This work presents microwave and RF technology from a circuit design viewpoint, rather than a set of electromagnetic problems. The emphasis is on gaining a practical understanding of often overlooked but vital physical processes.
This resource provides microwave circuit engineers with analytical techniques for understanding and designing high-frequency circuits almost entirely from a circuit point of view. Electromagnetic concepts are not avoided, but they are employed only as necessary to support circuit-theoretical ones or to describe phenomena such as radiation and surface waves in microstrip.

This book is a collection of things that I learned, largely on my own, over forty years in microwave circuit design. While almost all of the material in this book existed somewhere in some form, no single source was compre-hensive and accessible. I learned most of it by experience, talking to people and digging through technical papers and books. In some cases, I just had to figure it out on my own.
Forty years ago, relatively few books on high-frequency theory and technology, beyond a few classroom electromagnetics textbooks, existed. There are many more today, but few are oriented toward the microwave-circuit specialist. Most begin with electromagnetic concepts, then move on to some aspects of circuit theory. There are two problems with this ap-proach: first, while no one with any sense would doubt the importance of an understanding of electromagnetics in the design of high-frequency sys-tems and components, the actual design of such components rarely uses electromagnetic concepts directly, if at all, and instead is based on circuit-theoretical concepts. Second, because of the view that high-frequency cir-cuit analysis is fundamentally electromagnetic, useful circuit analysis tech-niques are not presented. The message delivered to the reader too often seems to be that high-frequency components should be viewed as electro-magnetic structures or not at all. This leaves out many ideas that are essen-tial for successful microwave circuit design. Indeed, all circuit theory is, at some level, an expression of electromagnetics; perhaps viewing microwave circuits through circuit theory is not really avoiding electromagnetics at all.
This book develops analytical techniques for understanding and de-signing high-frequency circuits almost entirely from a circuit point of view. Electromagnetic concepts are not avoided, but they are employed only as necessary to support circuit-theoretical ones or to describe phenomena, such as radiation and surface waves in microstrip, which inherently require an electromagnetic description. At the same time, my intention is to go much further than the conventional wisdom about microwave circuit theo-ry, such as it is. For example, the idea that Mason's rule, applied to network graphs, is the only viable method for analyzing circuits described by S pa-rameters is much too narrow. Methods involving direct manipulation of S matrices are more general and often just as easy—if not easier—to employ. Indeed, general graph analysis, a staple of analog circuit theory, is directly applicable to high-frequency circuits. Even Mason's rule itself is just a car-ryover from control-system theory. It is not specific to the RF and micro-wave world.
I would like to thank a couple of people. Most important is my wife, Julie, who never complains about being neglected when I steal away to my office to ruffle through piles of technical papers, peck at a keyboard, and stare at a computer screen for full days or longer. I am also grateful to the management of AWR Corporation for making available the software that I used in the design examples.
Stephen Maas
Long Beach, California

Preface xvii

Chapter 1 Transmission Lines 1

1.1 Transmission Lines 1

      1.1.1 Fundamental Relations 1

      1.1.2 Characteristic Impedance 4

      1.1.3 Lossy Transmission Lines 5

      1.1.4 Conditions at the Ends of Transmission Lines 6

      1.1.4.1 Reflection Coefficient 6

      1.1.4.2 Return Loss and VSWR 8

      1.1.4.3 Transmission Coefficient 9

      1.1.4.4 Equivalent Circuits 10

      1.1.5 MMatrix Relationships 11

      1.1.6 Input Impedance and Power Transfer 13

1.2 Practical Considerations 14

      1.2.1 Transmission Line Types 15

      1.2.1.1 Parallel-WireLine 15

      1.2.1.2 Coaxial Line 15

      1.2.1.3 Planar Transmission Structures 16

      1.2.2 Properties 17

      1.2.2.1 TEM Modes, Group Velocity, and the Quasi-TEM Approximation 17

      1.2.2.2 Quasistatic Analysis 20

      1.2.2.3 Loss 20

      1.2.2.4 Nonhomogeneous Lines 22

1.3 Application：RC Transmission Line 23

1.4 Application：MultisectionQuarter-Wave Transformer 24

Chapter 2 Coupled Transmission Lines and Modal Analysis 31

2.1 Even-and Odd-Mode Analysis 31

      2.1.1 Even and Odd Modes 31

      2.1.2 Even-and Odd-Mode Characteristics 33

      2.1.3 Coupled-Line Analysis 35

      2.1.4 Application: Coupled-Line Directional Coupler 36

      2.1.5 Effect of Unequal Modal Phase Velocities 40

2.2 General, Multiple Coupled Lines 41

      2.2.1 R, L, G, and C Matrices 41

      2.2.2 Transmission Line Equations 43

      2.2.3 Matrices 46

      2.2.4 Application: Lange Coupler 49

2.3 Balun Design 51

      2.3.1 Balun Properties 52

      2.3.2 Application: Parallel-StripBalun 54

      2.3.3 Application: March and Balun 57

      2.3.4 Application: Half-WaveBalun 62

Chapter 3 Scattering Parameters 67

3.1 Circuit Description in Terms of Wave Quantities 68

      3.1.1 Voltage Waves and Power Waves 68

      3.1.2 The Scattering Matrix 70

      3.1.3 S-Parameter Renormalization 73

      3.1.4 Circuit Interconnections 73

3.2 Properties of the Scattering Matrix 77

3.2.1 General Properties 77

3.2.2 Two-Ports 79

3.2.3 Three-Ports 80

3.2.4 Application: Baluns 83

3.2.5 Four-Ports 84

3.3 S Parameter Analysis of Two-Ports 88

      3.3.1 Gain and Reflection Coefficients 88

      3.3.1.1 Gain 89

      3.3.1.2 Input and Output Reflection Coefficients 92

      3.3.1.3 Determining S Parameters from Nodal Analysis 93

      3.3.2 Two-Port Gain Definitions 95

3.4 Stability 96

      3.4.1 Two-Port Stability 96

      3.4.2 Port Terminations and External Stability 97

      3.4.3 General Linear Circuit Stability 101

      3.4.3.1 A More General View of External Stability 101

      3.4.3.2 Internal Stability 103

      3.4.3.3 Interface Stability 105

3.5 Transfer Scattering Matrix 108

Chapter 4 Matching Circuits 113

4.1 Fundamentals 114

      4.1.1 Power Transfer and Port Impedances 114

      4.1.2 Impedance Normalization 115

4.2 Narrowband Matching 115

4.2.1 L-Section Matching Circuits Using LC Elements or Stubs 116

4.2.2 Realization of Land C Elements with Transmission Lines 118

4.2.3 Series-Line Matching 119

4.2.4 Quarter-Wave Transformer Matching 119

4.2.5 Simple Broadband ing Technique 121

4.3 Transmission-Line Transformers 122

      4.3.1 Wirewound Impedance Transformer 122

      4.3.2 Toroidal Balun 123

      4.3.3 Transmission Line "Auto transformer" 126

4.4 Classical Synthesis 131

      4.4.1 Matching Limitations 131

      4.4.2 Prototype Networks 132

      4.4.2.1 Series RL or Shunt RC 132

      4.4.2.2 Shunt RL or Series RC Loads 134

      4.4.3 Normalization and Frequency Scaling 134

      4.4.4 Load Scaling and the Decrement 135

      4.4.5 Examples 139

      4.4.5.1 Low-Pass Matching Circuit 139

      4.4.5.2 Bandpass Matching Circuit 142

      4.4.6 Impedance Transformations 144

4.5 Distributed Networks 147

      4.5.1 Simple Resonator Equivalents Based on Slope Parameters 148

      4.5.2 Converting Series Elements to Shunt 149

      4.5.2.1 Example: Conversion of a Series Resonator to Shunt 152

      4.5.2.2 Impedance and Admittance Inverters 152

      4.5.2.3 Example: UseofLumped-Element Inverters 156

      4.5.3 Richards' Transformation 158

      4.5.3.1 Example: Low-PassMatching Circuit 159

4.6 Modern Methods 159

      4.6.1 Direct Optimization 160

      4.6.2 Real Frequency Method 162

      4.6.3 Synthesis and Parasitic Absorption 164

Chapter 5 Circuit Analysis 167

5.1 Network Graph Analysis 167

      5.1.1 General Network Graphs 168

      5.1.2 Example: ATerminatedTwo-Port 173

      5.1.3 S Parameters and Mason's Rule 176

      5.1.4 S-Parameter Examples 178

      5.1.4.1 Input Reflection Coefficient 178

      5.1.4.2 Transducer Gain 181

      5.1.4.3 Interface Mismatch in Cascaded Two-Ports 182

5.2 Nodal Analysis 185

      5.2.1 Indefinite Admittance Matrix 185

      5.2.1.1 Matrix Stamps 186

      5.2.1.2 Voltage-Controlled Current Source 187

      5.2.1.3 Grounded Elements 188

      5.2.2 Matrix Reduction 190

Chapter 6 Circuit and Element Modeling 195

6.1 Circuit Characterization 195

      6.1.1 Wave and I/V Characterization 196

      6.1.2 Characterization of Discrete Components 196

      6.1.2.1 Measurement and Application 196

      6.1.2.2 Lumped-Element Model 199

      6.1.3 EM-Simulated Circuit Elements 201

      6.1.3.1 EM Simulators 201

      6.1.3.2 De-Embedding 202

      6.1.3.3 EM Database Elements 204

      6.1.3.4 Use of EM Results in Nonlinear Analysis 205

      6.1.4 Correction of Reference-Plane Locations 207

      6.1.5 De-Embedding by Negative Images 209

6.2 Some Useful Nonexistent Components 211

6.2.1 Transformer 211

6.2.2 Gyrators 215

      6.2.2.1 Transformers Modeled by Gyrator 216

      6.2.2.2 Circulator Model 219

      6.2.2.3 Current Sensor 219

      6.2.2.4 Controlled Sources 220

6.3 Some Problematical Circuit Elements 220

6.3.1 Bond Wires 222

6.3.2 Bond Wires to Chips 224

6.3.3 Cell Interconnections in Large Devices 224

6.3.4 Housing Effects 226

6.3.5 Transmission-Line Loss 227

6.3.6 Thick Metal in EM Simulations 228

6.3.7 Poorly Modeled Circuit Elements 228

Chapter 7 Active Two-Ports 231

7.1 Amplifier Theory 231

      7.1.1 Summary of Previous Results 231

      7.1.1.1 Gain 231

      7.1.1.2 Input and Output Reflection Coefficients 233

      7.1.1.3 External Stability 233

      7.1.2 Gain Circles 235

      7.1.3 Simultaneous Conjugate Match 236

      7.1.4 Figures of Merit for Solid-State Devices 238

      7.1.4.1 Maximum Available Gain and Maximum Stable Gain 238

      7.1.4.2 fmax and ft 238

      7.1.5 Power Considerations 241

      7.1.6 Distortion 244

7.2 Noise 247

      7.2.1 Noise Temperature and Noise Figure 247

      7.2.1.1 Noise Temperature 248

      7.2.1.2 Noise Figure 250

      7.2.2 Noise Figure Optimization 250

      7.2.3 Noise Figure of an Attenuator 252

      7.2.4 Cascaded Stages 253

7.3 Amplifier Design 254

      7.3.1 Device Bias in Amplifier Design 254

      7.3.1.1 Bipolar Devices 254

      7.3.1.2 FETs 255

      7.3.2 Narrowband Amplifier Design 256

      7.3.2.1 Matching Approach 256

      7.3.2.2 Example: Low-Noise Amplifier 257

      7.3.3 Broadband Design Using Negative-Image Models 260

      7.3.3.1 Negative-Image Modeling 261

      7.3.3.2 Example: LNA Design Using Negative-Image Modelling 263

      7.3.4 Small-Signal Power Amplifier Design 268

      7.3.4.1 Power Amplifier Design 268

      7.3.4.2 Example: Small-Signal, Class-A Amplifier 270

      7.3.5 Amplifier Design for Dynamic Range 273

      7.3.5.1 Dynamic Range in FET Amplifiers 273

      7.3.5.2 Wide Dynamic Range Bipolar Transistor Amplifiers 275

      7.3.5.3 Example: Wide Dynamic Range FET Amplifier 276

Chapter 8 Balanced and Quadrature-Coupled Circuits 281

8.1 90-and 180-Degree Hybrid Junctions 281

      8.1.1 Characteristics of Hybrids 281

      8.1.2 Quadrature Hybrids 283

      8.1.2.1 Coupled-Line Hybrid 283

      8.1.2.2 Branch-Line Hybrid 284

      8.1.2.3 Lumped-Element Quadrature Hybrids 284

      8.1.3 180-Degree Hybrids 289

      8.1.3.1 Rat-Race Hybrid 289

      8.1.3.2 Rat-Race Hybrid with Unequal Power Division 290

      8.1.3.3 Broadband Rat-Race Hybrid 292

      8.1.3.4 March and Hybrid 293

      8.1.3.5 Lumped-Element 180-Degree Hybrid 293

      8.1.4 Practical Considerations 295

8.2 Quadrature-Coupled Circuits 296

      8.2.1 The Terminated Quadrature Hybrid 297

      8.2.2 Quadrature-Coupled Amplifier 301

      8.2.2.1 Gain and Port Reflection Coefficients 301

      8.2.2.2 Large-Signal Performance 304

      8.2.2.3 Noise 305

8.3 Balanced Amplifiers Using Baluns and 180-Degree Hybrids 310

      8.3.1 The Terminated Balun 310

      8.3.1.1 Input Reflection Coefficient 310

      8.3.1.2 Even-and Odd-Mode Port Reflection Coefficients 313

      8.3.2 Balun-Coupled Balanced Circuits 316

      8.3.3 Even Harmonics and Even-Order Distortion 316

      8.3.4 Hybrid-Coupled Balanced Circuits 318

About the Author 321

Index 323

Stephen A. Maas is an independent consultant and the chief scientist of AWR Corporation. He earned his Ph.D. in electrical engineering from UCLA.

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