Practical RF System Design / Edition 1

by William F. Egan

Overview

The ultimate practical resource for today's RF system design professionals
Radio frequency components and circuits form the backbone of today's mobile and satellite communications networks. Consequently, both practicing and aspiring industry professionals need to be able to solve ever more complex problems of RF design.
Blending theoretical rigor with a wealth of practical expertise, Practical RF System Design addresses a variety of complex, real-world problems that system engineers are likely to encounter in today's burgeoning communications industry with solutions that are not easily available in the existing literature. The author, an expert in the field of RF module and system design, provides powerful techniques for analyzing real RF systems, with emphasis on some that are currently not well understood. Combining theoretical results and models with examples, he challenges readers to address such practical issues as:
* How standing wave ratio affects system gain
* How noise on a local oscillator will affect receiver noise figure and desensitization
* How to determine the dynamic range of a cascade from module specifications
* How phase noise affects system performance and where it comes from
* How intermodulation products (IMs) predictably change with signal amplitude, and why they sometimes change differently
An essential resource for today's RF system engineers, the text covers important topics in the areas of system noise and nonlinearity, frequency conversion, and phase noise. Along with a wealth of practical examples using MATLAB(r) and Excel, spreadsheets are available for download from an FTP Web site to help readers apply the methods outlined in this important resource.

Product Details

ISBN-13:	9780471200239
Publisher:	Wiley
Publication date:	04/17/2003
Series:	IEEE Press
Pages:	416
Product dimensions:	6.20(w) x 9.40(h) x 0.90(d)

About the Author

WILLIAM F. EGAN is an instructor at Santa Clara University, California, and formerly a Principle Engineer at TRW ESD and a Senior Technologist at GTE Government Systems. He received his PhD in electrical engineering from Stanford University and is the author of two previous books related to RF technology.

Read an Excerpt

Practical RF System Design

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By William F. Egan

John Wiley & Sons

ISBN: 0-471-20023-9

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Chapter One

INTRODUCTION

This book is about systems that operate at radio frequencies (RF) (including microwaves) where high-frequency techniques, such as impedance matching, are important. It covers the interactions of the RF modules between the antenna output and the signal processors. Its goal is to provide an understanding of how their characteristics combine to determine system performance. This chapter is a general discussion of topics in the book and of the system design process.

1.1 SYSTEM DESIGN PROCESS

We do system design by conceptualizing a set of functional blocks, and their specifications, that will interact in a manner that produces the required system performance. To do this successfully, we require imagination and an understanding of the costs of achieving the various specifications. Of course, we also must understand how the characteristics of the individual blocks affect the performance of the system. This is essentially analysis, analysis at the block level. By this process, we can combine existing blocks with new blocks, using the specifications of the former and creating specifications for the latter in a manner that will achieve the system requirements.

The specifications for a block generally consist of the parameter values we would like it to have plus allowed variations, that is, tolerances. We would like the tolerances to be zero, but that is notfeasible so we accept values that are compromises between costs and resulting degradations in system performance. Not until modules have been developed and measured do we know their parameters to a high degree of accuracy (at least for one copy). At that point we might insert the module parameters into a sophisticated simulation program to compute the expected cascade performance (or perhaps just hook them together to see how the cascade works). But it is important in the design process to ascertain the range of performance to be expected from the cascade, given its module specifications. We need this ability so we can write the specifications.

Spreadsheets are used extensively in this book because they can be helpful in improving our understanding, which is our main objective, while also providing tools to aid in the application of that understanding.

1.2 ORGANIZATION OF THE BOOK

It is common practice to list the modules of an RF system on a spreadsheet, along with their gains, noise figures, and intercept points, and to design into that spreadsheet the capability of computing parameters of the cascade from these module parameters. The spreadsheet then serves as a plan for the system. The next three chapters are devoted to that process, one chapter for each of these parameter.

At first it may seem that overall gain can be easily computed from individual gains, but the usual imperfect impedance matches complicate the process. In Chapter 2, we discover how to account for these imperfections, either exactly or, in most cases, by finding the range of system gains that will result from the range of module parameters permitted by their specifications.

The method for computing system noise figure from module noise figures is well known to many RF engineers but some subtleties are not. Ideally, we use noise figure values that were obtained under the same interface conditions as seen in the system. Practically, that information is not generally available, especially at the design concept phase. In Chapter 3, we consider how to use the information that is available to determine system noise figure and what variations are to be expected. We also consider how the effective noise figures of mixers are increased by image noise. Later we will study how the local oscillator (LO) can contribute to the mixer's noise figure.

The concept of intercept points, how to use intercept points to compute intermodulation products, and how to obtain cascade intercept points from those of the modules will be studied in Chapter 4. Anomalous intermods that do not follow the usual rules are also described.

The combined effects of noise and intermodulation products are considered in Chapter 5. One result is the concept of spur-free dynamic range. Another is the portrayal of noise distributions resulting from the intermodulation of bands of noise. The similarity between noise bands and bands of signals both aids the analysis and provides practical applications for it.

Having established the means for computing parameters for cascades of modules connected in series, in Chapter 6 we take a brief journey through various means of connecting modules or components in parallel. We discover the advantages that these various methods provide in suppressing spurious outputs and how their overall parameters are related to the parameters of the individual components.

Then, in Chapter 7, we consider the method for design of frequency converters that uses graphs to give an immediate picture of the spurs and their relationships to the desired signal bands, allowing us to visualize problems and solutions. We also learn how to predict spurious levels and those, along with the relationships between the spurs and the passbands, permit us to ascertain filter requirements.

The processes described in the initial chapters are linear, or almost so, except for the frequency translation inherent in frequency conversion. Some processes, however, are severely nonlinear and, while performance is typically characterized for the one signal that is supposed to be present, we need a method to determine what happens when small, contaminating, signals accompany that desired signal. This is considered in Chapter 8. The most important nonlinearity in many applications is that associated with the mixer's LO; so we emphasize the system effects of contaminants on the LO.

Lastly, in Chapter 9, we will study phase noise: where it comes from, how it passes through a system, and what are its important effects in the RF system.

1.3 APPENDIXES

Material that is not essential to the flow of the main text, but that is nevertheless important, has been organized in 17 appendixes. These are designated by letters, and an attempt has been made to choose a letter that could be associated with the content (e.g., G for gain, M for matrix) as an aid to recalling the location of the material. Some appendixes are tutorial, providing a reference for those who are unfamiliar with certain background material, or who may need their memory refreshed, without holding up other readers. Some appendixes expand upon the material in the chapters, sometimes providing more detailed explanations or backup. Others extend the material.

1.4 SPREADSHEETS

The spreadsheets were created in Microsoft(r) Excel and can be downloaded as Microsoft Excel 97/98 workbook files (see page xix). This makes them available for the readers' own use and also presents an opportunity for better understanding. One can study the equations being used and view the charts, which appear in black and white in the text, in color on the computer screen. One can also make use of Excel's Trace Precedents feature (see, e.g., Fig. 3.5) to illustrate the composition of various equations.

1.5 TEST AND SIMULATION

Ultimately, we know how a system performs by observing it in operation. We could also observe the results of an accurate simulation, that being one that produces the same results as the system. Under some conditions, it may be easier, quicker, or more economical to simulate a system than to build and test it. Even though the proof of the simulation model is its correspondence to the system, it can be valuable as an initial estimate of the system to be improved as test data becomes available. Once confidence is established, there may be advantages in using the model to estimate system performance under various conditions or to predict the effect of modifications. But modeling and simulating is basically the same as building and testing. They are the means by which system performance is verified. First there must be a system and, before that, a system design.

In the early stages of system design we use a general knowledge of the performance available from various system components. As the design progresses, we get more specific and begin to use the characteristics of particular realizations of the component blocks. We may initially have to estimate certain performance characteristics, possibly based on an understanding of theoretical or typical connections between certain specifications. As the design progresses we will want assurance of important parameter values, and we might ultimately test a number of components of a given type to ascertain the repeatability of characteristics. Finally we will specify the performance required from the system's component blocks to ensure the system meets its performance requirements.

Based on information concerning the likelihood of deviations from desired performance provided by our system design analysis, we may be led to accept a small but nonzero probability of performance outside of the desired bounds. Once the system has been built and tested, it may be possible to use an accurate simulation to show that the results achieved, even with expected component variations, are better than the worst case implied by the combination of the individual block specifications. To base expected performance on simulated or measured results, rather than on functional block specifications, however, requires that we have continuing control over the construction details of the components of various copies of the system, rather than merely ensuring that the blocks meet their specifications. For example, a particular amplifier design may produce a stable phase shift that has a fortuitous effect on system performance, but we would have to control changes in its design and in that of interacting components.

Another important aspect of test is general experimentation, not confined to a particular design, for the purpose of verifying the degree of applicability of theory to various practical components. Examples of reports giving such supporting experimental data can be seen in Egan (2000), relative to the theory in Chapter 8, and in Henderson (1993a), relative to Chapter 7. We can hope that these, and the other, chapters will suggest opportunities for additional worthwhile papers.

1.6 PRACTICAL SKEPTICISM

There is a tendency for engineering students to assume that anything written in a book is accurate. This comes naturally from our struggle just to approach the knowledge of the authors whose books we study (and to be able to show this on exams). With enough experience in using published information, however, we are likely to develop some skepticism, especially if we should spend many hours pursuing a development based on an erroneous parameter value or perhaps on a concept that applies almost universally - but not in our case. Even reviewed journals, which we might expect to be most nearly free of errors, and classic works contain sources of such problems. But the technical literature also contains valuable, even essential, information; so a healthy skepticism is one that leads us to consult it freely and extensively but to continually check what we learn. We check for accuracy in our reference sources, for accuracy in our use of the information, and to ensure that it truly applies to our development. We check by considering how concepts correlate with each other (e.g., does this make sense in terms of what I already know), by verifying agreement between answers obtained by different methods, and by testing as we proceed in our developments. The greater the cost of failure, the more important is verification. Unexpected results can be opportunities to increase our knowledge, but we do not want to pay too high a price for the educational experience.

1.7 REFERENCES

References are included for several reasons: to recognize the sources, to offer alternate presentations of the material, or to provide sources for associated topics that are beyond the scope of this work. The author-date style of referencing is used throughout the book. From these, one can easily find the complete reference descriptions in the References at the end of the text. Some notes are placed at the end of the chapter in which they are referenced.

(Continues...)

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Table of 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

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