1 Review of Electromagnetic Theory 1

1.1 Introduction to Microwave Engineering 1

Applications of Microwave Engineering 2

A Short History of Microwave Engineering 6

Electromagnetic Compatibility and Electromagnetic Interference 6

1.2 Maxwell's Equations 7

1.3 Fields in Media and Boundary Conditions 11

Fields at a General Material Interface 13

Fields at a Dielectric Interface 14

Fields at the Interface with a Perfect Conductor (Electric Wall) 14

The Magnetic Wall Boundary Condition 15

The Radiation Condition 15

1.4 The Wave Equation and Basic Plane Wave Solutions 15

The Helmholtz Equation 15

Plane Waves in a Lossless Medium 16

Plane Waves in a General Lossy Medium 17

Plane Waves in a Good Conductor 18

1.5 General Plane Wave Solutions 20

Circularly Polarized Plane Waves 23

1.6 Energy and Power 24

Power Absorbed by a Good Conductor 25

1.7 Plane Wave Reflection from a Media Interface 27

General Medium 27

Lossless Medium 28

Good Conductor 30

Perfect Conductor 31

The Surface Impedance Concept 31

1.8 Oblique Incidence at a Dielectric Interface 33

Parallel Polarization 34

Perpendicular Polarization 35

Total Reflection and Surface Waves 37

1.9 Some Useful Theorems 38

The Reciprocity Theorem 38

Image Theory 39

2 Transmission Line Theory 47

2.1 The Lumped-Element Circuit Model for a Transmission Line 47

Wave Propagation on a Transmission Line 48

The Lossless Line 49

2.2 Field Analysis of Transmission Lines 50

Transmission Line Parameters 50

The Telegrapher Equations Derived from Field Analysis of a Coaxial Line 52

Propagation Constant, Impedance, and Power Flow for the Lossless Coaxial Line 53

2.3 The Terminated Lossless Transmission Line 54

Special Cases of Lossless Terminated Lines 57

2.4 The Smith Chart 60

The Combined Impedance-Admittance Smith Chart 63

The Slotted Line 65

Online Smith Chart 68

2.5 Generator and Load Mismatches 68

Load Matched to Line 70

Generator Matched to Loaded Line 70

Conjugate Matching 70

2.6 Lossy Transmission Lines 72

The Low-Loss Line 72

The Distortionless Line 73

The Terminated Lossy Line 74

The Perturbation Method for Calculating Attenuation 74

The Wheeler Incremental Inductance Rule 76

2.7 Transients on Transmission Lines 78

Reflection of Pulses from a Terminated Transmission Line 78

Bounce Diagrams for Transient Propagation 80

3 Transmission Lines and Waveguides 87

3.1 General Solutions for TEM, TE, and TM Waves 88

TEM Waves 89

Impossibility of TEM Mode 91

TE Waves 91

TM Waves 92

Attenuation Due to Dielectric Loss 92

3.2 Parallel Plate Waveguide 93

TEM Modes 93

TM Modes 95

TE Modes 98

3.3 Rectangular Waveguide 101

TE Modes 101

TM Modes 105

TEm0 Modes of a Partially Loaded Waveguide 109

3.4 Circular Waveguide 112

TE Modes 113

TM Modes 116

3.5 Coaxial Line 121

TEM Modes 121

Higher Order Modes 122

3.6 Surface Waves on a Grounded Dielectric Sheet 125

TM Modes 125

TE Modes 127

3.7 Stripline 130

Formulas for Propagation Constant, Characteristic Impedance, and Attenuation 132

An Approximate Electrostatic Solution 134

3.8 Microstrip Line 136

Formulas for Effective Dielectric Constant, Characteristic Impedance, and Attenuation 137

Frequency-Dependent Effects and Higher Order Modes 139

3.9 The Transverse Resonance Technique 141

TE0n Modes of a Partially Loaded Rectangular Waveguide 142

3.10 Wave Velocities and Dispersion 143

Group Velocity 143

3.11 Summary of Transmission Lines and Waveguides 145

Other Types of Lines and Guides 146

4 Microwave Network Analysis 153

4.1 Impedance and Equivalent Voltages and Currents 154

Equivalent Voltages and Currents 154

The Concept of Impedance 157

Even and Odd Properties of Z(¿) and ¿(¿) 159

4.2 Impedance and Admittance Matrices 160

Reciprocal Networks 162

Lossless Networks 163

4.3 The Scattering Matrix 164

Reciprocal Networks and Lossless Networks 167

A Shift in Reference Planes 169

Power Waves and Generalized Scattering Parameters 171

4.4 The Transmission (ABCD) Matrix 174

Relation to Impedance Matrix 175

Equivalent Circuits for Two-Port Networks 177

4.5 Signal Flow Graphs 177

Decomposition of Signal Flow Graphs 180

Application to Thru-Reflect-Line Network Analyzer Calibration 183

4.6 Discontinuities and Modal Analysis 187

Modal Analysis of an H-Plane Step in Rectangular Waveguide 187

4.7 Excitation of Waveguides-Electric and Magnetic Currents 193

Current Sheets That Excite Only One Waveguide Mode 193

Mode Excitation from an Arbitrary Electric or Magnetic Current Source 195

5 Impedance Matching and Tuning 204

5.1 Matching with Lumped Elements (L Networks) 205

Analytical Solutions 205

Smith Chart Solutions 206

5.2 Single-Stub Tuning 209

Shunt Stubs 210

Series Stubs 213

5.3 Double-Stub Tuning 216

Smith Chart Solution 216

Analytical Solution 219

5.4 The Quarter-Wave Transformer 220

The Impedance Viewpoint 220

The Multiple-Reflection Viewpoint 222

Impedance Matching of the

Quarter-Wave Transformer 223

5.5 The Theory of Small Reflections 226

Single-Section Transformer 226

Multisection Transformer 228

5.6 Binomial Multisection Matching Transformers 228

5.7 Chebyshev Multisection Matching Transformers 232

Chebyshev Polynomials 232

Design of Chebyshev Transformers 233

5.8 Tapered Lines 236

Exponential Taper 237

Triangular Taper 238

Klopfenstein Taper 238

6 Microwave Resonators 244

6.1 Series and Parallel Resonant Circuits 244

Series Resonant Circuit 244

Parallel Resonant Circuit 247

Loaded and Unloaded Q 249

6.2 Transmission Line Resonators 249

Short-Circuited ¿¿2 Line 250

Short-Circuited ¿¿4 Line 252

Open-Circuited ¿¿2 Line 252

6.3 Rectangular Waveguide Cavity Resonators 254

Resonant Frequencies 254

Unloaded Q of the TE10¿ Mode 256

6.4 Circular Waveguide Cavity Resonators 258

Resonant Frequencies 258

Unloaded Q of the TEnm¿ Mode 260

6.5 Dielectric Resonators 263

Resonant Frequencies of TE01¿ Mode 263

6.6 Excitation of Resonators 266

The Coupling Coefficient and Critical Coupling 266

A Gap-Coupled Microstrip Resonator 268

7 Power Dividers and Directional Couplers 275

7.1 Basic Properties of Dividers and Couplers 275

Three-Port Networks (T-Junctions) 275

Four-Port Networks (Directional Couplers) 278

7.2 The T-Junction Power Divider 282

Lossless Divider 282

Resistive Divider 284

7.3 The Wilkinson Power Divider 285

Even-Odd Mode Analysis 285

Unequal Power Division and N-Way Wilkinson Dividers 288

7.4 Waveguide Directional Couplers 290

Bethe Hole Coupler 290

Design of Multihole Couplers 294

7.5 The Quadrature (90¿) Hybrid 298

Even-Odd Mode Analysis 299

7.6 Coupled Line Directional Couplers 302

Coupled Line Theory 302

Design of Coupled Line Couplers 306

Design of Multisection Coupled Line Couplers 310

7.7 The Lange Coupler 313

7.8 The 180¿ Hybrid 316

Even-Odd Mode Analysis of the Ring Hybrid 318

Even-Odd Mode Analysis of the Tapered Coupled Line Hybrid 321

Waveguide Magic-T 324

7.9 Other Couplers 325

8 Microwave Filters 333

8.1 Periodic Structures 334

Analysis of Infinite Periodic Structures 334

Terminated Periodic Structures 336

k-¿ Diagrams and Wave Velocities 337

8.2 Filter Design by the Image Parameter Method 340

Image Impedances and Transfer Functions for Two-Port Networks 340

Constant-k Filter Sections 342

m-Derived Filter Sections 344

Composite Filters 347

8.3 Filter Design by the Insertion Loss Method 349

Characterization by Power Loss Ratio 350

Maximally Flat Low-Pass Filter Prototype 352

Equal-Ripple Low-Pass Filter Prototype 355

Linear Phase Low-Pass Filter Prototypes 355

8.4 Filter Transformations 355

Impedance and Frequency Scaling 356

Bandpass and Bandstop Transformations 361

8.5 Filter Implementation 364

Richards' Transformation 364

Kuroda's Identities 364

Impedance and Admittance Inverters 369

8.6 Stepped-Impedance Low-Pass Filters 370

Approximate Equivalent Circuits for Short Transmission Line Sections 370

Comparison of Richards' Transformation and Stepped-Impedance Method 373

8.7 Coupled Line Filters 373