RF and Microwave Engineering

Preface x

Symbols and Abbreviations xii

About the Companion Website xvi

1 Introduction 1

1.1 Radiofrequency and Microwave Applications 1

1.2 Frequency Bands 4

1.3 Physical Phenomena in the High Frequency Domain 5

1.3.1 Electrically Short Transmission Line 5

1.3.2 Transmission Line with Length Greater Than One-Tenth of Wavelength 7

1.3.3 Radiation and Antennas 8

1.4 Outline of the Following Chapters 9

References 10

2 Electromagnetic Fields and Waves 11

2.1 Physical and Mathematical Basics 11

2.1.1 Electrostatic Fields 11

2.1.2 Steady Electric Current and Magnetic Fields 18

2.1.3 Differential Vector Operations 23

2.2 Maxwell’s Equations 24

2.2.1 Differential Form in the Time Domain 24

2.2.2 Differential Form for Harmonic Time Dependence 25

2.2.3 Integral Form 26

2.2.4 Constitutive Relations and Material Properties 28

2.2.5 Boundary Conditions 31

2.3 Classification of Electromagnetic Problems 32

2.3.1 Static Fields 32

2.3.2 Quasi-Static Fields 33

2.3.3 Coupled Electromagnetic Fields 33

2.4 Skin Effect 33

2.5 Electromagnetic Waves 36

2.5.1 Wave Equation and Plane Waves 36

2.5.2 Polarization of Waves 40

2.5.3 Reflection and Refraction 42

2.5.4 Spherical Waves 48

2.6 Summary 50

2.7 Problems 51

References 52

Further Readings 52

3 Transmission Line Theory and Transient Signals on Lines 55

3.1 Transmission Line Theory 55

3.1.1 Equivalent Circuit of a Line Segment 55

3.1.2 Telegrapher’s Equation 57

3.1.3 Voltage and Current Waves on Transmission Lines 59

3.1.4 Load-Terminated Transmission Line 62

3.1.5 Input Impedance 64

3.1.6 Lossless Transmission Lines 65

3.1.7 Low-loss Transmission Lines 68

3.1.8 Lossless Transmission Line with Different Terminations 69

3.1.9 Impedance Transformation with Lossless Lines 75

3.1.10 Reflection Coefficient 76

3.1.11 Smith Chart 80

3.2 Transient Signals on Transmission Lines 84

3.2.1 Step Function 84

3.2.2 Rectangular Function 91

3.3 Eye Diagram 94

3.4 Summary 95

3.5 Problems 97

References 98

Further Readings 98

4 Transmission Lines and Waveguides 99

4.1 Overview 99

4.2 Coaxial Line 102

4.2.1 Specific Inductance and Characteristic Line Impedance 102

4.2.2 Attenuation of Low-Loss Transmission Lines 105

4.2.3 Technical Frequency Range 107

4.2.4 Areas of Application 108

4.3 Two-Wire Line 108

4.3.1 Characteristic Line Impedance 109

4.3.2 Areas of Application 109

4.4 Microstrip Line 110

4.4.1 Characteristic Line Impedance and Effective Permittivity 110

4.4.2 Dispersion and Technical Frequency Range 113

4.4.3 Areas of Application 114

4.5 Stripline 114

4.5.1 Characteristic Line Impedance 114

4.5.2 Technical Frequency Range 115

4.5.3 Areas of Application 115

4.6 Rectangular Waveguide 115

4.6.1 General Considerations 116

4.6.2 Dominant Mode 119

4.6.3 Higher Order Modes 122

4.6.4 Areas of Application 123

4.6.5 Excitation of Waveguide Modes 125

4.6.6 Cavity Resonators 126

4.7 Substrate-Integrated Waveguide (SIW) 128

4.7.1 Geometrical Structure and Electrical Characteristics 128

4.7.2 Microstrip-to-SIW Transition 131

4.8 Three-Conductor Transmission Line 131

4.8.1 Even and Odd Modes 131

4.8.2 Characteristic Line Impedances and Propagation Constants 135

4.8.3 Line Termination for Even and Odd Modes 136

4.9 Problems 137

References 138

5 Scattering Parameters 139

5.1 Multi-Port Network Representations 139

5.2 Normalized Power Waves 141

5.3 Scattering Parameters and Power 142

5.4 S-Parameter Representation of Network Properties 145

5.4.1 Matching 145

5.4.2 Complex Conjugate Matching 146

5.4.3 Reciprocity 148

5.4.4 Symmetry 148

5.4.5 Passive and Lossless Circuits 148

5.4.6 Unilateral Circuits 149

5.4.7 Specific Characteristics of Three-Port Networks 149

5.5 Calculation of S-Parameters 150

5.5.1 Reflection Coefficients 150

5.5.2 Transmission Coefficients 150

5.5.3 Renormalization 153

5.6 Signal Flow Method 154

5.6.1 Source 156

5.6.2 One-port Network/Load Termination 156

5.6.3 Two-port Network 156

5.6.4 Three-port Network 157

5.6.5 Four-port Network 157

5.7 S-Parameter Measurement 160

5.8 Problems 164

References 166

Further Readings 166

6 RF Components and Circuits 167

6.1 Equivalent Circuits of Concentrated Passive Components 167

6.1.1 Resistor 167

6.1.2 Capacitor 169

6.1.3 Inductor 170

6.2 Transmission Line Resonator 172

6.2.1 Half-Wave Resonator 172

6.2.2 Quarter-Wave Resonator 174

6.3 Impedance Matching 175

6.3.1 LC-Networks 176

6.3.2 Matching Using Distributed Elements 178

6.4 LC-Filter 181

6.4.1 Classical LC-Filter Design 182

6.4.2 Butterworth Filter 184

6.5 Transmission Line Filter 190

6.5.1 Edge-Coupled Line Filters 191

6.5.2 Hairpin Filter 195

6.5.3 Stepped Impedance Filter 195

6.5.4 Parasitic Box Resonance 195

6.5.5 Waveguide Filter 198

6.6 Circulator 200

6.7 Power Divider 201

6.7.1 Wilkinson Power Divider 201

6.7.2 Unequal Split Power Divider 202

6.8 Branchline Coupler 204

6.8.1 Conventional 3 dB Coupler 204

6.8.2 Unequal Split Branchline Coupler 206

6.9 Rat Race Coupler 208

6.10 Directional Coupler 210

6.11 Balanced-to-Unbalanced Circuits 212

6.12 Electronic Circuits 213

6.12.1 Mixers 215

6.12.2 Amplifiers and Oscillators 217

6.13 RF Design Software 218

6.13.1 RF Circuit Simulators 218

6.13.2 Three-Dimensional Electromagnetic Simulators 219

6.14 Problems 222

References 223

7 Antennas 225

7.1 Fundamental Parameters 225

7.1.1 Antennas as Wave-Type Converters 225

7.1.2 Nearfield and Farfield 225

7.1.3 Isotropic Radiator 227

7.1.4 Radiation Pattern and Related Parameters 228

7.1.5 Impedance Matching and Bandwidth 233

7.2 Standard Types of Antennas 234

7.3 Mathematical Treatment of the Hertzian Dipole 237

7.4 Wire Antennas 241

7.4.1 Half-Wave Dipole 241

7.4.2 Monopole 244

7.4.3 Concepts for Reducing Antenna Height 245

7.5 Slot Antennas 246

7.6 Aperture Radiators and Horn Antennas 248

7.6.1 Aperture Radiators 248

7.6.2 Horn Antennas 251

7.7 Planar Antennas 252

7.7.1 Rectangular Patch Antenna 253

7.7.2 Circularly Polarizing Patch Antennas 257

7.7.3 Planar Dipole and Inverted-F Antenna 260

7.8 Antenna Arrays 261

7.8.1 Single Element Radiation Pattern and Array Factor 261

7.8.2 Phased Array Antennas 264

7.8.3 Beam Forming 271

7.9 Modern Antenna Concepts 275

7.10 Problems 276

References 277

8 Radio Wave Propagation 279

8.1 Propagation Mechanisms 279

8.1.1 Reflection and Refraction 279

8.1.2 Absorption 279

8.1.3 Diffraction 280

8.1.4 Scattering 282

8.2 Basic Propagation Models 284

8.2.1 Free Space Loss 284

8.2.2 Attenuation of Air 286

8.2.3 Reflection at Scattering Targets (Radar Cross-Section) 287

8.2.4 Doppler Effect 294

8.2.5 Plane Earth Loss 296

8.2.6 Point-to-Point Radio Links 299

8.2.7 Layered Media 301

8.3 Path Loss Models 303

8.3.1 Multipath Environment 304

8.3.2 Clutter Factor Model 306

8.3.3 Okumura–Hata Model 306

8.3.4 Physical Models and Numerical Methods 307

8.4 Summary 310

8.5 Problems 311

References 311

A Mathematical Relations and Resonant Circuits 313

A.1 Coordinate Systems 313

A.1.1 Cartesian Coordinate System 313

A.1.2 Cylindrical Coordinate System 314

A.1.3 Spherical Coordinate System 315

A.2 Characteristics of Resonant Circuits 316

A.2.1 Series Resonant Circuit 316

A.2.2 Parallel Resonant Circuit 321

A.3 Logarithmic Representation 326

A.3.1 Dimensionless Quantities 326

A.3.2 Relative and Absolute Ratios 326

A.3.3 Link Budget 327

Index 329