Figure / 255
9.4.4 Transfer from Local Oscillators / 255
9.4.5 Transfer from Data Clocks / 256
9.4.6 Integration of Phase Noise / 258
9.5 Determining the Effect on Data / 258
9.5.1 Error Probability / 258
9.5.2 Computing Phase Variance, Limits of
Integration / 259
9.5.3 Effect of the Carrier-Recovery Loop on Phase
Noise / 260
CONTENTS xiii
9.5.4 Effect of the Loop on Additive
Noise / 262
9.5.5 Contribution of Phase Noise to Data
Errors / 263
9.5.6 Effects of the Low-Frequency Phase
Noise / 268
9.6 Other Measures of Phase Noise / 269
9.6.1 Jitter / 269
9.6.2 Allan Variance / 271
9.7 Summary / 271
Endnote / 272
APPENDIX A OP AMP NOISE FACTOR CALCULATIONS 273
A.1 Invariance When Input Resistor Is Redistributed / 273
A.2 Effect of Change in Source Resistances / 274
A.3 Model / 276
APPENDIX B REPRESENTATIONS OF FREQUENCY BANDS,
IF NORMALIZATION 279
B.1 Passbands / 279
B.2 Acceptance Bands / 279
B.3 Filter Asymmetry / 286
APPENDIX C CONVERSION ARITHMETIC 289
C.1 Receiver Calculator / 289
C.2 Synthesis Calculator / 291
APPENDIX E EXAMPLE OF FREQUENCY CONVERSION 293
APPENDIX F SOME RELEVANT FORMULAS 303
F.1 Decibels / 303
F.2 Reflection Coefficient and SWR / 304
F.3 Combining SWRs / 306
F.3.1 Summary of Results / 306
F.3.2 Development / 307
F.3.3 Maximum SWR / 308
F.3.4 Minimum SWR / 309
F.3.5 Relaxing Restrictions / 309
F.4 Impedance Transformations in Cables / 310
F.5 Smith Chart / 310
xiv CONTENTS
APPENDIX G TYPES OF POWER GAIN 313
G.1 Available Gain / 313
G.2 Maximum Available Gain / 313
G.3 Transducer Gain / 314
G.4 Insertion Gain / 315
G.5 Actual Gain / 315
APPENDIX H FORMULAS RELATING TO IMs AND
HARMONICS 317
H.1 Second Harmonics / 317
H.2 Second-Order IMs / 318
H.3 Third Harmonics / 318
H.4 Third-Order IMs / 319
H.5 Definitions of Terms / 320
APPENDIX I CHANGING THE STANDARD IMPEDANCE 321
I.1 General Case / 321
I.2 Unilateral Module / 323
APPENDIX L POWER DELIVERED TO THE LOAD 325
APPENDIX M MATRIX MULTIPLICATION 327
APPENDIX N NOISE FACTORS—STANDARD AND
THEORETICAL 329
N.1 Theoretical Noise Factor / 329
N.2 Standard Noise Factor / 331
N.3 Standard Modules and Standard Noise Factor / 332
N.4 Module Noise Factor in a Standard Cascade / 333
N.5 How Can This Be? / 334
N.6 Noise Factor of an Interconnect / 334
N.6.1 Noise Factor with Mismatch / 335
N.6.2 In More Usable Terms / 336
N.6.3 Verification / 338
N.6.4 Comparison with Theoretical Value / 340
N.7 Effect of Source Impedance / 341
N.8 Ratio of Power Gains / 342
Endnote / 343
CONTENTS xv
APPENDIX P IM PRODUCTS IN MIXERS 345
APPENDIX S COMPOSITE S PARAMETERS 349
APPENDIX T THIRD-ORDER TERMS AT INPUT FREQUENCY 353
APPENDIX V SENSITIVITIES AND VARIANCE OF NOISE
FIGURE 355
APPENDIX X CROSSOVER SPURS 359
APPENDIX Z NONSTANDARD MODULES 363
Z.1 Gain of Cascade of Modules Relative to Tested Gain / 363
Z.2 Finding Maximum Available Gain of a Module / 366
Z.3 Interconnects / 367
Z.4 Equivalent S Parameters / 367
Z.5 S Parameters for Cascade of Nonstandard Modules / 368
Endnote / 369
REFERENCES 371
Endnote / 377
INDEX 379

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