Practical RF System Design

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

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

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

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

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

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 S_ϕ and L_ϕ 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

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

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

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