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 Sanchez
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
