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Electromagnetic
Waves and Antennas
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Electromagnetic
Waves and Antennas
To Monica and John
Sophocles J. Orfanidis
Rutgers University
viii
Electromagnetic Waves & Antennas – S. J. Orfanidis – June 21, 2004
4 Reflection and Transmission 86
Contents
4.1 Propagation Matrices, 86
4.2 Matching Matrices, 90
4.3 Reflected and Transmitted Power, 93
4.4 Single Dielectric Slab, 96
4.5 Reflectionless Slab, 99
4.6 Time-Domain Reflection Response, 107
4.7 Two Dielectric Slabs, 109
4.8 Reflection by a Moving Boundary, 111
4.9 Problems, 114
Preface xiv
5 Multilayer Structures 117
1 Maxwell’s Equations 1
5.1 Multiple Dielectric Slabs, 117
5.2 Antireflection Coatings, 119
5.3 Dielectric Mirrors, 124
5.4 Propagation Bandgaps, 135
5.5 Narrow-Band Transmission Filters, 135
5.6 Equal Travel-Time Multilayer Structures, 140
5.7 Applications of Layered Structures, 154
5.8 Chebyshev Design of Reflectionless Multilayers, 157
5.9 Problems, 165
1.1 Maxwell’s Equations, 1
1.2 Lorentz Force, 2
1.3 Constitutive Relations, 3
1.4 Boundary Conditions, 6
1.5 Currents, Fluxes, and Conservation Laws, 8
1.6 Charge Conservation, 9
1.7 Energy Flux and Energy Conservation, 10
1.8 Harmonic Time Dependence, 12
1.9 Simple Models of Dielectrics, Conductors, and Plasmas, 13
1.10 Problems, 21
6 Oblique Incidence 168
6.1 Oblique Incidence and Snell’s Laws, 168
6.2 Transverse Impedance, 170
6.3 Propagation and Matching of Transverse Fields, 173
6.4 Fresnel Reflection Coefficients, 175
6.5 Total Internal Reflection, 177
6.6 Brewster Angle, 183
6.7 Complex Waves, 186
6.8 Oblique Reflection by a Moving Boundary, 196
6.9 Geometrical Optics, 199
6.10 Fermat’s Principle, 202
6.11 Ray Tracing, 204
6.12 Problems, 215
2 Uniform Plane Waves 25
2.1 Uniform Plane Waves in Lossless Media, 25
2.2 Monochromatic Waves, 31
2.3 Energy Density and Flux, 34
2.4 Wave Impedance, 35
2.5 Polarization, 35
2.6 Uniform Plane Waves in Lossy Media, 42
2.7 Propagation in Weakly Lossy Dielectrics, 48
2.8 Propagation in Good Conductors, 49
2.9 Propagation in Oblique Directions, 50
2.10 Complex or Inhomogeneous Waves, 53
2.11 Doppler Effect, 55
2.12 Problems, 59
7 Multilayer Film Applications 217
7.1 Multilayer Dielectric Structures at Oblique Incidence, 217
7.2 Lossy Multilayer Structures, 219
7.3 Single Dielectric Slab, 221
7.4 Antireflection Coatings at Oblique Incidence, 223
7.5 Omnidirectional Dielectric Mirrors, 227
7.6 Polarizing Beam Splitters, 237
7.7 Reflection and Refraction in Birefringent Media, 240
7.8 Brewster and Critical Angles in Birefringent Media, 244
7.9 Multilayer Birefringent Structures, 247
7.10 Giant Birefringent Optics, 249
3 Propagation in Birefringent Media 65
3.1 Linear and Circular Birefringence, 65
3.2 Uniaxial and Biaxial Media, 66
3.3 Chiral Media, 68
3.4 Gyrotropic Media, 71
3.5 Linear and Circular Dichroism, 72
3.6 Oblique Propagation in Birefringent Media, 73
3.7 Problems, 80
vii
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Electromagnetic Waves & Antennas – S. J. Orfanidis – June 21, 2004
7.11 Problems, 254
11.4 Two-Section Dual-Band Chebyshev Transformers, 375
11.5 Quarter-Wavelength Transformer With Series Section, 381
11.6 Quarter-Wavelength Transformer With Shunt Stub, 384
11.7 Two-Section Series Impedance Transformer, 386
11.8 Single Stub Matching, 391
11.9 Balanced Stubs, 395
11.10 Double and Triple Stub Matching, 397
11.11 L-Section Lumped Reactive Matching Networks, 399
11.12 Pi-Section Lumped Reactive Matching Networks, 402
11.13 Reversed Matching Networks, 409
11.14 Problems, 411
8 Waveguides 255
8.1 Longitudinal-Transverse Decompositions, 256
8.2 Power Transfer and Attenuation, 261
8.3 TEM, TE, and TM modes, 263
8.4 Rectangular Waveguides, 266
8.5 Higher TE and TM modes, 268
8.6 Operating Bandwidth, 270
8.7 Power Transfer, Energy Density, and Group Velocity, 271
8.8 Power Attenuation, 273
8.9 Reflection Model of Waveguide Propagation, 276
8.10 Resonant Cavities, 278
8.11 Dielectric Slab Waveguides, 280
8.12 Problems, 288
12 S-Parameters 413
12.1 Scattering Parameters, 413
12.2 Power Flow, 417
12.3 Parameter Conversions, 418
12.4 Input and Output Reflection Coefficients, 419
12.5 Stability Circles, 421
12.6 Power Gains, 427
12.7 Generalized S-Parameters and Power Waves, 433
12.8 Simultaneous Conjugate Matching, 437
12.9 Power Gain Circles, 442
12.10 Unilateral Gain Circles, 443
12.11 Operating and Available Power Gain Circles, 445
12.12 Noise Figure Circles, 451
12.13 Problems, 456
9 Transmission Lines 290
9.1 General Properties of TEM Transmission Lines, 290
9.2 Parallel Plate Lines, 296
9.3 Microstrip Lines, 297
9.4 Coaxial Lines, 301
9.5 Two-Wire Lines, 306
9.6 Distributed Circuit Model of a Transmission Line, 308
9.7 Wave Impedance and Reflection Response, 310
9.8 Two-Port Equivalent Circuit, 312
9.9 Terminated Transmission Lines, 313
9.10 Power Transfer from Generator to Load, 316
9.11 Open- and Short-Circuited Transmission Lines, 318
9.12 Standing Wave Ratio, 321
9.13 Determining an Unknown Load Impedance, 323
9.14 Smith Chart, 327
9.15 Time-Domain Response of Transmission Lines, 331
9.16 Problems, 338
13 Radiation Fields 458
13.1 Currents and Charges as Sources of Fields, 458
13.2 Retarded Potentials, 460
13.3 Harmonic Time Dependence, 463
13.4 Fields of a Linear Wire Antenna, 465
13.5 Fields of Electric and Magnetic Dipoles, 467
13.6 Ewald-Oseen Extinction Theorem, 472
13.7 Radiation Fields, 477
13.8 Radial Coordinates, 480
13.9 Radiation Field Approximation, 482
13.10 Computing the Radiation Fields, 483
13.11 Problems, 485
10 Coupled Lines 347
10.1 Coupled Transmission Lines, 347
10.2 Crosstalk Between Lines, 353
10.3 Weakly Coupled Lines with Arbitrary Terminations, 356
10.4 Coupled-Mode Theory, 358
10.5 Fiber Bragg Gratings, 360
10.6 Diffuse Reflection and Transmission, 363
10.7 Problems, 365
14 Transmitting and Receiving Antennas 488
14.1 Energy Flux and Radiation Intensity, 488
14.2 Directivity, Gain, and Beamwidth, 489
14.3 Effective Area, 494
14.4 Antenna Equivalent Circuits, 498
14.5 Effective Length, 500
14.6 Communicating Antennas, 502
14.7 Antenna Noise Temperature, 504
11 Impedance Matching 366
11.1 Conjugate and Reflectionless Matching, 366
11.2 Multisection Transmission Lines, 368
11.3 Quarter-Wavelength Chebyshev Transformers, 369
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Electromagnetic Waves & Antennas – S. J. Orfanidis – June 21, 2004
14.8 System Noise Temperature, 508
14.9 Data Rate Limits, 514
14.10 Satellite Links, 516
14.11 Radar Equation, 519
14.12 Problems, 521
17.10 Radiation Patterns of Reflector Antennas, 618
17.11 Dual-Reflector Antennas, 627
17.12 Lens Antennas, 630
17.13 Problems, 631
18 Antenna Arrays 632
15 Linear and Loop Antennas 522
18.1 Antenna Arrays, 632
18.2 Translational Phase Shift, 632
18.3 Array Pattern Multiplication, 634
18.4 One-Dimensional Arrays, 644
18.5 Visible Region, 646
18.6 Grating Lobes, 647
18.7 Uniform Arrays, 650
18.8 Array Directivity, 654
18.9 Array Steering, 655
18.10 Array Beamwidth, 657
18.11 Problems, 659
15.1 Linear Antennas, 522
15.2 Hertzian Dipole, 524
15.3 Standing-Wave Antennas, 526
15.4 Half-Wave Dipole, 528
15.5 Monopole Antennas, 530
15.6 Traveling-Wave Antennas, 531
15.7 Vee and Rhombic Antennas, 534
15.8 Loop Antennas, 537
15.9 Circular Loops, 539
15.10 Square Loops, 540
15.11 Dipole and Quadrupole Radiation, 541
15.12 Problems, 543
19 Array Design Methods 661
16 Radiation from Apertures 544
19.1 Array Design Methods, 661
19.2 Schelkunoff’s Zero Placement Method, 664
19.3 Fourier Series Method with Windowing, 666
19.4 Sector Beam Array Design, 667
19.5 Woodward-Lawson Frequency-Sampling Design, 672
19.6 Narrow-Beam Low-Sidelobe Designs, 676
19.7 Binomial Arrays, 680
19.8 Dolph-Chebyshev Arrays, 682
19.9 Taylor-Kaiser Arrays, 694
19.10 Multibeam Arrays, 697
19.11 Problems, 700
16.1 Field Equivalence Principle, 544
16.2 Magnetic Currents and Duality, 546
16.3 Radiation Fields from Magnetic Currents, 548
16.4 Radiation Fields from Apertures, 549
16.5 Huygens Source, 552
16.6 Directivity and Effective Area of Apertures, 554
16.7 Uniform Apertures, 556
16.8 Rectangular Apertures, 556
16.9 Circular Apertures, 558
16.10 Vector Diffraction Theory, 561
16.11 Extinction Theorem, 565
16.12 Vector Diffraction for Apertures, 567
16.13 Fresnel Diffraction, 568
16.14 Knife-Edge Diffraction, 572
16.15 Geometrical Theory of Diffraction, 578
16.16 Problems, 584
20 Currents on Linear Antennas 701
20.1 Hallen and Pocklington Integral Equations, 701
20.2 Delta-Gap and Plane-Wave Sources, 704
20.3 Solving Hallen’s Equation, 705
20.4 Sinusoidal Current Approximation, 707
20.5 Reflecting and Center-Loaded Receiving Antennas, 708
20.6 King’s Three-Term Approximation, 711
20.7 Numerical Solution of Hallen’s Equation, 715
20.8 Numerical Solution Using Pulse Functions, 718
20.9 Numerical Solution for Arbitrary Incident Field, 722
20.10 Numerical Solution of Pocklington’s Equation, 724
20.11 Problems, 730
17 Aperture Antennas 587
17.1 Open-Ended Waveguides, 587
17.2 Horn Antennas, 591
17.3 Horn Radiation Fields, 593
17.4 Horn Directivity, 598
17.5 Horn Design, 601
17.6 Microstrip Antennas, 604
17.7 Parabolic Reflector Antennas, 610
17.8 Gain and Beamwidth of Reflector Antennas, 612
17.9 Aperture-Field and Current-Distribution Methods, 615

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