High Frequency Techniques

Joseph F. White is an instructor and consultant at JFW Industries, Inc. He has twenty-five years of design experience, was technical director at M/A-COM, Inc., and received the IEEE Microwave Theory and Techniques Society's Application Award for "Contributions to Phased Array Antennas." Dr. White edited Microwave Journal, Applied Microwave and Wireless, and Microwave Semiconductor Engineering. He is a Fellow of the IEEE.

Preface xv Acknowledgments xvii

1 Introduction 1

1.1 Beginning of Wireless 1

1.2 Current Radio Spectrum 4

1.3 Conventions Used in This Text 8

Sections 8

Equations 8

Figures 8

Exercises 8

Symbols 8

Prefixes 10

Fonts 10

1.4 Vectors and Coordinates 11

1.5 General Constants and Useful Conversions 14

2 Review of AC Analysis and Network Simulation 16

2.1 Basic Circuit Elements 16

The Resistor 16

Ohm’s Law 18

The Inductor 19

The Capacitor 20

2.2 Kirchhoff’s Laws 22

2.3 Alternating Current (AC) Analysis 23

Ohm’s Law in Complex Form 26

2.4 Voltage and Current Phasors 26

2.5 Impedance 28

Estimating Reactance 28

Addition of Series Impedances 29

2.6 Admittance 30

Admittance Definition 30

Addition of Parallel Admittances 30

The Product over the Sum 32

2.7 LLFPB Networks 33

2.8 Decibels, dBW, and dBm 33

Logarithms (Logs) 33

Multiplying by Adding Logs 34

Dividing by Subtracting Logs 34

Zero Powers 34

Bel Scale 34

Decibel Scale 35

Decibels—Relative Measures 35

Absolute Power Levels—dBm and dBW 37

Decibel Power Scales 38

2.9 Power Transfer 38

Calculating Power Transfer 38

Maximum Power Transfer 39

2.10 Specifying Loss 40

Insertion Loss 40

Transducer Loss 41

Loss Due to a Series Impedance 42

Loss Due to a Shunt Admittance 43

Loss in Terms of Scattering Parameters 44

2.11 Real RLC Models 44

Resistor with Parasitics 44

Inductor with Parasitics 44

Capacitor with Parasitics 44

2.12 Designing LC Elements 46

Lumped Coils 46

High μ Inductor Cores—the Hysteresis Curve 47

Estimating Wire Inductance 48

Parallel Plate Capacitors 49

2.13 Skin Effect 51

2.14 Network Simulation 53

3 LC Resonance and Matching Networks 59

3.1 LC Resonance 59

3.2 Series Circuit Quality Factors 60

Q of Inductors and Capacitors 60

QE, External Q 61

QL, Loaded Q 62

3.3 Parallel Circuit Quality Factors 62

3.4 Coupled Resonators 63

Direct Coupled Resonators 63

Lightly Coupled Resonators 63

3.5 Q Matching 67

Low to High Resistance 67

Broadbanding the Q Matching Method 70

High to Low Resistance 71

4 Distributed Circuits 78

4.1 Transmission Lines 78

4.2 Wavelength in a Dielectric 81

4.3 Pulses on Transmission Lines 82

4.4 Incident and Reflected Waves 83

4.5 Reflection Coefficient 85

4.6 Return Loss 86

4.7 Mismatch Loss 86

4.8 Mismatch Error 87

4.9 The Telegrapher Equations 91

4.10 Transmission Line Wave Equations 92

4.11 Wave Propagation 94

4.12 Phase and Group Velocities 97

4.13 Reflection Coefficient and Impedance 100

4.14 Impedance Transformation Equation 101

4.15 Impedance Matching with One Transmission Line 108

4.16 Fano’s (and Bode’s) Limit 109

Type A Mismatched Loads 109

Type B Mismatched Loads 112

Impedance Transformation Not Included 113

5 The Smith Chart 119

5.1 Basis of the Smith Chart 119

5.2 Drawing the Smith Chart 124

5.3 Admittance on the Smith Chart 130

5.4 Tuning a Mismatched Load 132

5.5 Slotted-Line Impedance Measurement 135

5.6 VSWR = r 139

5.7 Negative Resistance Smith Chart 140

5.8 Navigating the Smith Chart 140

5.9 Smith Chart Software 145

5.10 Estimating Bandwidth on the Smith Chart 147

5.11 Approximate Tuning May Be Better 148

5.12 Frequency Contours on the Smith Chart 150

5.13 Using the Smith Chart without Transmission Lines 150

5.14 Constant Q Circles 151

5.15 Transmission Line Lumped Circuit Equivalent 153

6 Matrix Analysis 161

6.1 Matrix Algebra 161

6.2 Z and Y Matrices 164

6.3 Reciprocity 166

6.4 The ABCD Matrix 167

6.5 The Scattering Matrix 172

6.6 The Transmission Matrix 177

7 Electromagnetic Fields and Waves 183

7.1 Vector Force Fields 183

7.2 E and H Fields 185

7.3 Electric Field E 185

7.4 Magnetic Flux Density 187

7.5 Vector Cross Product 188

7.6 Electrostatics and Gauss’s Law 193

7.7 Vector Dot Product and Divergence 194

7.8 Static Potential Function and the Gradient 196

7.9 Divergence of the B Field 200

7.10 Ampere’s Law 201

7.11 Vector Curl 202

7.12 Faraday’s Law of Induction 208

7.13 Maxwell’s Equations 209

Maxwell’s Four Equations 209

Auxiliary Relations and Definitions 210

Visualizing Maxwell’s Equations 211

7.14 Primary Vector Operations 214

7.15 The Laplacian 215

7.16 Vector and Scalar Identities 218

7.17 Free Charge within a Conductor 219

7.18 Skin Effect 221

7.19 Conductor Internal Impedance 224

7.20 The Wave Equation 227

7.21 The Helmholtz Equations 229

7.22 Plane Propagating Waves 230

7.23 Poynting’s Theorem 233

7.24 Wave Polarization 236

7.25 EH Fields on Transmission Lines 240

7.26 Waveguides 246

General Waveguide Solution 246

Waveguide Types 250

Rectangular Waveguide Fields 251

Applying Boundary Conditions 252

Propagation Constants and Waveguide Modes 253

Characteristic Wave Impedance for Waveguides 256

Phase and Group Velocities 257

TE and TM Mode Summary for Rectangular Waveguide 257

7.27 Fourier Series and Green’s Functions 261

Fourier Series 261

Green’s Functions 263

7.28 Higher Order Modes in Circuits 269

7.29 Vector Potential 271

7.30 Retarded Potentials 274

7.31 Potential Functions in the Sinusoidal Case 275

7.32 Antennas 275

Short Straight Wire Antenna 275

Radiation Resistance 279

Radiation Pattern 280

Half-Wavelength Dipole 280

Antenna Gain 283

Antenna Effective Area 284

Monopole Antenna 285

Aperture Antennas 286

Phased Arrays 288

7.33 Path Loss 290

7.34 Electromagnetic (EM) Simulation 294

8 Directional Couplers 307

8.1 Wavelength Comparable Dimensions 307

8.2 The Backward Wave Coupler 307

8.3 Even- and Odd-Mode Analysis 309

8.4 Reflectively Terminated 3-dB Coupler 320

8.5 Coupler Specifications 323

8.6 Measurements Using Directional Couplers 325

8.7 Network Analyzer Impedance Measurements 326

8.8 Two-Port Scattering Measurements 327

8.9 Branch Line Coupler 327

8.10 Hybrid Ring Coupler 330

8.11 Wilkinson Power Divider 330

9 Filter Design 335

9.1 Voltage Transfer Function 335

9.2 Low-Pass Prototype 336

9.3 Butterworth or Maximally Flat Filter 337

9.4 Denormalizing the Prototype Response 339

9.5 High-Pass Filters 343

9.6 Bandpass Filters 345

9.7 Bandstop Filters 349

9.8 Chebyshev Filters 351

9.9 Phase and Group Delay 356

9.10 Filter Q 361

9.11 Diplexer Filters 364

9.12 Top-Coupled Bandpass Filters 367

9.13 Elliptic Filters 369

9.14 Distributed Filters 370

9.15 The Richards Transformation 374

9.16 Kuroda’s Identities 379

9.17 Mumford’s Maximally Flat Stub Filters 381

9.18 Filter Design with the Optimizer 384

9.19 Statistical Design and Yield Analysis 386

Using Standard Part Values 386

The Normal Distribution 387

Other Distributions 391

10 Transistor Amplifier Design 399

10.1 Unilateral Design 399

Evaluating S Parameters 399

Transistor Biasing 400

Evaluating RF Performance 403

10.2 Amplifier Stability 405

10.3 K Factor 409

10.4 Transducer Gain 413

10.5 Unilateral Gain Design 416

10.6 Unilateral Gain Circles 422

Input Gain Circles 422

Output Gain Circles 424

10.7 Simultaneous Conjugate Match Design 428

10.8 Various Gain Definitions 431

10.9 Operating Gain Design 433

10.10 Available Gain Design 437

10.11 Noise in Systems 442

Thermal Noise Limit 442

Other Noise Sources 444

Noise Figure of a Two-Port Network 445

Noise Factor of a Cascade 447

Noise Temperature 448

10.12 Low-Noise Amplifiers 450

10.13 Amplifier Nonlinearity 455

Gain Saturation 455

Intermodulation Distortion 456

10.14 Broadbanding with Feedback 460

10.15 Cascading Amplifier Stages 466

10.16 Amplifier Design Summary 468

Appendices

A. Symbols and Units 474

B. Complex Mathematics 478

C. Diameter and Resistance of Annealed Copper Wire by Gauge Size 483

D. Properties of Some Materials 485

E. Standard Rectangular Waveguides 486

Frequently Used Relations 487

Index 491