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Contents Preface to the First Edition xv Preface to the Second Edition xvii 1 Introduction 1 1.1 Array Background 1 1.2 Systems Factors 2 1.3 Annotated Reference Sources 3 1.3.1 Adaptive Antenna Reference Books 5 References 5 2 Basic Array Characteristics 7 2.1 Uniformly Excited Linear Arrays 7 2.1.1 Patterns 7 2.1.2 Beamwidth 9 2.1.3 Sidelobes 11 2.1.4 Grating Lobes 11 2.1.5 Bandwidth 15 2.2 Planar Arrays 17 2.2.1 Array Coordinates 17 2.2.2 Beamwidth 18 2.2.3 Grating Lobes: Rectangular Lattice 21 2.2.4 Grating Lobes: Hexagonal Lattice 23 2.3 Beam Steering and Quantization Lobes 25 2.3.1 Steering Increment 25 2.3.2 Steering Bandwidth 26 2.3.3 Time Delay Deployment 27 2.3.4 Phaser Quantization Lobes 28 2.3.5 Sub-array Quantization Lobes 32 2.3.6 QL Decollimation: Overlapped Sub-arrays 35 2.4 Directivity 36 2.4.1 Linear Array Directivity 36 2.4.2 Directivity of Arrays of Short Dipoles 39 2.4.3 Directivity of Arrays of Resonant Elements 40 2.4.4 Planar Array Directivity 42 References 46 3 Linear Array Pattern Synthesis 49 3.1 Introduction 49 3.1.1 Pattern Formulations 49 3.1.2 Physics versus Mathematics 51 3.1.3 Taylor Narrow-Beam Design Principles 52 3.2 Dolph–Chebyshev Arrays 53 3.2.1 Half-Wave Spacing 53 3.2.2 Spacing Less Than Half-Wave 59 3.3 Taylor One-Parameter Distribution 60 3.3.1 One-Parameter Design 60 3.3.2 Bickmore–Spellmire Two-Parameter Distribution 65 3.4 Taylor N-Bar Aperture Distribution 66 3.5 Low-Sidelobe Distributions 72 3.5.1 Comparison of Distributions 72 3.5.2 Average Sidelobe Level 75 3.6 Villeneuve N-Bar Array Distribution 76 3.7 Difference Patterns 79 3.7.1 Canonical Patterns 79 3.7.2 Bayliss Patterns 81 3.7.3 Sum and Difference Optimization 85 3.7.4 Discrete Zolotarev Distributions 87 3.8 Sidelobe Envelope Shaping 89 3.9 Shaped Beam Synthesis 92 3.9.1 Woodward–Lawson Synthesis 92 3.9.2 Elliott Synthesis 94 3.10 Thinned Arrays 98 3.10.1 Probabilistic Design 98 3.10.2 Space Tapering 102 3.10.3 Minimum Redundancy Arrays 103 4 Planar and Circula

Contents List of contributors xvi Foreword xvii Acknowledgements xx Electromagnetism and antennas – a historical perspective 1 1 Fundamentals of electromagnetism 7 1.1 Maxwell’s equations 7 1.1.1 Maxwell’s equations in an arbitrary medium 7 1.1.2 Linear media 10 1.1.3 Conducting media 12 1.1.4 Reciprocity theorem 14 1.2 Power and energy 15 1.2.1 Power volume densities 15 1.2.2 Energy volume densities 16 1.2.3 Poynting vector and power 17 1.3 Plane waves in linear media 18 1.3.1 Plane waves in an isotropic linear medium 18 1.3.2 Skin effect 24 Further reading 26 Exercises 27 2 Radiation 31 2.1 Plane wave spectrum 32 2.1.1 Spectral domain 32 2.1.2 Electromagnetic field in a semi-infinite space with no sources 34 2.1.3 The far field 39 2.2 Kirchhoff’s formulation 44 2.2.1 Green’s identity and Green’s functions 44 2.2.2 Kirchhoff’s integral formulation 46 2.2.3 Plane wave spectrum and Kirchhoff’s formulation 48 Further reading 49 Exercises 50 3 Antennas in transmission 53 3.1 Far field radiation 54 3.1.1 Vector characteristic of the radiation from the antenna 54 3.1.2 Translation theorem 55 3.1.3 Application: radiation produced by an arbitrary current 55 3.1.4 Radiated power 58 3.2 Field radiated from an antenna 59 3.2.1 Elementary dipoles 59 3.2.2 Plane-aperture radiation 62 3.3 Directivity, gain, radiation pattern 66 3.3.1 Radiated power 66 3.3.2 Directivity 67 3.3.3 Gain 68 3.3.4 Radiation pattern 70 3.3.5 Input impedance 72 Further reading 73 Exercises 74 4 Receiving antennas 79 4.1 Antenna reciprocity theorem 79 4.1.1 Reciprocity theorem applied to a source-free closed surface 79 4.1.2 Relation between the field on transmit and the field on receive 83 4.2 Antenna effective receiving area 84 4.2.1 Definition 84 4.2.2 Relationship between gain and effective receiving area 85 4.3 Energy transmission between two antennas 86 4.3.1 The Friis transmission formula 86 4.3.2 Radar equation 87 4.3.3 Antenna Radar Cross Section (RCS) 89 4.4 Antenna behaviour in the presence of

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