Title Page
Copyright Page
Table of Contents
List of contributors
Foreword
Acknowledgements
Electromagnetism and antennas - a historical perspective
INTRODUCTION
FURTHERREADING
1 Fundamentals of electromagnetism
1.1 MAXWELL'S EQUAnONS1
1.1.1 Maxwell's equations in an arbitrary medium
1.1.2 Linear media
1.1.3 Conducting media
1.1.4 Reciprocity theorem
1.2POWER AND ENERGY
1.2.1 Power volume densities
1.2.2 Energy volume densities
1.2.3 Poynting vector and power
1.3 PLANE WAVES IN LINEAR MEDIA
1.3.1 Plane waves in an isotropic linear medium
1.3.2 Skin effect
FURTHER READING
EXERCISES
1.1 Field propagation equations in a linear medium
1.2 Electromagnetic potentials
1.3 Propagation in the direction Oz
1.4 Polarization
1.5 Volume density ofcharge
1.6 Skin effect
2 Radiation
2.1 PLANE WAVE SPECTRUM
2.1.1 Spectral domain
2.1.2 Electromagnetic field in a semi-infinite space with no sources
2.1.3 The far field
2.2 KIRCHHOFF'S FORMULAnON
2.2.1 Green's identity and Green's functions
2.2.2 Kirchhoff's integral formulation
2.2.3 Plane wave spectrum and Kirchhoff's formulation
FURTHER READING
EXERCISES
2.1 2D Fourier transforms
2.2 2D Fourier transform ofexpC-ikr)/r
3 Antennas in transmission
3.1 FAR FIELD RADIATION
3.1.1 Vector characteristic of the radiation from the antenna
3.1.2 Translation theorem
3.1.3 Application: radiation produced by an arbitrary current
3.1.4 Radiated power
3.2 FIELD RADIATED FROM AN ANTENNA
3.2.1 Elementary dipoles
3.2.2 Plane-aperture radiation
3.3 DIRECTIVITY, GAIN, RADIATION PATTERN
3.3.1 Radiated power
3.3.2 Directivity
3.3.3 Gain
3.3.4 Radiation pattern
3.3.5 Input impedance
FURTHER READING
EXERCISES
3.1 Realization ofcircular polarization
3.2 Crossed dipoles
3.3 Two electric dipoles
3.4 Electric dipole and magnetic dipole
3.5 Antenna radiating into a half-space with a function cosve
3.6 Maximum directivity of an aperture antenna
3.7 Rectangular aperture
3.8 Circular aperture
3.9 Uniformly illuminated circular aperture
4 Receiving antennas
4.1 ANTENNA RECIPROCITY THEOREM
4.1.1 Reciprocity theorem applied to a source-free closed surface
4.1.2 Relation between the field on transmit and the field on receive
4.2 ANTENNA EFFECTIVE RECEIVING AREA
4.2.1 Definition
4.2.2 Relationship between gain and effective receiving area
4.3 ENERGY TRANSMISSION BETWEEN TWO ANTENNAS
4.3.1 The Friis transmission formula
4.3.2 Radar equation
4.3.3 Antenna Radar Cross Section (RCS)!Β·2.3.4
4.4 ANTENNA BEHAVIOUR IN THE PRESENCE OF NOISE
4.4.1 Power radiated by a body at absolute temperature T
4.4.2 Noise temperature of the antenna
4.4.3 Noise temperature of the receiving system
FURTHER READING
EXERCISES
4.1 Earth-Moon radio link
4.2 Radiocommunication link
4.3 DBSTV
4.4 Radio link
5 Antennas of simple geometry
5.1 APERTURE ANTENNAS
5.1.1 Parabolic antennas
5.1.2 Rectangular horns (see also Β§8.2)
5.2 WIRE ANTENNAS
5.2.1 Electric dipoles
5.2.2 Travelling wave rectilinear antennas
5.2.3 Loops and helical antennas
FURTHER READING
EXERCISES
5.1 Half-wave dipole
5.2 Parabolic reflector ofdiameter D small compared with the wavelength /l, uniformly illuminated by a primary feed
5.3 Pyramidal horn
5.4 Rectilinear travelling wave antenna
5.5 Power radiated by a loop carrying a constant current
6 Printed antennas
6.1 INTRODUCTION
6.2 DIFFERENT TYPES OF PRINTED RADIATING ELEMENTS
6.3 FIELD ANALYSIS METHODS
6.3.1 Methods of analysis of printed antennas
6.3.2 The cavity method
6.3.3 Application to a rectangular patch
6.3.4 Application to a circular patch
6.4 INPUTIMPEDANCE, BANDWIDTH AND RADIAnONPATTERN
6.4.1 Input impedance
6.4.2 Bandwidth
6.4.3 Radiation pattern
6.4.4 Polarization
6.5 LOW-PROFILE, WIDEBAND OR MULTIBAND ANTENNAS FOR MOBILE COMMUNICATIONS AND SHORT-RANGE APPLICATIONS
6.5.1 Miniaturization
6.5.2 Enlargement of the bandwidth and realization of multibandantennas
6.5.3 Example: multiband antenna for telecommunications5
FURTHER READING
EXERCISES
6.1 Simplified model ora rectangular printed patch
6.2 Semi-circular patch analyzed using the cavity method
6.3 Dual-frequency rectangular microstrip antenna
7 Large antennas and microwave antennas
7.1 INTRODUCTION
7.2 STRUCTURES AND APPLICAnONS
7.2.1 Structures
7.2.2 External characteristics required in applications
7.3 FUNDAMENTAL PROPAGATION LAWS
7.3.1 Wavefronts
7.3.2 The Huygens-Fresnel principle of wave propagation
7.3.3 Stationary phase principle
7.3.4 Geometrical optics ray theory
7.3.5 Ray theory in quasi-homogeneous media
7.4 ANTENNAS AS RADIATING APERTURES
7.4.1 Antenna radiation and equivalent aperture method
7.4.2 Examples of microwave antennas and equivalent apertures
7.4.3 Far-field radiation from an aperture
7.4.5 Polarization of the radiated field: case where the field in the aperture has the characteristic of a plane wave
7.4.6 Geometrical properties of the Huygens coordinates
7.4.7 Aperture radiation in the near field
7.4.8 Gain factorof a radiating aperture
Appendix 7A: Deduction of the Huygens-Fresnel principle (Β§7.3.2) from the Kirchhoff integral
FURTHER READING
EXERCISES
7.1 Factor ormerit ora ground station antenna
7.2 Effect ofcosecant-squared pattern on maximum gain
7.3 Wave propagation in a laminar medium
7.4 Gain ofan aperture with tapered illumination
8 Primary feeds
8.1 GENERAL PROPERTIES
8.1.1 Introduction
8.1.2 General characteristics of primary feeds
8.1.3 Radiation from radially-symmetric structures
8.1.4 Primary aperture in an incident field
8.2 HORNS3
8.2.1 General properties
8.2.2 Small flare angle horns and open-ended guides
8.2.3 Flared horns
8.2.4 Multimode horns5
8.3 HYBRID MODES AND CORRUGATED HORNS
8.3.1 Circular aperture radiating a pure polarization
8.3.2 Search for hybrid mode waves
8.3.3 Radiation pattern
FURTHER READING
EXERCISES
8.1 Circular horn
8.2 Astigmatic horn
9 Axially-symmetric systems
9.1 INTRODUCTION
9.2 SYMMETRY PROPERTIES - PROPAGATION OF POLARIZATION, RADIATION PATTERNS
9.3 PRINCIPAL SURFACE
9.3.1 Definition
9.3.2 Pupil - aperture angle - focal length
9.3.3 Equivalent aperture of the system
9.4 TRANSFER FUNCTION
9.5 SYSTEM GAIN
9.5.1 General expression
9.5.2 Expression obtained from the primary gain g' and the transfer function
9.5.3 Effect of various factors in the gain function
9.5.4 Concept of optimal primary directivity
9.6 RADIATION PATTERNS
9.6.1 Equivalent aperture illumination
9.6.2 Axisymmetric primary pattern with pure polarization
9.6.3 Effect of blockage
9.7 ABERRATIONS IN AXIALLY-SYMMETRIC SYSTEMS
9.7.1 Introduction
9.7.2 Main aberrations in the defocusing plane
9.8 AXIALLY SYMMETRIC SYSTEM CONSIDERED IN RECEPTION: DIFFRACTION PATTERN
9.8.1 Effect of transfer function
9.8.2 Diffraction in the vicinity of the focus F of an element dS' of a spherical wave S'
9.8.3 Analysis of a diffraction pattern - contribution of an elementary crown of the spherical wave - hybrid waves
9.8.4 Axial field
9.8.5 Transverse distribution of the diffracted field in the focal plane
9.8.6 Axially-symmetric systems with a small aperture 00
9.8.7 Constant transfer function
9.8.8 Non-constant transfer function
9.8.9 General case: system with a very large aperture
9.9 SYSTEM CONSIDERED IN RECEPTION: TRANSFER OF THE ENERGY CONTAINED IN THE DIFFRACTION PATTERN TO THE PRIMARY APERTURE
9.9.1 Diffraction pattern produced around the focus by an incident non-axial plane wave
9.9.2 Radiation pattern of the system associated with a given primary aperture
9.9.3 Examples of applications
9.9.4 Axial gain of an axially-symmetric system - effect of the diameter of the primary aperture
9.10 RADIATION IN THE FRESNEL ZONE OF A GAUSSIAN ILLUMINATION - APPLICATION TO THE TRANSPORT OF ENERGY BY RADIATION (GOUBEAU'S WAVES)6
FURTHER READING
EXERCISES
9.1 Axial gain ofa tocusing system operating in a planar space
9.2 Characteristic radiation function ofan annular feed with radialpolarization
9.3 Radiation in the Fresnel zone ora Gaussian illumination
10 Focused systems
10.1 INTRODUCTION
10.2 THE CASSEGRAIN ANTENNA
10.2.1 Introductlon1
10.2.2 Geometry
10.2.3 Equivalent primary feed
10.2.4 Principal surface (Fig. 10.1)
10.2.5 Cassegrain with shaped reflectors2
10.2.6 Diffraction pattern of the subreflector
10.2.7 Blockage by the sub reflector
10.2.8 Schwarzschild aplanatic reflector
10.3 TRACKING SYSTEMS
10.3.1 Introduction
10.3.2 General characteristics ofradar echoes
10.3.3 Conical scanning
10.3.4 'Monopulse' antennas
10.3.5 Beacon tracking
10.4 NON AXIALLY-SYMMETRIC SYSTEMS
10.4.1 Offset reflector
10.4.2 Shaped reflectors - pattern synthesis
FURTHER READING
EXERCISES
10.1 Cassegrain antenna
10.2 Monopulse null depth
10.3 Monopulse feed with radial polarization
11 Arrays
11.1 INTRODUCTION
11.1.1 Phased arrays
11.1.2 Bandwidth - use of delay lines - subarrays
11.1.3 Active arrays
11.2 GENERAL STRUCTURE OF A PHASED ARRAY (EXAMPLES)
11.2.1 General structure
11.2.2 Examples of array structures
11.3 LINEAR ARRAY THEORy1
11.3.1 Basic equation - array factor
11.3.2 Uniform illumination and constant phase gradient
11.3.3 Half-power beamwidth
11.3.4 Spectral bandwidth available on a phased array
11.3.5 Condition to prevent grating lobes from occurring in the scanning region
11.3.6 Effect of weighting the array illumination function
11.3.7 Effect of element directivity
11.4 VARIATION OF GAIN AS A FUNCTION OF POINTINGDIRECTION2, 3, 4
11.4.1 Array operating on transmission
11.4.2 Array on receive
11.4.3 Array active reflection coefficient - mutual coupling5
11.4.4 Blind angle phenomenon 5, 6, 7
11.4.5 Case where the element spacing is relatively large
11.4.6 Study of an array of open-ended guides considered as a periodic structure
11.5 EFFECTS OF PHASE QUANTIZATION
11.5.1 Case where all phase shifters are fed in phase
11.5.2 Effects of quantization when the phase origin varies from one phase shifter to another
11.6 FREQUENCY-SCANNED ARRAYS
11.7 ANALOGUE BEAMFORMING MATRICES
11.7.1 Introduction
11.7.2 General properties of multi-port networks
11.7.3 Beamforming applications
11.7.4 Examples of matrices
11.7.5 Non-orthogonal directional beams
11.8 FURTHER TOPICS
11.8.1 Active modules
11.8.2 Digital beamforming
11.8.3 MEMS technology in phased arrays
11.8.4 Circular, cylindrical, spherical and conformal arrays
11.8.5 Sparse and random arrays
11.8.6 Retrodirective and self-phasing arrays28
APPENDIX 11A: COMPARISON OF LINEAR AND CIRCULAR ARRAYS
11A.1 Gain of an arbitrary array
11A.2 Gain of a beam cophasal circular array
11A.3 Radiation pattern of a beam cophasal circular array
11A.4 Example: cosaelement patterns
11 A.5 Comparison of linear and circular arrays
FURTHER READING
EXERCISES
11.1 Design ofan electronically-scanned array antenna
11.2 Grating lobes produced by use ofphased subarrays fed by delay lines
12 Fundamentals of polarimetry
12.1 INTRODUCTION
12.1.1 Applications of polarimetry in
radar and telecommunications
12.1.2 Some historical references
12.1.3 Basics
12.2 FULLY POLARIZED WAVES
12.2.1 Definition
12.2.2 Algebraic representation of elliptical polarization
12.2.3 Normalized Cartesian coordinate system
12.2.4 Base of circular polarizations
12.2.5 Polarization ratio
12.2.6 Polarization diagram
12.2.7 Polarization coupling to the receiving antenna
12.3 PARTIALLY POLARISED WAVES
12.3.1 Definition and physical origin
12.3.2 Coherence matrix
12.3.3 Completely unpolarized wave
12.3.4 Completely polarized wave
12.3.5 Stokes parameters (Stokes, 1819-1903)
12.3.6 Decomposition of a partially polarized wave
12.3.7 Geometrical interpretation of the preceding results: Stokes parameters and Poincare sphere
12.3.8 Polarization coupling and Stokes vectors
12.4 POLARIMETRIC REPRESENTAnON OF RADAR TARGETS
12.4.1 Introduction
12.4.2 Sinclair diffraction matrix
12.5 PARTIALLY POLARIZED WAVES: THE MUELLER MATRIX
12.5.1 The Mueller matrix
12.5.2 Application example
12.5.3 Examples of responses to different incident polarizations (Fig.12.18)
12.6 POLARIZERS AND POLARIZATION SEPARATORS FOR TELECOMMUNICATIONS ANTENNAS AND POLARIMETRIC RADARS
12.6.1 Introduction
12.6.2 Non-symmetrical polarization separator
12.6.3 Semi-symmetrical polarization separator
12.6.4 Symmetrical polarization separator (turnstile)
12.6.5 Dielectric vane polarizer
FURTHER READING
EXERCISES
13 Antennas and signal theory
13.1 INTRODUCTION
13.2 EQUIVALENCE OF AN APERTURE AND A SPATIAL FREQUENCY FILTER
13.2.1 Concept of spatial frequency
13.2.2 Consequences of the limitation of the aperture dimensions on the properties of the radiation characteristic function
13.2.3 Consequences of the limitation of the aperture dimensions on the 'gain' function of the antenna
13.3 SYNTHESIS OF AN APERTURE TO RADIATE A GIVEN RADIATION PATTERN
13.3.1 Statement of problem
13.3.2 Generalization of the approximation method
13.3.3 Use of sampling methods
13.3.4 Role of phase - stationary phase method
13.3.5 Pattern synthesis for a focusing system
13.4 SUPERDIRECTIVE ANTENNAS
13.4.1 Introduction
13.4.2 Role ofthe 'invisible' domain ofradiation
13.5 THE ANTENNA AS A FILTER OF ANGULAR SIGNALS6,7
13.5.1 Introduction
13.5.2 Optical or microwave imaging and linear filters
13.5.3 False echoes and resolving power
13.5.4 Case where the antenna is treated as an aperture
13.5.5 Spectrum of fixed echoes of a rotating radar
FURTHER READING
EXERCISES
13.1 Woodward synthesis
13.2 Optimum 'difference' illumination
14 Signal processing antennas
14.1 INTRODUCTION
14.2 SYNTHETIC ANTENNAS IN RADAR AND SONAR
14.2.1 Principles of synthetic antennas
14.2.2 Synthetic receive array with non-directional beam
14.2.3 Synthetic receive array with multiple beams
14.2.4 Examples of spatio-temporal coding
14.3 IMAGING OF COHERENT SOURCES
14.3.1 Introduction
14.3.2 Two-source distribution
14.3.3 Estimation of the elevation angle of a low-altitude target above a reflecting plane
14.3.4 Effect of noise: a posteriori probabilities and decision theory
14.4 IMAGING OF INCOHERENT SOURCES
14.4.1 Introduction
14.4.2 Conditions for incoherence
14.4.3 Multiplicative arrays
14.4.4 Relationship between an angular distribution of incoherent sources and the observed field: the Van Cittert-Zernicke Theorem
14.4.5 Sampling of the coherence function
14.4.6 Measurement of the coefficients of correlation or covarianceC(n-n')
14.4.7 The covariance matrix
14.5 HIGH RESOLUTION IMAGERY AND THE MAXIMUM ENTROPY METHOD
14.5.1 Introduction
14.5.2 Classical method of 'correlogram'
14.5.3 Method of Maximum Entropys6
14.5.5 Factorization of T(r) - properties
14.5.6 Determination of the coefficients anin equation (14.71)
14.5.7 Generalization: ARMA model
14.5.8 Numerical example
14.5.9 Minimum redundance arrays
14.6 OTHER METHODS OF SPECTRAL ESTIMATION
14.6.1 Introduction
14.6.2 The MUSIC algorithm
14.6.3 Illustration of the MUSIC algorithm
14.6.4 Other superresolution algorithms
14.6.5 Superresolution with circular arrays
14.7 SPATIAL FILTERING
14.7.1 Introduction
14.7.2 What is an adaptive array?
14.7.3 Simple example: two-element array
14.7.4 Howells-Applebaum correlation loop17
14.7.5 Minimum noise criterion
14.7.6 Effect of internal receiver noise
14.7.7 Multiple correlation loops: the coherent sidelobe canceller (CSLC)
14.7.8 The optimum array
14.7.9 Interpretation
14.7.10 Digital implementation
14.7.11 Smart antennas
APPENDIX 14A: ENTROPY AND PROBABILITY
14A.l Uncertainty of an event A of probability peA)
14A.2 Information gained by the knowledge of an event
14A.3 Uncertainty relative to an alternative
14A.4 First generalization: entropy of a set of events
14A.5 Second generalization: random variable
14A.6 Decision theory: Maximum Entropy
14A.7 Entropy and spectral density
14A.8 Justification of this relationship
FURTHER READING
EXERCISES
14.1 Coherence function ofthe Sun
15 Antenna measurements
15.1 INTRODUCTION
15.2 GAIN MEASUREMENTS
15.2.1 Comparison with a standard-gain horn
15.2.2 Two-antenna measurement
15.2.3 Three-antenna measurement
15.2.4 Extrapolation
15.3 RADIATION PATTERN MEASUREMENTS
15.3.1 Anechoic chambers and far-field ranges
15.3.2 Compact ranges
15.3.3 Wavefront quality
15.3.4 Near-field techniques
15.3.5 Other techniques
15.3.6 Polarization
15.4 TIME-DOMAIN GATING
15.4.1 Principles
15.4.2 Limitations
15.5 ANTENNA NOISE TEMPERATURE AND GfT
15.5.1 Measurement of antenna noise temperature
15.5.2 Direct measurement of GfT using solar noise
15.6 IMPEDANCE AND BANDWIDTH
15.7 MEASUREMENTS OF CELLULAR RADIO HANDSET ANTENNAS
15.7.1 Specific Absorption Rate
15.7.2 Reverberation chambers
FURTHER READING
EXERCISES
15.1 Purcell's method
15.2 Three antenna measurement
15.3 Rayleigh distance
15.4 Solar method ofG/T measurement
Index