Microwave Circuit Design Using Linear and Nonlinear Techniques

Four leaders in the field of microwave circuit design share their newest insights into the latest aspects of the technology

The third edition of Microwave Circuit Design Using Linear and Nonlinear Techniques delivers an insightful and complete analysis of microwave circuit design, from their intrinsic and circuit properties to circuit design techniques for maximizing performance in communication and radar systems. This new edition retains what remains relevant from previous editions of this celebrated book and adds brand-new content on CMOS technology, GaN, SiC, frequency range, and feedback power amplifiers in the millimeter range region. The third edition contains over 200 pages of new material.

The distinguished engineers, academics, and authors emphasize the commercial applications in telecommunications and cover all aspects of transistor technology. Software tools for design and microwave circuits are included as an accompaniment to the book. In addition to information about small and large-signal amplifier design and power amplifier design, readers will benefit from the book's treatment of a wide variety of topics, like:

• An in-depth discussion of the foundations of RF and microwave systems, including Maxwell's equations, applications of the technology, analog and digital requirements, and elementary definitions
• A treatment of lumped and distributed elements, including a discussion of the parasitic effects on lumped elements
• Descriptions of active devices, including diodes, microwave transistors, heterojunction bipolar transistors, and microwave FET
• Two-port networks, including S-Parameters from SPICE analysis and the derivation of transducer power gain

Perfect for microwave integrated circuit designers, the third edition of Microwave Circuit Design Using Linear and Nonlinear Techniques also has a place on the bookshelves of electrical engineering researchers and graduate students. It's comprehensive take on all aspects of transistors by world-renowned experts in the field places this book at the vanguard of microwave circuit design research.

George D. Vendelin is a technical consultant with over 40 years of microwave engineering design and teaching experience. HIs clients include Texas Instruments, Anritsu, Ford Aerospace/Loral Space & Communications/Lockheed Martin, and Litton/Filtronics. He is an adjunct professor at Stanford University, Santa Clara University, San Jose State University, and UC-Berkeley-Extension. Prof. Vendelin is a Fellow of the IEEE.

Anthony M. Pavio, Ph.D., is an independent consultant, specializing in the design of RF and microwave components for military and commercial electronics. During the last eight years, his consulting projects for General Dynamics encompassed the development of several broadband hand-held transceivers and power amplifiers for X-band phased array RADAR. He was previously the manager of the Integrated RF Ceramics Center for Motorola Labs, which focused on the development of highly integrated active LTCC modules for communications. Dr. Pavio was also a technical director of the microwave products division of Texas Instruments and is a Fellow of the IEEE.

Ulrich L. Rohde is Chairman of Synergy Microwave Corporation; a partner of Rohde & Schwarz, a firm specializing in test equipment and advanced communications systems; and Professor of Microwave and RF Technology at the Technische Universitat Cottbus, Germany and other Universities. Prof. Rohde specializes in Low Noise Oscillators, High Performance Mixers and Synthesizers and has published more than 200 papers and eight books. Prof. Rohde is a Fellow of the IEEE.

Matthias Rudolph, PhD, is the Ulrich-L.-Rohde Professor for RF and Microwave Techniques at Brandenburg University of Technology, Cottbus, Germany. Previously he worked at the Ferdinand-Braun-Institut, Leibniz-Institut fuer Hoechstfrequenztechnik (FBH), Berlin, where he was responsible for the modeling of GaN HEMTs and GaAs HBTs and for heading the low noise components group. Prof. Rudolph is a Senior member of the IEEE.

Foreword xv

Preface xvii

1 RF/Microwave Systems 1

1.1 Introduction 1

1.2 Maxwell's equations 12

1.3 Frequency bands, modes, and waveforms of operation 12

1.4 Analog and digital signals 16

1.5 Elementary functions 25

1.6 Basic RF transmitters and receivers 31

1.7 RF wireless/microwave/millimeter wave applications 33

1.8 Modern CAD for nonlinear circuit analysis 37

1.9 Dynamic Load Line 37

2 Lumped and Distributed Elements 43

2.1 Introduction 43

2.2 Transition from RF to Microwave Circuits 43

2.3 Parasitic E_ects on Lumped Elements 46

2.4 Distributed Elements 54

2.5 Hybrid Element: Helical Coil 55

v

vi CONTENTS

3 Active Devices 61

3.1 Microwave Transistors 61

3.1.1 Transistor Classi_cation 61

3.1.2 Bipolar Transistor Basics 63

3.1.3 GaAs and InP Heterojunction Bipolar Transistors 77

3.1.4 SiGe HBTs 90

3.1.5 Field-E_ect Transistor Basics 95

3.1.6 GaN, GaAs, and InP HEMTs 106

3.1.7 MOSFETs 112

3.1.8 Packaged Transistors 130

3.2 Example: Selecting Transistor and Bias for Low-Noise

Ampli_cation 134

3.3 Example: Selecting Transistor and Bias for Oscillator Design 138

3.4 Example: Selecting Transistor and Bias for Power Ampli_cation 141

3.4.1 Biasing HEMTs 143

3.4.2 Biasing HBTs 145

4 Two-Port Networks 153

4.1 Introduction 153

4.2 Two-Port Parameters 154

4.3 S Parameters 163

4.4 S Parameters from SPICE Analysis 164

4.5 Mason Graphs 165

4.6 Stability 168

4.7 Power Gains, Voltage Gain, and Current Gain 171

4.7.1 Power Gain 171

4.7.2 Voltage Gain and Current Gain 177

4.7.3 Current Gain 178

4.8 Three-Ports 179

4.9 Derivation of Transducer Power Gain 182

4.10 Di_erential S Parameters 184

4.10.1 Measurements 186

4.10.2 Example 187

4.11 Twisted-Wire Pair Lines 187

4.12 Low-Noise and High-Power Ampli_er Design 190

4.13 Low-Noise Ampli_er Design Examples 193

5 Impedance Matching 209

5.1 Introduction 209

5.2 Smith Charts and Matching 209

5.3 Impedance Matching Networks 217

CONTENTS vii

5.4 Single-Element Matching 217

5.5 Two-Element Matching 219

5.6 Matching Networks Using Lumped Elements 220

5.7 Matching Networks Using Distributed Elements 221

5.7.1 Twisted-Wire Pair Transformers 221

5.7.2 Transmission Line Transformers 223

5.7.3 Tapered Transmission Lines 224

5.8 Bandwidth Constraints for Matching Networks 225

6 Microwave Filters 241

6.1 Introduction 241

6.2 Low-Pass Prototype Filter Design 242

6.2.1 Butterworth Response 242

6.2.2 Chebyshev Response 245

6.3 Transformations 247

6.3.1 Low-Pass Filters: Frequency and Impedance Scaling 247

6.3.2 High-Pass Filters 250

6.3.3 Bandpass Filters 251

6.3.4 Narrow-Band Bandpass Filters 255

6.3.5 Band-Stop Filters 259

6.4 Transmission Line Filters 260

6.4.1 Semilumped Low-Pass Filters 263

6.4.2 Richards Transformation 266

6.5 Exact Designs and CAD Tools 274

6.6 Real-Life Filters 275

6.6.1 Lumped Elements 275

6.6.2 Transmission Line Elements 275

6.6.3 Cavity Resonators 275

6.6.4 Coaxial Dielectric Resonators 276

6.6.5 Thin-Film Bulk-Wave Acoustic Resonator (FBAR) 276

7 Noise in Linear and Nonlinear Two-Ports 281

7.1 Introduction 281

7.2 Signal-to-Noise Ratio 283

7.3 Noise Figure Measurements 285

7.4 Noise Parameters and Noise Correlation Matrix 286

7.4.1 Correlation Matrix 287

7.4.2 Method of Combining Two-Port Matrix 288

7.4.3 Noise Transformation Using the [ABCD] Noise

Correlation Matrices 288

7.4.4 Relation Between the Noise Parameter and [CA] 289

viii CONTENTS

7.4.5 Representation of the ABCD Correlation Matrix in

Terms of Noise Parameters [13]: 290

7.4.6 Noise Correlation Matrix Transformations 291

7.4.7 Matrix De_nitions of Series and Shunt Element 292

7.4.8 Transferring All Noise Sources to the Input 292

7.4.9 Transformation of the Noise Sources 294

7.4.10 ABCD Parameters for CE, CC, and CB Con_gurations 294

7.5 Noisy Two-Port Description 295

7.6 Noise Figure of Cascaded Networks 301

7.7 Inuence of External Parasitic Elements 303

7.8 Noise Circles 305

7.9 Noise Correlation in Linear Two-Ports Using Correlation

Matrices 309

7.10 Noise Figure Test Equipment 312

7.11 How to Determine Noise Parameters 313

7.12 Noise in Nonlinear Circuits 314

7.12.1 Noise sources in the nonlinear domain 316

7.13 Transistor Noise Modeling 319

7.13.1 Noise modeling of bipolar and heterobipolar transistors 320

7.13.2 Noise Modeling of Field-e_ect Transistors 332

7.14 Bibliography 342

8 Small- and Large-Signal Ampli_er Design 347

8.1 Introduction 347

8.2 Single-Stage Ampli_er Design 349

8.2.1 High Gain 349

8.2.2 Maximum Available Gain and Unilateral Gain 350

8.2.3 Low-Noise Ampli_er 357

8.2.4 High-Power Ampli_er 359

8.2.5 Broadband Ampli_er 360

8.2.6 Feedback Ampli_er 362

8.2.7 Cascode Ampli_er 364

8.2.8 Multistage Ampli_er 370

8.2.9 Distributed Ampli_er and Matrix Ampli_er 371

8.2.10 Millimeter-Wave Ampli_ers 376

8.3 Frequency Multipliers 376

8.3.1 Introduction 376

8.3.2 Passive Frequency Multiplication 377

8.3.3 Active Frequency Multiplication 378

8.4 Design Example of 1.9-GHz PCS and 2.1-GHz W-CDMA

Ampli_ers 380

8.5 Stability Analysis and Limitations 384

CONTENTS ix

8.6 Problems 391

9 Power Ampli_er Design 393

9.1 Introduction 393

9.2 Characterizing transistors for power-ampli_er design 396

9.3 Single-Stage Power Ampli_er Design 402

9.4 Multistage Design 408

9.5 Power-Distributed Ampli_ers 417

9.6 Class of Operation 433

9.6.1 Optimizing Conduction Angle 437

9.6.2 Optimizing Harmonic Termination 446

9.6.3 Analog Switch-Mode Ampli_ers 451

9.7 E_ciency and Linearity Enhancement PA Topologies 456

9.7.1 The Doherty Ampli_er 456

9.7.2 Outphasing Ampli_ers 460

9.7.3 Kahn EER and Envelope Tracking Ampli_ers 462

9.8 Digital Microwave Power Ampli_ers (class-D/S) 473

9.8.1 Voltage-Mode Topology 475

9.8.2 Current-Mode Topology 480

9.9 Power Ampli_er Stability 487

10 Oscillator Design 499

10.1 Introduction 499

10.2 Compressed Smith Chart 502

10.3 Series or Parallel Resonance 506

10.4 Resonators 507

10.4.1 Dielectric Resonators 508

10.4.2 YIG Resonators 512

10.4.3 Varactor Resonators 517

10.4.4 Ceramic Resonators 518

10.4.5 Coupled Resonator 519

10.4.6 Resonator Measurements 525

10.5 Two-Port Oscillator Design 531

10.6 Negative Resistance From Transistor Model 535

10.7 Oscillator Q and Output Power 547

10.8 Noise in Oscillators: Linear Approach 550

10.8.1 Leeson's Oscillator Model 550

10.8.2 Low-Noise Design 557

10.9 Analytic Approach to Optimum Oscillator Design Using

S Parameters 568

10.10 Nonlinear Active Models for Oscillators 583

x CONTENTS

10.10.1 Diodes with Hyperabrupt Junction 584

10.10.2 Silicon Versus Gallium Arsenide 585

10.10.3 Expressions for gm and Gd 587

10.10.4 Nonlinear Expressions for Cgs, Ggf , and Ri 590

10.10.5 Analytic Simulation of I{V Characteristics 591

10.10.6 Equivalent-Circuit Derivation 591

10.10.7 Determination of Oscillation Conditions 591

10.10.8 Nonlinear Analysis 594

10.10.9 Conclusion 596

10.11 Oscillator Design Using Nonlinear Cad Tools 596

10.11.1 Parameter Extraction Method 600

10.11.2 Example of Nonlinear Design Methodology: 4-GHz

Oscillator{ Ampli_er 604

10.11.3 Conclusion 610

10.12 Microwave Oscillators Performance 610

10.13 Design of an Oscillator Using Large-Signal Y Parameters 614

10.14 Example for Large-Signal Design Based on Bessel Functions 617

10.15 Design Example for Best Phase Noise and Good Output Power 622

10.16 A Design Example for a 350MHz _xed frequency Colpitts

Oscillator 630

10.16.1 1/f Noise: 644

10.17 2400 MHz MOSFET-Based Push{Pull Oscillator 645

10.17.1 Design Equations 647

10.17.2 Design Calculations 652

10.17.3 Phase Noise 653

10.18 CAD Solution for Calculating Phase Noise in Oscillators 656

10.18.1 General Analysis of Noise Due to Modulation and

Conversion in Oscillators 656

10.18.2 Modulation by a Sinusoidal Signal 657

10.18.3 Modulation by a Noise Signal 658

10.18.4 Oscillator Noise Models 659

10.18.5 Modulation and Conversion Noise 661

10.18.6 Nonlinear Approach for Computation of Noise Analysis

of Oscillator Circuits 661

10.18.7 Noise Generation in Oscillators 663

10.18.8 Frequency Conversion Approach 663

10.18.9 Conversion Noise Analysis 664

10.18.10Noise Performance Index Due to Frequency Conversion 664

10.18.11Modulation Noise Analysis 666

10.18.12Noise Performance Index Due to Contribution of

Modulation Noise 668

10.18.13PM{AM Correlation Coe_cient 669

CONTENTS xi

10.19 Phase Noise Measurement 670

10.19.1 Phase Noise Measurement Techniques 671

10.20 Back to Conventional Phase Noise Measurement System

(Hewlett-Packard) 684

10.21 State-of-the-art 688

10.21.1 ANALOG SIGNAL PATH 689

10.21.2 DIGITAL SIGNAL PATH 690

10.21.3 PULSED PHASE NOISE MEASUREMENT 692

10.21.4 CROSS-CORRELATION 693

10.22 INSTRUMENT PERFORMANCE 694

10.23 Noise in Circuits and Semiconductors [10.87, 10.88, 10.99] 695

10.24 Validation Circuits 699

10.24.1 1000-MHz Ceramic Resonator Oscillator (CRO) 699

10.24.2 4100-MHz Oscillator with Transmission Line Resonators 703

10.24.3 2000-MHz GaAs FET-Based Oscillator 707

10.25 Analytical Approach For Designing E_cient Microwave FET

and Bipolar Oscillators (Optimum Power) 709

10.25.1 Series Feedback (MESFET) 709

10.25.2 Parallel Feedback (MESFET) 714

10.25.3 Series Feedback (Bipolar) 716

10.25.4 Parallel Feedback (Bipolar) 719

10.25.5 An FET Example 720

10.25.6 Simulated Results 729

10.25.7 Synthesizers 732

10.25.8 Self-Oscillating Mixer 732

10.26 Introduction 735

10.27 Large signal noise analysis 735

10.28 Quantifying Phase Noise 743

10.29 Summary 745

11 Frequency Synthesizer 769

11.1 Building block of synthesizer 771

11.1.1 Voltage controlled oscillator 771

11.1.2 Reference oscillator 771

11.1.3 Frequency divider 771

11.1.4 Phase-Frequency Comparators 774

11.1.5 Loop Filters - Filters for Phase Detectors Providing

Voltage Output 779

11.1.6 Example 784

11.2 Important Characteristics of Synthesizers 787

11.2.1 Frequency Range 787

11.2.2 Phase Noise 788

xii CONTENTS

11.2.3 Spurious Response 788

11.2.4 Transient Behavior of Digital Loops Using Tri-State

Phase Detectors 788

11.3 Practical Circuits 796

11.4 The Fractional-N Principle 799

11.4.1 Example: 802

11.4.2 Spur-Suppression Techniques 805

11.5 Digital Direct Frequency Synthesizer 808

11.5.1 DDS advantages 811

12 Microwave Mixer Design 815

12.1 Introduction 815

12.2 Diode Mixer Theory 823

12.3 Single-Diode Mixers 836

12.4 Single-Balanced Mixers 847

12.5 Double-Balanced Mixers 863

12.6 FET Mixer Theory 891

12.7 Balanced FET Mixers 915

12.8 Resistive (Reective) FET Mixers 930

12.9 Special Mixer Circuits 938

12.10 Mixer Noise 950

12.10.1 Mixer Noise Analysis (MOSFET) 950

12.10.2 Noise in resistive GaAs HEMT mixers1 958

13 RF Switches and Attenuators 971

13.1 pin Diodes 971

13.2 pin Diode Switches 974

13.3 pin Diode Attenuators 985

13.4 FET Switches 987

14 Simulation of Microwave Circuits 995

14.1 Introduction 995

14.2 Design Types 997

14.2.1 Printed Circuit Board 997

14.2.2 Monolithic Microwave Integrated Circuits 998

14.3 Design Entry 999

14.3.1 Schematic Capture 999

14.3.2 Board and MMIC Layout 1000

1Based on Michael Margraf, “Niederfrequenz-Rauschen und Intermodulationen von resistiven FET-Mischern,”

PhD dissertation at Berlin Institute of Technology, 2004 (in German) [12]. Figures reprinted with permission.

The mixer noise modeling approach was also published in [13, 14, 15].

CONTENTS xiii

14.4 Linear Circuit Simulation 1001

14.4.1 Small-Signal AC and S-parameter Simulation 1001

14.4.2 Example: Microwave Filter, Schematic Based 1004

14.5 Nonlinear Simulation 1004

14.5.1 Newton's Method 1006

14.5.2 Transistor Modeling 1007

14.5.3 Transient Simulation 1008

14.5.4 Example: Transient 1010

14.5.5 Harmonic Balance Simulation 1012

14.5.6 Example: Harmonic Balance, One-tone Ampli_er 1016

14.5.7 Example: Harmonic Balance, Two-tone Ampli_er 1017

14.5.8 Envelope Simulation 1019

14.5.9 Example: Envelope, Modulated Ampli_er 1023

14.5.10 Mixing Circuit and Thermal Simulation 1024

14.5.11 Example: Electrothermal 1027

14.6 Electromagnetic Simulation 1029

14.6.1 Method of Moments 1031

14.6.2 Finite Element Method 1031

14.6.3 Finite Di_erence Time Domain 1032

14.6.4 Performing an EM Simulation 1032

14.6.5 Example: Microwave Filter, EM Based 1034

14.7 Design for Manufacturing 1034

14.7.1 Circuit Optimization 1035

14.7.2 Example: Optimization 1037

14.7.3 Component Variation 1041

14.7.4 Monte Carlo Analysis 1042

14.7.5 Example: Monte Carlo Analysis 1044

14.7.6 Yield Analysis and Yield Optimization 1047

14.8 Oscillator Design and Simulation Example 1048

14.8.1 STW Delay Line 1048

14.8.2 Behavioral Simulation 1050

14.8.3 Choosing an Ampli_er 1050

14.8.4 DC Feed Design 1053

14.8.5 Wilkinson Divider Design 1053

14.8.6 Matching and Linear Oscillator Analysis 1053

14.8.7 Optimization of Loop Gain and Phase 1057

14.8.8 Nonlinear Oscillator Analysis 1057

14.8.9 1/f Noise Characterization 1059

14.8.10 Phase Noise Simulation 1066

14.8.11 Oscillator Start-up Time 1069

14.8.12 Layout EM Cosimulation 1069

14.8.13 Oscillator Design Summary 1070

xiv CONTENTS

14.9 Conclusion 1071

References 1073

Appendix A: Derivations for Unilateral Gain

Section 1075

Appendix B: Vector Representation of Two-Tone Intermodulation Products 1077

Introduction 1077

Single-Tone Analysis 1078

Two-Tone Analysis 1080

Bias-Induced Distortion 1086

Summary 1089

Single-Tone Volterra Series Expansion 1090

Fundamental Term 1091

dc Term 1091

Nonlinear Parallel RC Network 1092

Acknowledgments 1094

Bibliography 1095

Appendix C: Passive Microwave Elements 1097

Lumped Elements 1098

Distributed Elements 1100

Discontinuities 1107

Monolithic Elements 1110

Special-Purpose Elements 1113

Index 1119

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