J. Helszajn9780470258781, 0470258780
The stripline junction circulator is a unique three-port non-reciprocal microwave junction used to connect a single antenna to both a transmitter and a receiver. Its operation relies on the interaction between an electron spin in a suitably magnetized insulator with an alternating radio frequency magnetic field. In its simplest form, it consists of a microwave planar gyromagnetic resonator symmetrically coupled by three transmission lines.
This book explores the magnetic interaction involved in the stripline circulator’s operation, the nature of the microwave resonator shape, and the network problem that arises in coupling the microwave resonator to the microwave circuit. The stripline circulator is an important device met across a wide range of industries, including wireless, military, radar, and satellite communications. The book’s design tables are a unique feature, offering valuable design support.
Written by an international authority on non-reciprocal microwave circuits and devices, the book is organized into logical blocks of chapters that focus on specific effects and circuit aspects of the stripline circulator. Among the highlights of coverage are:
Spatial shape demagnetizing factors of magnetic insulators
Standing wave solutions of wye gyromagnetic planar resonators
Lumped element circulators
Negative permeability tracking and semi-tracking circulators
Four-port single-junction circulators
Fabrication of very weakly and weakly magnetized microstrip circulators
The final chapter explores important and continuing discrepancies between theoretical models and actual practice. For designers building circulators, isolators, and phase shifters; researchers working on the limitation of ferrite devices; and graduate students intending to work in the field, Dr. Helszajn’s insights and perspectives are invaluable.
Table of contents :
The Stripline Circulator……Page 4
Contents……Page 8
Preface……Page 18
1.2 Phenomenological Description of Stripline Circulator……Page 20
1.3 Adjustment of Junction Circulator……Page 21
1.4 Gyrotropy in Magnetic Insulators……Page 26
1.5 Planar Resonators……Page 27
1.6 Parallel Plate Waveguide Model of Microstrip Circulators……Page 28
1.8 Switched Resonators……Page 31
1.9 Composite Resonators……Page 32
1.10 Power Rating of Gyromagnetic Resonator……Page 34
1.11 Quarter-Wave Coupled Circulator……Page 35
1.12 Four-Port Single Junction Circulator……Page 36
1.13 Edge Mode Circulator……Page 37
1.15 Duplexing Using Junction Circulators……Page 40
2.1 Introduction……Page 42
2.2 Tensor Permeability……Page 43
2.3 Damping……Page 46
2.4 Scalar Permeabilities……Page 49
2.5 Effective Permeability and Gyrotropy……Page 51
2.6 Kittel Line……Page 53
2.7 Low-Field Losses in Unsaturated Magnetic Insulator……Page 54
2.8 Magnetic Bias Points Above and Below the Kittel Line……Page 56
2.9 Spinwave Manifold……Page 57
2.10 Magnetization Values of Various Ferrites……Page 60
2.11 The Origin of the Uniform Linewidth in Magnetic Insulators……Page 61
3.1 Introduction……Page 66
3.2 Shape Demagnetizing Factors……Page 67
3.3 Magnetic Field Intensity and Flux Density in Magnetic Insulator……Page 68
3.4 The Spatial Demagnetizing Factor of a Flat Disk Magnetic Insulator……Page 69
3.5 The Coupled Disk Geometry……Page 75
3.6 The Irregular Hexagonal Magnetic Insulator……Page 79
3.7 Reentrant Magnetic Circuits……Page 80
3.9 Tensor Elements in Partially Magnetized Magnetic Insulator……Page 82
3.10 Partial Magnetization in a Magnetic Insulator……Page 83
4.1 Introduction……Page 86
4.2 The Scattering Matrix……Page 87
4.3 Circulator Definition by Means of Cyclic Substitution……Page 90
4.4 The Unitary Condition……Page 91
4.5 Network Definition of Junction Circulator……Page 92
4.6 Semi-Ideal Circulator……Page 94
4.7 Dissipation Matrix……Page 95
4.8 Terminal Planes of Junctions……Page 96
4.9 Insertion Phase Shift……Page 97
4.10 Specification of Three-Port Circulators with Nonideal Loads……Page 98
4.11 Swept Frequency Description of Scattering Parameters……Page 101
5.1 Introduction……Page 104
5.2 Scattering Matrix, Eigenvalues, and Eigenvectors……Page 105
5.3 Eigenvalue Adjustment of Three-Port Circulator……Page 106
5.4 Eigenvectors……Page 109
5.5 Scattering Matrix of Three-Port Junction Circulator……Page 114
5.6 Diagonalization……Page 116
5.7 Dissipation Eigenvalues……Page 117
5.8 Evaluation of Degenerate Counterrotating Eigenvalue……Page 119
5.9 Evaluation of In-Phase Eigenvalue……Page 121
5.10 Split Frequencies of Gyromagnetic Resonators……Page 123
5.11 Phase Angle of In-Phase Eigenvalue……Page 124
5.12 Adjustment of Triple Pole Circulator……Page 126
6.1 Introduction……Page 128
6.2 Impedance Matrix of Junction Circulator……Page 129
6.3 Eigenvalues of Immittance Matrices……Page 130
6.4 Complex Gyrator Immittance of Three-Port Circulator……Page 132
6.5 Synthesis of Junction Circulators Using Resonant In-Phase Eigen-Network……Page 135
6.6 Equivalent Circuit of Three-Port Circulator……Page 137
6.7 Quality Factor of Junction Circulator……Page 140
6.8 Degenerate Counterrotating Eigen-Network (s1)……Page 141
6.9 In-Phase Eigen-Network……Page 144
6.10 Split Eigen-Networks of Junction Circulator……Page 145
6.11 Gyrator Conductance of Circulator……Page 146
6.12 The Gyrator Network……Page 148
7.1 Introduction……Page 150
7.2 Input Immittance of Terminated Circulator in Terms of Open-Circuit Parameters……Page 151
7.3 Input Impedance of Terminated Circulator in Terms of Eigenvalues……Page 152
7.4 Gyrator Circuit……Page 154
7.5 Real Part Condition……Page 155
7.6 Synthesis of Complex Admittance of Terminated Circulator……Page 158
7.7 Topologies of Terminated Circulator at the Split Frequencies……Page 160
7.8 Degree-2 Topology……Page 162
8.1 Introduction……Page 164
8.2 Cloverleaf Resonator……Page 165
8.3 Finite Element Method……Page 166
8.4 Cutoff Space of Isotropic Cloverleaf Resonator with Threefold Symmetry……Page 168
8.5 Cutoff Space of Isotropic Cloverleaf Resonator with Fourfold Symmetry……Page 170
8.6 Field Patterns in Cloverleaf Resonators……Page 172
8.8 Split Cutoff Space of Gyromagnetic Cloverleaf Resonator with Threefold Symmetry……Page 181
8.9 Standing Wave Solution of Circulators Using Cloverleaf Resonators……Page 183
9.1 Introduction……Page 184
9.2 Cutoff Space of Wye Planar Resonator……Page 185
9.4 Resonant Frequencies of UE Loaded Disk Magnetized Resonators……Page 188
9.5 The Gyromagnetic Cutoff Space……Page 196
9.6 Open-Circuit Parameters of Circulators Using Wye Resonators……Page 198
9.7 The Short UE……Page 200
10.1 Introduction……Page 204
10.2 Dominant Mode Charts for Planar Resonators with Radial Magnetic Wall Ridges……Page 205
10.3 Higher Order Mode Charts in Planar Resonators with Radial Magnetic Wall Ridges……Page 209
10.4 Fay and Comstock Circulation Solution……Page 212
10.5 Quality Factor of Circulators Using Planar Resonators with Triplets of Radial Magnetic Walls……Page 214
10.6 Experimental Mode Charts of Circulators Using Planar Resonators Slot–Hole……Page 219
10.7 Circumferential Magnetic Wall……Page 220
10.8 Impedance Zero……Page 221
11.2 Eigenvalue Diagrams of Semi-Ideal Circulation……Page 222
11.3 Constituent Resonator……Page 224
11.4 Unloaded, External, and Loaded Q-Factors……Page 226
11.5 Measurement of Unloaded Split Q-Factors……Page 227
11.6 Experimental Data……Page 229
11.7 Insertion Loss of Junction Circulators……Page 232
11.9 Scattering Matrix of Semi-Ideal Circulators……Page 237
12.1 Introduction……Page 240
12.2 Lumped Element Circulator……Page 241
12.3 Complex Gyrator Circuit of Lumped Element Circulator……Page 243
12.4 Gain-Bandwidth Product of Lumped Element Circulator……Page 245
12.5 Inductance of Constituent Lumped Element Resonator……Page 247
12.6 Magnetic Variables of Lumped Element Circulator……Page 248
12.7 Degree-2 Lumped Element Circulator……Page 249
12.8 Degree-3 Lumped Element Circulator……Page 253
12.9 Quasi Lumped Element Circulators……Page 254
12.10 Lowpass Matching Circuit……Page 255
13.1 Introduction……Page 258
13.2 Mode Chart of Gyromagnetic Disk Resonator……Page 259
13.3 Impedance Matrix of Three-Port Junction Circulator……Page 264
13.4 Eigenvalue Solution……Page 266
13.5 Complex Gyrator Circuit……Page 269
13.6 Single Pole Circulation Solution……Page 271
13.7 Frequency Response of Weakly Magnetized Circulator……Page 273
13.8 Very Weakly Magnetized Gyromagnetic Resonator……Page 275
14.2 Green’s Function Matrix of Junction Circulator……Page 276
14.3 Wave Impedance Matrix of Three-Port Circulator……Page 281
15.1 Introduction……Page 286
15.2 Green’s Function Analysis Using Finite Element Method……Page 287
15.3 Normalized Eigenfunction……Page 290
15.4 Finite Element Procedure……Page 291
15.5 Complex Gyrator Circuit of Junction Circulator……Page 293
15.6 Contour Integral Method……Page 296
16.1 Introduction……Page 304
16.2 Eigenfunctions of Equilateral Triangle……Page 305
16.3 TM Field Patterns of Triangular Planar Resonator……Page 310
16.4 TM(1,0,–1) Field Components of Triangular Planar Resonator……Page 311
16.5 TM(1,1,–2) Field Components of Triangular Planar Resonator……Page 312
16.6 Electric Field Pattern in Circulator Using Triangular Resonator……Page 313
16.7 Stored Energy……Page 317
16.8 The Irregular Hexagonal Resonator……Page 318
16.9 Cutoff Space of Planar Irregular Hexagonal Resonator……Page 320
16.10 Split Frequencies of Irregular Hexagonal Resonator……Page 323
16.11 Quality Factor of Circulator Using Apex-Coupled Triangular Resonator……Page 326
16.13 Gyrator Conductance……Page 327
16.14 Susceptance Slope Parameters of Disk and Triangular Resonators……Page 329
16.15 Transmission Phase Angle of Degree-1 Circulator……Page 332
17.1 Introduction……Page 334
17.2 Eigenvalues of Tracking Circulators……Page 335
17.3 Complex Gyrator Circuit……Page 338
17.4 Three Eigen-Network Theory of Tracking Circulator……Page 342
17.5 Synthesis of Semitracking Stripline Junction Circulators……Page 346
17.6 Semitracking Circulation Solutions……Page 348
17.7 Synthesis of Degree-3 Circulator……Page 351
17.8 Frequency Response of Quarter-Wave Coupled Circulators……Page 354
18.1 Introduction……Page 358
18.2 Negative Permeability Gyromagnetic Resonator……Page 359
18.3 Impedance Poles of Very Strongly Magnetized Junction……Page 362
18.4 Circulation Solution Using Nondegenerate Resonator Modes……Page 363
18.6 Negative Permeability Tracking Solution……Page 365
18.7 Frequency Response……Page 370
18.8 Complex Gyrator Circuit of 100% Circulator……Page 372
18.9 Composite Gyromagnetic Resonator……Page 376
19.1 Introduction……Page 382
19.2 Complex Gyrator Circuits of Circulators Using Radial/Lumped Element Resonators……Page 383
19.3 Synthesis of Quarter-Wave Coupled Junction Circulators Using Distributed/Lumped Element Resonators……Page 388
19.4 Mixed Distributed Radial/Lumped Element Resonator……Page 391
19.5 1–2 GHz Device……Page 392
19.6 Synthesis of Weakly Magnetized Undersized Junctions……Page 394
20.1 Introduction……Page 396
20.2 Eigenvalues and Eigenvectors of m-Port Symmetric Planar Junction Circulator……Page 397
20.3 Open-Circuit Parameters of a Three-Port Circulator with Three-Fold Symmetry……Page 399
20.4 Eigenvalues of Symmetrical m-Port Gyromagnetic Resonator……Page 401
20.5 Augmented Eigenvalues……Page 403
20.7 Complex Gyrator Circuit……Page 406
21.1 Introduction……Page 410
21.2 Standing Wave Solution……Page 411
21.3 Symmetry Properties of Circulators……Page 412
21.4 Open-Circuit Parameters of a Junction with Two Degrees of Threefold Symmetry……Page 415
21.5 Constituent Problem Regions of a Six-Port Junction Having Two Degrees of Threefold Symmetry……Page 419
21.6 3 × 3 Impedance Matrix of Circulators Using Wye Resonators……Page 422
21.7 Short-Circuit Parameters of Quarter-Wave Coupled Circulator……Page 424
22.1 Introduction……Page 426
22.2 Symmetry Properties of Circulators……Page 427
22.3 Similarity Transformation……Page 428
22.4 Eigenvalue Adjustment……Page 431
22.5 Eigenvectors, Eigenvalues, and Eigen-Networks……Page 433
22.6 Phenomenological Adjustment……Page 435
22.7 Four-Port Single Junction Circulator Using TM(±1,1,0) and TM(0,1,0) Modes……Page 436
22.8 Four-Port Single Junction Circulator Using TM(±3,1,0) and TM(0,1,0) Modes……Page 439
22.9 Four-Port Single Junction Circulator Using TM(1,1,0) and TM(1,2,0) Modes……Page 442
22.10 Standing Wave Solutions of Planar X Resonators……Page 443
22.11 Resonant Frequencies of Four-Port UE Loaded Disk Magnetized Resonators……Page 445
23.1 Introduction……Page 450
23.2 Equivalent Circuit of Reciprocal Three-Port Junction……Page 451
23.3 Eigen-Networks of Reciprocal Junction……Page 453
23.4 Reflection Coefficient of Reciprocal Junction……Page 455
23.5 Frequency Response of Degree-n Network……Page 458
23.6 Degree-1 Three-Port Junction Circulator……Page 459
23.7 Degree-2 and Degree-3 Circuits……Page 461
23.8 Degree-2 Circulator……Page 463
24.1 Introduction……Page 468
24.2 Eigenvalues of the Scattering Matrix……Page 469
24.3 Eigenvalues of Augmented Scattering Matrix……Page 471
24.4 Circulation Adjustment……Page 474
24.5 Quarter-Wave Coupled-Below-Resonance Stripline Circulator……Page 476
24.6 Frequency Variation of Quarter-Wave Coupled Circulator……Page 478
24.7 Frequency Response of Quarter-Wave Coupled Circulator with Capacitive Tuning……Page 480
25.1 Introduction……Page 484
25.2 β-Plane Insertion Loss Function for Quarter-Wave Long Stepped Impedance Transducers……Page 485
25.3 t-Plane Synthesis of Quarter-Wave Long Stepped Impedance Transducers……Page 487
25.4 Network Parameters of Quarter-Wave Long Impedance Transducers……Page 490
25.5 t-Plane Synthesis of Short-Line Matching Network……Page 496
25.6 Network Parameters of Short-Line Impedance Transducers……Page 498
26.1 Introduction……Page 504
26.2 Wave Impedance and Wavenumber in UHF Gyromagnetic Circuits……Page 505
26.3 Gyromagnetic Space of Above-Resonance Circulators……Page 506
26.4 Approximate Relationships of Permeability Tensor……Page 507
26.5 H(0)/M(0) Space……Page 510
26.6 The Kittel Line……Page 511
26.7 Temperature Stability of Kittel Line……Page 514
26.8 Mode Charts of UHF Gyromagnetic Irregular Hexagonal Planar Resonator……Page 515
26.9 Radial Magnetic Walls……Page 519
26.10 Magnetic Variables of Gyromagnetic Resonators……Page 521
26.11 Complex Gyrator Circuit of UHF Circulators……Page 523
26.12 Real Part Condition……Page 525
26.13 Quality Factor of UHF Circulators……Page 526
27.1 Introduction……Page 530
27.2 Parallel Plate Waveguide Model of Microstrip Circulators……Page 531
27.3 Very Weakly Magnetized Problem Region……Page 534
27.4 Weakly Magnetized Problem Region……Page 537
27.5 Experimental Evaluation of Complex Gyrator Circuits……Page 539
27.6 Synthesis Procedure……Page 545
27.7 Commercial Practice……Page 547
28 The Stripline Circulator: Theory and Practice……Page 550
28.1 Complex Gyrator Circuit of Weakly Magnetized Junction Circulator……Page 551
28.3 Weakly Magnetized Gyromagnetic Resonator……Page 553
28.4 Moderately Magnetized Gyromagnetic Resonator……Page 555
28.5 The Degree-2 Circulator……Page 556
28.6 Gap Effects in Circulator Assemblies……Page 560
28.7 Suspended Planar Resonator……Page 562
28.8 Passband Frequencies of a Three-Port Junction in Immittance Plane……Page 564
28.9 Open Walls……Page 567
28.10 Spinwave Instability in Magnetic Insulators……Page 569
28.11 Frequency Doubling in Ferrites……Page 571
28.12 Second-Order Intermodulation in Magnetic Insulators……Page 572
28.13 Temperature Stability of Magnetic Insulators Below the Kittel Line……Page 574
28.13.2 Nonuniform Magnetic Field……Page 576
28.13.3 Edge Mode Effect……Page 577
28.14 Third-Order Intermodulation Products in Nonlinear Devices……Page 580
Bibliography……Page 584
Index……Page 598
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