Foundations for Microwave Engineering, 2nd Edition

Preface xv

1 Introduction 1

1.1 Microwave Frequencies 1

1.2 Microwave Applications 3

1.3 Microwave Circuit Elements and Analysis 6

2 Electromagnetic Theory 17

2.1 Maxwell's Equations 17

2.2 Constitutive Relations 23

2.3 Static Fields 28

2.4 Wave Equation 31

2.5 Energy and Power 33

2.6 Boundary Conditions 39

2.7 Plane Waves 44

2.8 Reflection from a Dielectric Interface 49

2.9 Reflection from a Conducting Plane 53

2.10 Potential Theory 56

2.11 Derivation of Solution for Vector Potential 59

2.12 Lorentz Reciprocity Theorem 62

3 Transmission Lines and Waveguides 72

Part 1 Waves on Transmission Lines 72

3.1 Waves on An Ideal Transmission Line 72

3.2 Terminated Transmission Line: Resistive Load 78

3.3 Capacitive Termination 82

3.4 Steady-State Sinusoidal Waves 85

3.5 Waves on a Lossy Transmission Line 86

3.6 Terminated Transmission Line: Sinusoidal Waves 89

Part 2 Field Analysis of Transmission Lines 96

3.7 Classification of Wave Solutions 96

3.8 Transmission Lines (Field Analysis) 104

3.9 Transmission-Line Parameters 112

3.10 Inhomogeneously Filled Parallel-Plate Transmission Line 117

3.11 Planar Transmission Lines 125

3.12 Microstrip Transmission Line 130

3.13 Coupled Microstrip Lines 164

3.14 Strip Transmission Lines 170

3.15 Coupled Strip Lines 173

3.16 Coplanar Transmission Lines 175

Part 3 Rectangular and Circular Waveguides 180

3.17 Rectangular Waveguide 181

3.18 Circular Waveguides 194

3.19 Wave Velocities 198

3.20 Ridge Waveguide 205

3.21 Fin Line 208

4 Circuit Theory for Waveguiding Systems 220

4.1 Equivalent Voltages and Currents 221

4.2 Impedance Description of Waveguide Elements and Circuits 224

4.3 Foster's Reactance Theorem 230

4.4 Even and Odd Properties of Z_{in 232}

4.5 iV-Port Circuits 233

4.6 Two-Port Junctions 238

4.7 Scattering-Matrix Formulation 248

4.8 Scattering Matrix for a Two-Port Junction 254

4.9 Transmission-Matrix Representation 257

4.10 Signal Flow Graphs 260

4.11 Generalized Scattering Matrix for Power Waves 268

4.12 Excitation of Waveguides 276

4.13 Waveguide Coupling by Apertures 284

5 Impedance Transformation and Matching 303

5.1 Smith Chart 304

5.2 Impedance Matching with Reactive Elements 308

5.3 Double-Stub Matching Network 312

5.4 Triple-Stub Tuner 317

5.5 Impedance Matching with Lumped Elements 319

5.6 Design of Complex Impedance Terminations 330

5.7 Invariant Property of Impedance Mismatch Factor 334

5.8 Waveguide Reactive Elements 339

5.9 Quarter-Wave Transformers 343

5.10 Theory of Small Reflections 347

5.11 Approximate Theory for Multisection Quarter-Wave Transformers 348

5.12 Binomial Transformer 350

5.13 Chebyshev Transformer 352

5.14 Chebyshev Transformer (Exact Results) 356

5.15 Filter Design Based on Quarter-Wave-Transformer Prototype Circuit 360

5.16 Tapered Transmission Lines 370

5.17 Synthesis of Transmission-Line Tapers 373

5.18 Chebyshev Taper 380

5.19 Exact Equation for the Reflection Coefficient 383

6 Passive Microwave Devices 394

6.1 Terminations 394

6.2 Attenuators 397

6.3 Phase Shifters 404

6.4 Directional Couplers 413

6.5 Hybrid Junctions 435

6.6 Power Dividers 442

6.7 Microwave Propagation in Ferrites 450

6.8 Faraday Rotation 460

6.9 Microwave Devices Employing Faraday Rotation 464

6.10 Circulators 468

6.11 Other Ferrite Devices 476

7 Electromagnetic Resonators 481

7.1 Resonant Circuits 481

7.2 Transmission-Line Resonant Circuits 485

7.3 Microstrip Resonators 490

7.4 Microwave Cavities 500

7.5 Dielectric Resonators 508

7.6 Equivalent Circuits for Cavities 517

7.7 Field Expansion in a General Cavity 525

7.8 Oscillations in a Source-Free Cavity 533

7.9 Excitation of Cavities 538

7.10 Cavity Perturbation Theory 541

8 Periodic Structures and Filters 550

8.1 Capacitively Loaded Transmission-Line-Circuit Analysis 551

8.2 Wave Analysis of Periodic Structures 557

8.3 Periodic Structures Composed of Unsymmetrical Two-Port Networks 559

8.4 Terminated Periodic Structures 560

8.5 Matching of Periodic Structures 563

8.6 k₀-β Diagram 564

8.7 Group Velocity and Energy Flow 566

8.8 Floquet's Theorem and Spatial Harmonics 569

8.9 Periodic Structures for Traveling-Wave Tubes 571

8.10 Sheath Helix 580

8.11 Some General Properties of a Helix 583

8.12 Introduction to Microwave Filters 585

8.13 Image-Parameter Method of Filter Design 587

8.14 Filter Design by Insertion-Loss Method 591

8.15 Specification of Power Loss Ratio 592

8.16 Some Low-Pass-Filter Designs 595

8.17 Frequency Transformations 598

8.18 Impedance and Admittance Inverters 603

8.19 A Microstrip Half-Wave Filter 617

8.20 Microstrip Parallel Coupled Filter 626

8.21 Quarter-Wave-Coupled Cavity Filters 635

8.22 Direct-Coupled Cavity Filters 639

8.23 Other Types of Filters 642

9 Microwave Tubes 648

9.1 Introduction 648

9.2 Electron Beams with dc Conditions 650

9.3 Space-Charge Waves on Beams with Confined Flow 654

9.4 Space-Charge Waves on Unfocused Beams 661

9.5 Ac Power Relations 667

9.6 Velocity Modulation 670

9.7 Two-Cavity Klystron 678

9.8 Reflex Klystron 686

9.9 Magnetron 690

9.10 O-Type Traveling-Wave Tube 692

9.11 M-Type Traveling-Wave Tube 699

9.12 Gyrotrons 701

9.13 Other Types of Microwave Tubes 708

10 Solid-State Amplifiers 713

10.1 Bipolar Transistors 716

10.2 Field-Effect Transistors 721

10.3 Circle-Mapping Properties of Bilinear Transformations 725

10.4 Microwave Amplifier Design Using Sij Parameters 726

10.5 Amplifier Power Gain 728

10.6 Amplifier Stability Criteria 735

10.7 Constant Power-Gain Circles 744

10.8 Basic Noise Theory 760

10.9 Low-Noise Amplifier Design 767

10.10 Constant Mismatch Circles 776

10.11 Microwave Amplifier Design 780

10.12 Other Aspects of Microwave Amplifier Design 793

11 Parametric Amplifiers 799

11.1 p-n Junction Diodes 800

11.2 Manley-Rowe Relations 804

11.3 Linearized Equations for Parametric Amplifiers 807

11.4 Parametric Up-Converter 809

11.5 Negative-Resistance Parametric Amplifier 814

11.6 Noise Properties of Parametric Amplifiers 821

12 Oscillators and Mixers 831

12.1 Gunn Oscillators 832

12.2 IMPATT Diodes 837

12.3 Transistor Oscillators 840

12.4 Three-Port Description of a Transistor 843

12.5 Oscillator Circuits 849

12.6 Oscillator Design 851

12.7 Mixers 856

12.8 Mixer Noise Figure 864

12.9 Balanced Mixers 865

12.10 Other Types of Mixers 868

12.11 Mixer Analysis Using Harmonic Balancing 869

Appendixes

I Useful Relations from Vector Analysis 876

I.1 Vector Algebra 876

I.2 Vector Operations in Common Coordinate Systems 877

I.3 Vector Identities 879

I.4 Green's Identities 880

II Bessel Functions 881

II.1 Ordinary Bessel Functions 881

II.2 Modified Bessel Functions 883

III Conformal Mapping Techniques 886

III.1 Conformal Mapping 886

III.2 Elliptic Sine Function 889

III.3 Capacitance between Two Parallel Strips 892

III.4 Strip Transmission Line 896

III.5 Conductor Loss 898

III.6 Conductor Losses for a Microstrip Transmission Line 903

III.7 Attenuation for a Coplanar Line 905

IV Physical Constants and Other Data 911

IV.1 Physical Constants 911

IV.2 Conductivities of Materials 912

IV.3 Dielectric Constants of Materials 912

IV.4 Skin Depth in Copper 912

Index 913