Microwave Polarizers, Power Dividers, Phase Shifters, Circulators, and Switches
IEEE Press Series

Discusses the fundamental principles of the design and development of microwave satellite switches utilized in military, commercial, space, and terrestrial communication

This book deals with important RF/microwave components such as switches and phase shifters, which are relevant to many RF/microwave applications. It provides the reader with fundamental principles of the operation of some basic ferrite control devices and explains their system uses. This in-depth exploration begins by reviewing traditional nonreciprocal components, such as circulators, and then proceeds to discuss the most recent advances.

This sequential approach connects theoretical and scientific characteristics of the devices listed in the title with practical understanding and implementation in the real world. Microwave Polarizers, Power Dividers, Phase Shifters, Circulators and Switches covers the full scope of the subject matter and serves as both an educational text and resource for practitioners. Among the many topics discussed are microwave switching, circular polarization, planar wye and equilateral triangle resonators, and many others.

• Translates concepts and ideas fundamental to scientific knowledge into a more visual description
• Describes a wide array of devices including waveguides, shifters, and circulators
• Covers the use of finite element algorithms in design

Microwave Polarizers, Power Dividers, Phase Shifters, Circulators and Switches is an ideal reference for all practitioners and graduate students involved in this niche field.

Preface xiii

Acknowledgments xv

List of Contributors xvii

1 Microwave Switching Using Junction Circulators 1

Joseph Helszajn

1.1 Microwave Switching Using Circulators 1

1.2 The Operation of the Switched Junction Circulator 1

1.3 The Turnstile Circulator 4

1.4 Externally and Internally Latched Junction Circulators 7

1.5 Standing Wave Solution of Resonators with Threefold Symmetry 7

1.6 Magnetic Circuit Using Major Hysteresis Loop 8

1.7 Display of Hysteresis Loop 9

1.8 Switching Coefficient of Magnetization 11

1.9 Magnetostatic Problem 13

1.10 Multiwire Magnetostatic Problem 14

1.11 Shape Factor of Cylindrical Resonator 15

Bibliography 16

2 The Operation of Nonreciprocal Microwave Faraday Rotation Devices and Circulators 19

Joseph Helszajn

2.1 Introduction 19

2.2 Faraday Rotation 20

2.3 Magnetic Variables of Faraday Rotation Devices 25

2.4 The Gyrator Network 27

2.5 Faraday Rotation Isolator 29

2.6 Four-port Faraday Rotation Circulator 30

2.7 Nonreciprocal Faraday Rotation-type Phase Shifter 31

2.8 Coupled Wave Theory of Faraday Rotation Section 32

2.9 The Partially Ferrite-filled Circular Waveguide 33

Bibliography 34

3 Circular Polarization in Parallel Plate Waveguides 37

Joseph Helszajn

3.1 Circular Polarization in Rectangular Waveguide 37

3.2 Circular Polarization in Dielectric Loaded Parallel Plate Waveguide with Open Sidewalls 40

Bibliography 47

4 Reciprocal Quarter-wave Plates in Circular Waveguides 49

Joseph Helszajn

4.1 Quarter-wave Plate 50

4.2 Coupled Mode Theory of Quarter-wave Plate 53

4.3 Effective Waveguide Model of Quarter-wave Plate 58

4.4 Phase Constants of Quarter-wave Plate Using the Cavity Method 59

4.5 Variable Rotor Power Divider 62

Bibliography 63

5 Nonreciprocal Ferrite Quarter-wave Plates 65

Joseph Helszajn

5.1 Introduction 65

5.2 Birefringence 65

5.3 Nonreciprocal Quarter-wave Plate Using the Birefringence Effect 67

5.4 Circulator Representation of Nonreciprocal Quarter-wave Plates 71

5.5 Coupled and Normal Modes in Magnetized Ferrite Medium 72

5.6 Variable Phase-shifters Employing Birefringent, Faraday Rotation, and Dielectric Half-wave Plates 73

5.7 Circulators and Switches Using Nonreciprocal Quarter-wave Plates 76

5.8 Nonreciprocal Circular Polarizer Using Elliptical Gyromagnetic Waveguide 77

Bibliography 79

6 Ridge, Coaxial, and Stripline Phase-shifters 81

Joseph Helszajn

6.1 Differential Phase-shift, Phase Deviation, and Figure of Merit of Ferrite Phase-shifter 82

6.2 Coaxial Differential Phase-shifter 82

6.3 Ridge Waveguide Differential Phase-shifter 88

6.4 The Stripline Edge Mode Phase-shifter 90

6.5 Latched Quasi-TEM Phase-shifters 91

Bibliography 92

7 Finite Element Adjustment of the Rectangular Waveguide-latched Differential Phase-shifter 95

Joseph Helszajn and Mark McKay

7.1 Introduction 95

7.2 FE Discretization of Rectangular Waveguide Phase-shifters 97

7.3 LS Modes Limit Waveguide Bandwidths 98

7.4 Cutoff Numbers and Split Phase Constants of a Twin Slab Ferrite Phase-shifter 99

7.5 The Waveguide Toroidal Phase-shifter 102

7.6 Industrial Practice 103

7.7 Magnetic Circuits Using Major and Minor Hysteresis Loops 103

7.8 Construction of Latching Circuits 106

7.9 Temperature Compensation Using Composite Circuits 107

Bibliography 109

8 Edge Mode Phase-shifter 111

Joseph Helszajn and Henry Downs

8.1 Edge Mode Effect 112

8.2 Edge Mode Characteristic Equation 115

8.3 Fields and Power in Edge Mode Devices 115

8.4 Circular Polarization and the Edge Mode Effect 118

8.5 Edge Mode Phase-shifter 120

8.6 Edge Mode Isolators, Phase-shifters, and Circulators 123

Bibliography 124

9 The Two-port On/Off H-plane Waveguide Turnstile Gyromagnetic Switch 127

Joseph Helszajn, Mark McKay, Alicia Casanueva, and Angel Mediavilla Sánchez

9.1 Introduction 127

9.2 Two-port H-plane Turnstile On/Off Switch 127

9.3 Even and Odd Eigenvectors of E-plane Waveguide Tee Junction 129

9.4 Eigenvalue Adjustment of Turnstile Plane Switch 130

9.5 Eigen-networks 132

9.6 Numerical Adjustments of Passbands 133

9.7 An Off/On H-plane Switch 134

Bibliography 136

10 Off/On and On/Off Two-port E-plane Waveguide Switches Using Turnstile Resonators 137

Joseph Helszajn, Mark McKay, and John Sharp

10.1 Introduction 137

10.2 The Shunt E-plane Tee Junction 138

10.3 Operation of Off/On and On/Off E-plane Switches 140

10.4 Even and Odd Eigenvector of H-plane Waveguide Tee Junction 141

10.5 Phenomenological Description of Two-port Off/On and On/Off Switches 142

10.6 Eigenvalue Diagrams of Small- and Large-gap E-plane Waveguide Tee Junction 144

10.7 Eigenvalue Diagrams of E-plane Waveguide Tee Junction 145

10.8 Eigen-networks of E-plane Tee Junction 146

10.9 Eigenvalue Algorithm 147

10.10 Pass and Stop Bands in Demagnetized E-plane Waveguide Tee Junction 148

Bibliography 150

11 Operation of Two-port On/Off and Off/On Planar Switches Using the Mutual Energy–Finite Element Method 153

Joseph Helszajn and David J. Lynch

11.1 Introduction 153

11.2 Impedance and Admittance Matrices from Mutual Energy Consideration 154

11.3 Impedance and Admittance Matrices for Reciprocal Planar Circuits 157

11.4 Immittance Matrices of n-Port Planar Circuits Using Finite Elements 160

11.5 Frequency Response of Two-port Planar Circuits Using the Mutual Energy–Finite Element Method 161

11.6 Stripline Switch Using Puck/Plug Half-spaces 166

Bibliography 169

12 Standing Wave Solutions and Cutoff Numbers of Planar WYE and Equilateral Triangle Resonators 171

Joseph Helszajn

12.1 Introduction 171

12.2 Cutoff Space of WYE Resonator 172

12.3 Standing Wave Circulation Solution of WYE Resonator 174

12.4 Resonant Frequencies of Quasi-wye Magnetized Resonators 175

12.5 The Gyromagnetic Cutoff Space 179

12.6 TM Field Patterns of Triangular Planar Resonator 180

12.7 TM1,0,−1 Field Components of Triangular Planar Resonator 182

12.8 Circulation Solutions 182

Bibliography 184

13 The Turnstile Junction Circulator: First Circulation Condition 185

Joseph Helszajn

13.1 Introduction 185

13.2 The Four-port Turnstile Junction Circulator 186

13.3 The Turnstile Junction Circulator 188

13.4 Scattering Matrix 190

13.5 Frequencies of Cavity Resonators 193

13.6 Effective Dielectric Constant of Open Dielectric Waveguide 193

13.7 The Open Dielectric Cavity Resonator 196

13.8 The In-phase Mode 198

13.9 First Circulation Condition 200

Bibliography 200

14 The Turnstile Junction Circulator: Second Circulation Condition 203

Joseph Helszajn and Mark McKay

14.1 Introduction 203

14.2 Complex Gyrator of Turnstile Circulator 204

14.3 Susceptance Slope Parameter, Gyrator Conductance, and Quality Factor 207

14.4 Propagation in Gyromagnetic Waveguides 208

14.5 Eigen-network of Turnstile Circulator 209

14.6 The Quality Factor of the Turnstile Circulator 211

14.7 Susceptance Slope Parameter of Turnstile Junction 213

Bibliography 213

15 A Finite-Element Algorithm for the Adjustment of the First Circulation Condition of the H-plane Turnstile Waveguide Circulator 217

Joseph Helszajn

15.1 Introduction 217

15.2 Bandpass Frequency of a Turnstile Junction 219

15.3 In-phase and Counterrotating Modes of Turnstile Junction 221

15.4 Reference Plane 222

15.5 FE Algorithm 222

15.6 FE Adjustment 224

15.7 The Reentrant Turnstile Junction in Standard WR75 Waveguide 230

15.8 Susceptance Slope Parameter of Degree-1 Junction 230

15.9 Split Frequencies of Gyromagnetic Resonators 233

References 236

16 The E-plane Waveguide Wye Junction: First Circulation Conditions 239

Joseph Helszajn and Marco Caplin

16.1 Introduction 239

16.2 Scattering Matrix of Reciprocal E-plane Three-port Y-junction 240

16.3 Reflection Eigenvalue Diagrams of Three-port Junction Circulator 242

16.4 Eigen-networks 244

16.5 Pass Band and Stop Band Characteristic Planes 246

16.6 The Dicke Eigenvalue Solution 247

16.7 Stop Band Characteristic Plane 248

16.8 The E-plane Geometry 249

16.9 First Circulation Condition 251

16.10 Calculations of Eigenvalues 253

Bibliography 254

17 Adjustment of Prism Turnstile Resonators Latched by Wire Loops 257

Joseph Helszajn and William D’Orazio

17.1 Introduction 257

17.2 The Prism Resonator 258

17.3 Split Frequency of Cavity Resonator with Up or Down Magnetization 260

17.4 Quality Factor of Gyromagnetic Resonator with Up and Down Magnetization 261

17.5 Shape Factor of Tri-toroidal Resonator 262

17.6 Squareness Ratio 264

17.7 The Complex Gyrator Circuit of the Three-port Junction Circulator 265

17.8 The Alternate Line Transformer 266

17.9 Effective Complex Gyrator Circuit 267

Bibliography 267

18 Numerical Adjustment of Waveguide Ferrite Switches Using Tri-toroidal Resonators 269

Joseph Helszajn and Mark McKay

18.1 Introduction 269

18.2 The Tri-toroidal Resonator 270

18.3 The Wire Carrying Slot Geometry 272

18.4 The Magnetostatic Problem 273

18.5 Quality Factor of Junction Circulators with Up and Down Magnetization 274

18.6 Split Frequencies of Planar and Cavity Gyromagnetic Resonators 275

18.7 The Split Frequencies of Prism Resonator with Up and Down Magnetization 276

18.8 Exact Calculation of Split Frequencies in Tri-toroidal Cavity 277

18.9 Calculation and Experiment 278

18.10 Tri-toroidal Composite Prism Resonator 279

18.11 Tri-toroidal Wye Resonator with Up and Down Magnetization 280

Bibliography 282

19 The Waveguide H-plane Tee Junction Circulator Using a Composite Gyromagnetic Resonator 285

Joseph Helszajn

19.1 Introduction 285

19.2 Eigenvalue Problem of the H-plane Reciprocal Tee Junction 286

19.3 Electrically Symmetric H-plane Junction at the Altman Planes 289

19.4 Characteristic Planes 290

19.5 The Septum-loaded H-plane Waveguide 292

19.6 The Waveguide Tee Junction Using a Dielectric Post Resonator: First Circulation Condition 294

19.7 The Waveguide Tee Junction Circulator Using a Gyromagnetic Post Resonator: Second Circulation Condition 296

19.8 Composite Dielectric Resonator 297

Bibliography 299

20 0 , 90 , and 180 Passive Power Dividers 301

Joseph Helszajn and Mark McKay

20.1 Introduction 301

20.2 Wilkinson Power Divider 302

20.3 Even and Odd Mode Adjustment of the Wilkinson Power Divider 302

20.4 Scattering Matrix of 90 Directional Coupler 305

20.5 Even and Odd Mode Theory of Directional Couplers 309

20.6 Power Divider Using 90 Hybrids 311

20.7 Variable Power Dividers 313

20.8 180 Waveguide Hybrid Network 314

Bibliography 318

Index 321

JOSEPH HELSZAJN, PHD, is an international authority on non-reciprocal microwave circuits and devices. He has made a significant contribution to the characterization of the complex gyrator circuits and gain-bandwidth products of planar gyromagnetic resonators and other gyromagnetic devices. Professor Helszajn is a Fellow of the Institute of Electrical and Electronic Engineers (FIEEE), the City and Guilds Institute (FGCI), the Royal Society of Edinburgh (FRSE), and the Royal Academy of Engineering (FREng). He previously authored thirteen books, nine of which were published by Wiley.