9781402032165

List of contributors

xvi

Foreword

xvii

Acknowledgements

Electromagnetism and antennas – a historical perspective

(322)

1 Fundamentals of electromagnetism

(24)

1.1 Maxwell's equations

(8)

1.1.1 Maxwell's equations in an arbitrary medium

(3)

1.1.2 Linear media

(2)

1.1.3 Conducting media

(2)

1.1.4 Reciprocity theorem

(1)

1.2 Power and energy

(3)

1.2.1 Power volume densities

(1)

1.2.2 Energy volume densities

(1)

1.2.3 Poynting vector and power

(1)

1.3 Plane waves in linear media

(8)

1.3.1 Plane waves in an isotropic linear medium

(6)

1.3.2 Skin effect

(2)

Further reading

(1)

Exercises

(4)

2 Radiation

(22)

2.1 Plane wave spectrum

(12)

2.1.1 Spectral domain

(2)

2.1.2 Electromagnetic field in a semi-infinite space with no sources

(5)

2.1.3 The far field

(5)

2.2 Kirchhoff's formulation

(5)

2.2.1 Green's identity and Green's functions

(2)

2.2.2 Kirchhoff's integral formulation

(2)

2.2.3 Plane wave spectrum and Kirchhoff s formulation

(1)

Further reading

(1)

Exercises

(3)

3 Antennas in transmission

(26)

3.1 Far field radiation

(5)

3.1.1 Vector characteristic of the radiation from the antenna

(1)

3.1.2 Translation theorem

(1)

3.1.3 Application: radiation produced by an arbitrary current

(3)

3.1.4 Radiated power

(1)

3.2 Field radiated from an antenna

(7)

3.2.1 Elementary dipoles

(3)

3.2.2 Plane-aperture radiation

(4)

3.3 Directivity, gain, radiation pattern

(7)

3.3.1 Radiated power

(1)

3.3.2 Directivity

(1)

3.3.3 Gain

(2)

3.3.4 Radiation pattern

(2)

3.3.5 Input impedance

(1)

Further reading

(1)

Exercises

(5)

4 Receiving antennas

(20)

4.1 Antenna reciprocity theorem

(5)

4.1.1 Reciprocity theorem applied to a source-free closed surface

(4)

4.1.2 Relation between the field on transmit and the field on receive

(1)

4.2 Antenna effective receiving area

(2)

4.2.1 Definition

(1)

4.2.2 Relationship between gain and effective receiving area

(1)

4.3 Energy transmission between two antennas

(4)

4.3.1 The Friis transmission formula

(1)

4.3.2 Radar equation

(2)

4.3.3 Antenna Radar Cross Section (RCS)

(1)

4.4 Antenna behaviour in the presence of noise

(5)

4.4.1 Power radiated by a body at absolute temperature T

(3)

4.4.2 Noise temperature of the antenna

(1)

4.4.3 Noise temperature of the receiving system

(1)

Further reading

(1)

Exercises

(3)

5 Antennas of simple geometry

(32)

5.1 Aperture antennas

(15)

5.1.1 Parabolic antennas

(6)

5.1.2 Rectangular horns

105

(9)

5.2 Wire antennas

114

(13)

5.2.1 Electric dipoles

114

(6)

5.2.2 Travelling wave rectilinear antennas

120

(3)

5.2.3 Loops and helical antennas

123

(4)

Further reading

127

(1)

Exercises

128

(3)

6 Printed antennas

131

(32)

6.1 Introduction

131

(1)

6.2 Different types of printed radiating elements

132

(3)

6.3 Field analysis methods

135

(9)

6.3.1 Methods of analysis of printed antennas

136

(1)

6.3.2 The cavity method

136

(3)

6.3.3 Application to a rectangular patch

139

(3)

6.3.4 Application to a circular patch

142

(2)

6.4 Input impedance, bandwidth and radiation pattern

144

(8)

6.4.1 Input impedance

144

(1)

6.4.2 Bandwidth

145

(3)

6.4.3 Radiation pattern

148

(1)

6.4.4 Polarization

149

(3)

6.5 Low profile, wideband or multiband antennas for mobile communications and short-range applications

152

(8)

6.5.1 Miniaturization

153

(1)

6.5.2 Enlargement of the bandwidth and realization of multiband antennas

154

(2)

6.5.3 Example: multiband antenna for telecommunications

156

(4)

Further reading

160

(1)

Exercises

161

(2)

7 Large antennas and microwave antennas

163

(72)

7.1 Introduction

163

(2)

7.2 Structures and applications

165

(11)

7.2.1 Structures

165

(4)

7.2.2 External characteristics required in applications

169

(7)

7.3 Fundamental propagation laws

176

(20)

7.3.1 Wavefronts

176

(1)

7.3.2 The Huygens-Fresnel principle of wave propagation

177

(1)

7.3.3 Stationary phase principle

178

(3)

7.3.4 Geometrical optics ray theory

181

(4)

7.3.5 Ray theory in quasi-homogeneous media

185

(11)

7.4 Antennas as radiating apertures

196

(31)

7.4 1 Antenna radiation and equivalent aperture method

196

(1)

7.4.2 Examples of microwave antennas and equivalent apertures

197

(3)

7.4.3 Far field radiation from an aperture

200

(5)

7.4.4 Examples of radiating apertures

205

(8)

7.4.5 Polarization of the radiated field: case where the field in the aperture has the characteristic of a plane wave

213

(4)

7.4.6 Geometrical properties of the Huygens coordinates

217

(3)

7.4.7 Aperture radiation in the near field

220

(3)

7.4.8 Gain factor of a radiating aperture

223

(4)

Appendix 7A Deduction of the Huygens-Fresnel principle from the Kirchhoff integral

227

(1)

Further reading

228

(1)

Exercises

229

(6)

8 Primary feeds

235

(38)

8.1 General properties

235

(16)

8.1.1 Introduction

235

(1)

8.1.2 General characteristics of primary feeds

236

(7)

8.1.3 Radiation from radially-symmetric structures

243

(7)

8.1.4 Primary aperture in an incident field

250

(1)

8.2 Horns

251

(6)

8.2.1 General properties

251

(1)

8.2.2 Small flare angle horns and open-ended guides

252

(1)

8.2.3 Flared horns

253

(1)

8.2.4 Multimode horns

254

(3)

8.3 Hybrid modes and corrugated horns

257

(11)

8.3.1 Circular aperture radiating a pure polarization

257

(1)

8.3.2 Search for hybrid mode waves

258

(5)

8.3.3 Radiation pattern

263

(5)

Further reading

268

(1)

Exercises

269

(4)

9 Axially symmetric systems

273

(50)

9.1 Introduction

273

(1)

9.2 Symmetry properties - propagation of polarization, radiation patterns

274

(2)

9.3 Principal surface

276

(3)

9.3.1 Definition

276

(1)

9.3.2 Pupil - aperture angle - focal length

277

(1)

9.3.3 Equivalent aperture of the system

278

(1)

9.4 Transfer function

279

(2)

9.5 System gain

281

(5)

9.5.1 General expression

281

(1)

9.5.2 Expression obtained from the primary gain g' and the transfer function

281

(1)

9.5.3 Effect of various factors in the gain function

282

(2)

9.5.4 Concept of optimal primary directivity

284

(2)

9.6 Radiation patterns

286

(4)

9.6.1 Equivalent aperture illumination

286

(1)

9.6.2 Axisymmetric primary pattern with pure polarization

286

(3)

9.6.3 Effect of blockage

289

(1)

9.7 Aberrations in axially-symmetric systems

290

(6)

9.7.1 Introduction

290

(1)

9.7.2 Main aberrations in the defocusing plane

291

(5)

9.8 Axially symmetric systems considered in reception: diffraction pattern

296

(12)

9.8.1 Effect of transfer function

296

(1)

9.8.2 Diffraction in the vicinity of the focus F of an element dS' of a spherical wave S'

297

(2)

9.8.3 Analysis of a diffraction pattern - contribution of an elementary crown of the spherical wave - hybrid waves

299

(1)

9.8.4 Axial field

300

(1)

9.8.5 Transverse distribution of the diffracted field in the focal plane

301

(1)

9.8.6 Axially-symmetric systems with a small aperture 90

302

(1)

9.8.7 Constant transfer function

303

(3)

9.8.8 Non-constant transfer function

306

(1)

9.8.9 General case: system with a very large aperture

306

(2)

9.9 System considered in reception: transfer of the energy contained in the diffraction pattern to the primary aperture

308

(6)

9.9.1 Diffraction pattern produced around the focus by an incident non-axial plane wave

308

(1)

9.9.2 Radiation pattern of the system associated with a given primary aperture

309

(1)

9.9.3 Examples of applications

310

(2)

9.9.4 Axial gain of an axially-symmetric system - effect of the diameter of the primary aperture

312

(2)

9.10 Radiation in the Fresnel zone of a Gaussian illumination - application to the transport of energy by radiation (Goubeau's waves)

314

(3)

Further reading

317

(1)

Exercises

318

(5)

10 Focused systems

323

(70)

10.1 Introduction

323

(1)

10.2 The Cassegrain antenna

324

(17)

10.2.1 Introduction

324

(1)

10.2.2 Geometry

325

(2)

10.2.3 Equivalent primary feed

327

(1)

10.2.4 Principal surface

328

(1)

10.2.5 Cassegrain with shaped reflectors

329

(3)

10.2.6 Diffraction pattern of the subreflector

332

(6)

10.2.7 Blockage by the subreflector

338

(3)

10.2.8 Schwartzschild aplanetic reflector

341

(1)

10.3 Tracking systems

341

(33)

10.3.1 Introduction

341

(3)

10.3.2 General characteristics of radar echoes

344

(4)

10.3.3 Conical scanning

348

(9)

10.3.4 'Monopulse' antennas

357

(16)

10.3.5 Beacon tracking

373

(1)

10.4 Non axially-symmetric systems

374

(11)

10.4.1 Offset reflector

374

(4)

10.4.2 Shaped reflectors - pattern synthesis

378

(7)

Further reading

385

(1)

Exercises

386

(7)

11 Arrays

393

(106)

11.1 Introduction

393

(5)

11.1.1 Phased arrays

394

(1)

11.1.2 Bandwidth - use of delay lines - subarrays

394

(2)

11.1.3 Active arrays

396

(2)

11.2 General structure of a phased array (examples)

398

(10)

11.2.1 General structure

398

(5)

11.2.2 Examples of array structures

403

(5)

11.3 Linear array theory

408

(8)

11.3.1 Basic equation - array factor

408

(1)

11.3.2 Uniform illumination and constant phase gradient

409

(3)

11.3.3 Half-power beamwidth

412

(1)

11.3.4 Spectral bandwidth available on a phased array

413

(1)

11.3.5 Condition to prevent grating lobes from occurring in the scanning region

413

(1)

11.3.6 Effect of weighting of the array illumination function

414

(1)

11.3.7 Effect of element directivity

415

(1)

11.4 Variation of gain as a function of pointing direction

416

(8)

11.4.1 Array operating on transmission

416

(2)

11.4.2 Array on receive

418

(1)

11.4.3 Array active reflection coefficient - mutual coupling

418

(2)

11.4.4 Blind angle phenomenon

420

(3)

11.4.5 Case where the element spacing is relatively large

423

(1)

11.4.6 Study of an array of open-ended guides considered as a periodic structure

423

(1)

11.5 Effects of phase quantization

424

(6)

11.5.1 Case where all phase shifters are fed in phase

424

(2)

11.5.2 Effects of quantization when the phase origin varies from one phase shifter to another

426

(4)

11.6 Frequency-scanned arrays

430

(2)

11.7 Analogue beamforming matrices

432

(16)

11.7.1 Introduction

432

(1)

11.7.2 General properties of multi-port networks

433

(2)

11.7.3 Beamforming applications

435

(3)

11.7.4 Examples of matrices

438

(6)

11.7.5 Non-orthogonal directional beams

444

(4)

11.8 Further topics

448

(39)

11.8.1 Active modules

448

(4)

11.8.2 Digital beamforming

452

(3)

11.8.3 MEMS technology in phased arrays

455

(3)

11.8.4 Circular, cylindrical, spherical and conformal arrays

458

(17)

11.8.5 Sparse and random arrays

475

(6)

11.8.6 Retrodirective and self-phasing arrays

481

(6)

Appendix 11A Comparison of linear and circular arrays

487

(7)

11A.1 Gain of an arbitrary array

487

(2)

11A.2 Gain of a beam cophasal circular array

489

(1)

11A.3 Radiation pattern of a beam cophasal circular array

490

(1)

11A.4 Example: cos α element patterns

491

(1)

11A.5 Comparison of linear and circular arrays

492

(2)

Further reading

494

(1)

Exercises

495

(4)

12 Fundamentals of polarimetry

499

(50)

12.1 Introduction

499

(4)

12.1.1 Application of polarimetry in radar and telecommunications

499

(2)

12.1.2 Some historical references

501

(1)

12.1.3 Basics

501

(2)

12.2 Fully polarized waves

503

(12)

12.2.1 Definition

503

(1)

12.2.2 Algebraic representation of elliptical polarization

503

(2)

12.2.3 Normalized Cartesian coordinate system

505

(1)

12.2.4 Base of circular polarizations

506

(2)

12.2.5 Polarization ratio

508

(1)

12.2.6 Polarization diagram

509

(3)

12.2.7 Polarization coupling to the receiving antenna

512

(3)

12.3 Partially polarized waves

515

(12)

12.3.1 Definition and physical origin

515

(2)

12.3.2 Coherence matrix

517

(2)

12.3.3 Completely unpolarized wave

519

(1)

12.3.4 Completely polarized wave

520

(1)

12.3.5 Stokes parameters

521

(1)

12.3.6 Decomposition of a partially polarized wave

521

(1)

12.3.7 Geometrical interpretation of the preceding results: Stokes parameters and Poincaré sphere

522

(3)

12.3.8 Polarization coupling and Stokes vectors

525

(2)

12.4 Polarimetric representation of radar targets

527

(11)

12.4.1 Introduction

527

(1)

12.4.2 Sinclair diffraction matrix

527

(11)

12.5 Partially polarized waves: The Mueller Matrix

538

(4)

12.5.1 The Mueller matrix

538

(1)

12.5.2 Application example

538

(2)

12.5.3 Examples of responses to different incident polarizations

540

(2)

12.6 Polarizers and polarization separators for telecommunications antennas and polarimetric radars

542

(5)

12.6.1 Introduction

542

(1)

12.6.2 Non-symmetrical polarization separator

542

(1)

12.6.3 Semi-symmetrical polarization separator

543

(1)

12.6.4 Symmetrical polarization separator (turnstile)

544

(1)

12.6.5 Dielectric vane polarizer

545

(2)

Further reading

547

(1)

Exercises

547

(2)

13 Antennas and signal theory

549

(28)

13.1 Introduction

549

(1)

13.2 Equivalence of an aperture and a spatial frequency filter

550

(6)

13.2.1 Concept of spatial frequency

550

(1)

13.2.2 Consequences of the limitation of the aperture dimensions on the properties of the radiation characteristic function

551

(4)

13.2.3 Consequences of the limitation of the aperture dimensions on the 'gain' function of the antenna

555

(1)

13.3 Synthesis of an aperture to radiate a given radiation pattern

556

(10)

13.3.1 Statement of problem

556

(2)

13.3.2 Generalization of the approximation method

558

(1)

13.3.3 Use of sampling methods

559

(3)

13.3.4 Role of phase - stationary phase method

562

(3)

13.3.5 Pattern synthesis for a focusing system

565

(1)

13.4 Superdirective antennas

566

(3)

13.4.1 Introduction

566

(1)

13.4.2 Role of the 'invisible' domain of radiation

566

(3)

13.5 The antenna as a filter of angular signals

569

(4)

13.5.1 Introduction

569

(1)

13.5.2 Optical or microwave imaging and linear filters

570

(1)

13.5.3 False echoes and resolving power

571

(1)

13.5.4 Case where the antenna is treated as an aperture

571

(1)

13.5.5 Spectrum of fixed echoes of a rotating radar

572

(1)

Further reading

573

(1)

Exercises

574

(3)

14 Signal processing antennas

577

(74)

14.1 Introduction

577

(1)

14.2 Synthetic antennas in radar and sonar

578

(8)

14.2.1 Principles of synthetic antennas

578

(1)

14.2.2 Synthetic receive array with non-directional beam

579

(1)

14.2.3 Synthetic receive array with multiple beams

580

(1)

14.2.4 Examples of spatio-temporal coding

581

(5)

14.3 Imaging of coherent sources

586

(6)

14.3.1 Introduction

586

(1)

14.3.2 Two-source distribution

587

(1)

14.3.3 Estimation of the elevation angle of a low-altitude target above a reflecting plane

587

(3)

14.3.4 Effect of noise: a posteriori probabilities and decision theory

590

(2)

14.4 Imaging of incoherent sources

592

(10)

14.4.1 Introduction

592

(1)

14.4.2 Conditions for incoherence

593

(1)

14.4.3 Multiplicative arrays

594

(2)

14.4.4 Relationship between an angular distribution of incoherent sources and the observed field: the Van Cittert-Zernicke Theorem

596

(3)

14.4.5 Sampling of the coherence function

599

(1)

14.4.6 Measurement of the coefficients of correlation or covariance - C(n—n')

600

(1)

14.4.7 The covariance matrix

601

(1)

14.5 High resolution imagery and the maximum entropy method

602

(9)

14.5.1 Introduction

602

(1)

14.5.2 Classical method of 'correlogram'

603

(1)

14.5.3 Method of Maximum Entropy

604

(1)

14.5.4 Estimation of T under conditions of Maximum Entropy

604

(1)

14.5.5 Factorization of T(τ) - properties

605

(1)

14.5.6 Determination of the coefficients an in equation (14.71)

606

(2)

14.5.7 Generalization: ARMA model

608

(1)

14.5.8 Numerical example

609

(1)

14.5.9 Minimum redundance arrays

609

(2)

14.6 Other methods of spectral estimation

611

(8)

14.6.1 Introduction

611

(1)

14.6.2 The MUSIC algorithm

612

(4)

14.6.3 Illustration of the MUSIC algorithm

616

(1)

14.6.4 Other superresolution algorithms

617

(1)

14.6.5 Superresolution with circular arrays

618

(1)

14.7 Spatial filtering

619

(21)

14.7.1 Introduction

619

(1)

14.7.2 What is an adaptive array ?

619

(1)

14.7.3 Simple example: two-element array

620

(3)

14.7.4 Howells-Applebaum correlation loop

623

(3)

14.7.5 Minimum noise criterion

626

(1)

14.7.6 Effect of internal receiver noise

626

(2)

14.7.7 Multiple correlation loops: the coherent sidelobe canceller (CSLC)

628

(2)

14.7.8 The optimum array

630

(3)

14.7.9 Interpretation

633

(1)

14.7.10 Digital implementation

633

(1)

14.7.11 Smart antennas

634

(6)

Appendix 14A Entropy and probability

640

(7)

14A.1 Uncertainty of an event A of probability p(A)

640

(1)

14A.2 Information gained by the knowledge of an event

640

(1)

14A.3 Uncertainty relative to an alternative

640

(1)

14A.4 First generalization: entropy of a set of events

641

(1)

14A.5 Second generalization: random variable

642

(1)

14A.6 Decision theory: Maximum Entropy

643

(1)

14A.7 Entropy and spectral density

643

(1)

14A.8 Justification of this relationship

644

(3)

Further reading

647

(2)

Exercises

649

(2)

15 Antenna measurements

651

(32)

15.1 Introduction

651

(1)

15.2 Gain measurements

652

(2)

15.2.1 Comparison with a standard-gain horn

652

(1)

15.2.2 Two-antenna measurement

652

(1)

15.2.3 Three-antenna measurement

653

(1)

15.2.4 Extrapolation

653

(1)

15.3 Radiation pattern measurements

654

(15)

15.3.1 Anechoic chambers and far-field ranges

655

(4)

15.3.2 Compact ranges

659

(2)

15.3.3 Wavefront quality

661

(1)

15.3.4 Near-field techniques

662

(3)

15.3.5 Other techniques

665

(3)

15.3.6 Polarization

668

(1)

15.4 Time-domain gating

669

(3)

15.4.1 Principles

669

(2)

15.4.2 Limitations

671

(1)

15.5 Antenna noise temperature and GIT

672

(2)

15.5.1 Measurement of antenna noise temperature

672

(1)

15.5.2 Direct measurement of GIT using solar noise

672

(2)

15.6 Impedance and bandwidth

674

(2)

15.7 Measurement of cellular radio handset antennas

676

(4)

15.7.1 Specific Absorption Rate

677

(1)

15.7.2 Reverberation chambers

678

(2)

Further reading

680

(1)

Exercises

681

(2)

Index

683

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Modern Antennas

1402032161

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