Networks and Devices Using Planar Transmissions Lines

Networks and Devices Using Planar Transmission Lines......Page 1
ABSTRACT......Page 4
The Author......Page 5
CONTENTS......Page 6
PREFACE......Page 12
1.1Generalities......Page 13
1.2“Telegraphist” and “Transmission line” equations......Page 14
1.3Solutions of transmission line equations......Page 17
1.4Propagation constant and characteristic impedance......Page 20
a.Terminations at the INPUT of the Line......Page 23
b.Terminations at the OUTPUT of the Line......Page 24
1.6“Transmission” and “Impedance” Matrices......Page 27
a. Ratio of Bandwidth Limits......Page 30
c. Octave......Page 31
1.8Reflection coefficients and standing wave ratio......Page 33
1.9Nonuniform transmission lines......Page 41
1.10Quarter wave transformers......Page 45
1.11Coupled transmission lines......Page 52
1.12The Smith chart......Page 67
1.13Some examples using the Smith chart......Page 74
1.14Notes on planar transmission line fabrication......Page 80
References......Page 81
2.1Geometrical characteristics......Page 83
2.2Electric and magnetic field lines......Page 84
2.3Solution techniques for the electromagnetic problem......Page 85
2.4Quasi static analysis methods......Page 86
2.5Coupled modes analysis method......Page 89
2.6Full wave analysis method......Page 90
2.7Design equations......Page 92
2.8Attenuation......Page 95
2.9Practical considerations......Page 99
REFERENCES......Page 100
3.1Geometrical characteristics......Page 103
3.3Solution techniques for the electromagnetic problem......Page 104
3.4Extraction of stripline impedance with a conformal transformation......Page 105
3.5Design equations......Page 107
3.6Attenuation......Page 109
3.8Practical considerations......Page 112
REFERENCES......Page 114
4.1Radiation......Page 116
4.2Surface waves......Page 118
4.3Higher order modes......Page 120
4.3.1mStrip Case......Page 121
4.3.2Stripline Case......Page 122
4.4Typical discontinuities......Page 123
4.5Bends......Page 124
4.5.1mStrip Case......Page 125
4.6.1mStrip Case......Page 127
4.7Gap......Page 129
4.7.2Stripline Case......Page 130
4.8.1mStrip Case......Page 131
4.9“T” Junctions......Page 133
4.9.1mStrip Case......Page 134
4.9.2Stripline Case......Page 135
4.10.1mStrip Case......Page 136
REFERENCES......Page 138
5.2Electric and magnetic field lines......Page 141
5.4Quasi static analysis methods......Page 143
5.5Coupled modes analysis method......Page 145
5.6Full wave analysis method......Page 147
5.7Design equations......Page 149
5.8Attenuation......Page 154
5.9A particular coupled microstrip structure: the meander line......Page 157
REFERENCES......Page 162
6.1Geometrical Characteristics......Page 164
6.2Electric and magnetic field lines......Page 165
6.3Solution techniques for the electromagnetic problem......Page 167
6.4.1SCS......Page 168
6.4.2BCS......Page 169
6.4.3OBCS......Page 171
6.5Attenuation......Page 173
6.6A particular coupled stripline structure: the meander line......Page 176
REFERENCES......Page 182
7.1Simple two port networks......Page 184
a.Stubs......Page 185
e.RESONATORS......Page 188
g.BALUN......Page 191
7.2.1Branch Line......Page 193
7.2.2.“Rat Race” or “Magic T”......Page 198
7.2.3“In-Line” or “Wilkinson”......Page 203
7.2.4Step Coupled Lines......Page 213
7.2.5Tapered Coupling......Page 231
7.2.6Interdigital or “Lange”......Page 239
7.3Signal Combiners......Page 247
7.3.2“Rat Race” or “Magic T”......Page 248
7.3.3“In Line” or “Wilkinson”......Page 249
7.3.4Step Coupled Lines......Page 251
7.4.1Resonant Ring......Page 257
7.4.2Transverse Resonant Lines......Page 261
7.5.1Coupled Lines or “Schiffman”......Page 266
7.5.2Transverse Stubs or “Wilds”......Page 273
7.5.3Reflection Type......Page 276
7.6The Three Port Circulator......Page 281
7.7.1Reciprocal......Page 291
7.7.2Nonreciprocal......Page 294
a.Using a Circular Polarized “RF” Magnetic Field......Page 295
b.Using “Field Displacement”......Page 298
7.8.2Resonance Isolator......Page 303
7.9Comparison among ferrimagnetic phase shifters......Page 304
REFERENCES......Page 305
8.3Directional couplers......Page 310
8.6Phase shifters......Page 311
8.7The three port circulator......Page 312
8.8.1Reciprocal......Page 314
8.8.2Nonreciprocal......Page 315
a.Using Circular Polarized “RF” Magnetic Field......Page 316
b.Using “Field Displacement”......Page 317
8.9.1Field Displacement......Page 319
REFERENCES......Page 320
9.2Electric and magnetic field lines......Page 322
9.3Solution techniques for the electromagnetic problem......Page 324
a.Line of Magnetic Current Method......Page 325
b.Transverse Resonance Method......Page 327
9.4Closed form equations for slot line characteristic impedance......Page 328
9.5Connections between slot lines and other lines......Page 331
b.Connection with Microstrip......Page 332
d.Connection with Coplanar Waveguide......Page 334
a.180° Reciprocal Phase Shifters......Page 335
b.Magic “T”......Page 336
c.Mixers......Page 337
9.7Magnetization of slot lines on ferrimagnetic substrates......Page 338
9.8.1Resonance Isolator......Page 340
9.8.2Field Displacement Isolator......Page 341
9.9.1“Discon” Phase Shifter......Page 344
9.9.2Field Displacement Phase Shifter......Page 346
9.10.1General Characteristics......Page 347
9.10.2Analysis......Page 348
REFERENCES......Page 350
10.1Geometrical characteristics......Page 353
10.2Electric and magnetic field lines......Page 354
a.Conformal Transformation Method: CTM......Page 355
b.Finite Difference Method: FDM......Page 358
10.4Closed form equations for “CPW” characteristic impedance......Page 359
10.5Closed form equations for “CPW” attenuation......Page 361
b.Connection with Microstrip......Page 364
c.Connection with Slot Line......Page 365
a.Mixers......Page 367
b.Directional Couplers......Page 368
10.8Magnetization of “CPW” on ferrimagnetic substrates......Page 370
10.9.2Field Displacement Isolator......Page 371
10.10“CPW” ferrimagnetic phase shifters......Page 373
10.10.2Field Displacement Phase Shifter......Page 374
10.11.1The “CPW” with Bottom Ground Conductor......Page 376
10.11.2“CPW” with Bottom Ground Conductor and Lateral Planes with Limited Extension......Page 377
10.12.1General Characteristics......Page 378
10.12.2Analysis......Page 379
REFERENCES......Page 381
11.1Geometrical characteristics......Page 384
11.3Solution Techniques for the Electromagnetic Problem......Page 385
11.4Design equations......Page 388
11.5Attenuation......Page 389
11.7Use of “CPS”......Page 392
REFERENCES......Page 393
b.Poisson and Laplace Equations......Page 395
c.Boundary Conditions......Page 396
d.Green’s Function......Page 397
e.Gauss’s Law......Page 399
c.Conformal Transformation Method......Page 400
A1.3Finite Difference Method......Page 401
A1.4Image Charge Method......Page 403
A1.5Fundamentals on Functions with Complex VariableS......Page 406
A1.6Conformal Transformation Method......Page 409
A1.7The Schwarz-Christoffel Transformation......Page 410
REFERENCES......Page 414
A2.2Maxwell’s Equations and Boundary Conditions......Page 415
A2.3Wave equations in harmonic time dependence......Page 417
A2.4The propagation vectors and their relationships with electric and magnetic fields......Page 420
A2.6Plane wave definitions......Page 423
A2.7Evaluation of electromagnetic energy......Page 425
A2.8Waves in guiding structures with curvilinear orthogonal coordinate reference system......Page 427
A2.9“TE” and “TM” modes in rectangular waveguide......Page 432
1.TE Mode......Page 434
2.“TM” Mode......Page 436
A2.10“TE” and “TM” modes in circular waveguide......Page 438
1.TE Mode......Page 441
2.TM Mode......Page 445
A2.11.1Modes Inside a Coaxial Cable......Page 447
b.“TE” Mode......Page 448
c.“TEM” Mode......Page 450
A2.11.2Uniform Plane Wave......Page 453
A2.12Dispersion......Page 455
1.Associated Network for a “TM” Mode......Page 458
2.Associated Network for a “TE” Mode......Page 462
3.Associated Network for a “TEM” Mode......Page 463
4.Associated Network for a “UPW”......Page 464
A2.14Field penetration inside nonideal conductors......Page 465
REFERENCES......Page 470
b.[Y] Matrix......Page 471
c.ABCD or “Chain” Matrix......Page 472
A3.2Scattering parameters and conversion formulas......Page 473
d.Conversion from “[Z]” to “[ABCD]”......Page 476
A3.3Conditions on scattering matrix for reciprocal and lossless networks......Page 477
A3.4Three port networks......Page 478
A3.5Four port networks......Page 482
A3.6Quality parameters for directional couplers......Page 484
b.Isolation.......Page 486
A3.7Scattering parameters in unmatched case......Page 487
REFERENCES......Page 488
A4.1The intrinsic losses of real elements......Page 489
A4.2The quality factor “Q”......Page 490
A4.3Elements of filter theory......Page 496
2.Stop Band Region......Page 498
3.Transition Band Region......Page 499
A4.5Filter generation from a normalized low pass......Page 504
a.High Pass Filters......Page 507
c.Band Stop Filters......Page 508
A4.6Filters with lossy elements......Page 509
REFERENCES......Page 512
c.Third Principle of Dynamics......Page 513
4.Couple and Momentum of a Couple......Page 514
5. Vector “Quantity of Motion” and Vector “Angular Orbital Momentum of the Quantity of Motion”......Page 515
7.The Theorem of the Quantity of Motion......Page 516
A5.3Forces working on lone electric charges......Page 517
3.Lorentz Force......Page 518
4.Potential Energy of a Charge......Page 519
3.Vector “Magnetic Momentum” Produced by a Current in a Closed Wire......Page 520
1.Laplace Expression......Page 521
3.Ampere’s Expression......Page 522
2.The Energy-Frequency Relationship......Page 523
A5.7The foundations of atom theory......Page 524
A5.8The atom structure in quantum mechanics......Page 527
A5.9The precession motion of the atomic magnetic momentum......Page 530
A5.10Principles of wave mechanics......Page 536
REFERENCES......Page 541
A6.2Fundamental relationships for static magnetic fields and materials......Page 542
c.Ferromagnetic Materials......Page 544
A6.4Statistics functions for particle distribution in energy levels......Page 545
b.Bose-Einstein Function......Page 546
c.Fermi-Dirac Function......Page 547
A6.5Statistic evaluation of atomic magnetic moments......Page 551
b.Magnetostriction......Page 554
A6.7The Weiss domains in ferromagnetic materials......Page 555
A6.8Application of Weiss’ theory to some ferromagnetic phenomena......Page 557
a.Spontaneous Magnetization and Curie’s Temperature......Page 558
b.Ferromagnetic Paramagnetism......Page 559
c.First Magnetization Curve and Hysteresis Loop......Page 560
A6.9The Heisenberg Theory for the Molecular Field......Page 561
A6.11Antiferromagnetism......Page 564
A6.12Ferrimagnetism......Page 565
REFERENCES......Page 566
A7.2The chemical composition of ferrites......Page 567
a.Permanent Magnetization......Page 568
c.Paramagnetism......Page 569
d.Precession Motion......Page 570
A7.4The Permeability Tensor of Ferrites......Page 571
A7.5“TEM” wave inside an isodirectional magnetized ferrite......Page 581
A7.6Linear polarized, uniform plane wave inside an isodirectional magnetized ferrite: The Farada.........Page 589
A7.7Electromagnetic wave inside a transverse magnetized ferrite......Page 593
A7.8Considerations on demagnetization and anisotropy......Page 598
A7.9The behavior of not statically saturated ferrite......Page 602
A7.10The quality factor of ferrites at resonance......Page 604
a.The Conduction Losses “Lc”......Page 605
c.The Residual Losses “Lr”......Page 606
a.Nonreciprocal Isolators......Page 607
b.Nonreciprocal Phase Shifters......Page 609
c.Circulators......Page 611
a.Nonreciprocal Isolators......Page 612
b.Phase Shifters......Page 613
c.Circulators......Page 614
A7.14Field displacement isolators and phase shifters......Page 615
a.Nonreciprocal Isolators......Page 621
b.Phase Shifters......Page 622
a.The Ferrite As Microstrip Substrate......Page 623
b.Nonreciprocal Isolators......Page 625
d.Three Port Circulators......Page 626
b.Tunable Filters......Page 629
A7.17Use of ferrite until UHF......Page 631
A7.18Harmonic signal generation in ferrite......Page 632
A7.19Main resonance reduction and secondary resonance in ferrite......Page 634
a.Main Resonance Peak Reduction......Page 635
b.Secondary Resonance......Page 636
REFERENCES......Page 637
A8.2.1Associated to Vectors......Page 639
A8.2.3General......Page 640
A8.3.1 : Vector Operator Nabla or Vector Operator Delta......Page 641
A8.4Delta operator functions in cartesian orthogonal coordinate system......Page 642
A8.5Delta operator functions in a cylindrical coordinate system......Page 644
A8.6Delta operator functions in a spherical coordinate system......Page 646
b.Stokes Theorem......Page 648
f.Green Two Dimensional Second Identity......Page 649
A8.8Elliptic integrals and their approximations......Page 650
REFERENCES......Page 651