Conformal Array Antenna Theory and Design

Preface.

Abbreviations and Acronyms.

1 INTRODUCTION.

1.1 The Definition of a Conformal Antenna.

1.2 Why Conformal Antennas?

1.3 History.

1.4 Metal Radomes.

1.5 Sonar Arrays.

References.

2 CIRCULAR ARRAY THEORY.

2.1 Introduction.

2.2 Fundamentals.

2.2.1 Linear Arrays.

2.2.2 Circular Arrays.

2.3 Phase Mode Theory.

2.3.1 Introduction.

2.3.2 Discrete Elements.

2.3.3 Directional Elements.

2.4 The Ripple Problem in Omnidirectional Patterns.

2.4.1 Isotropic Radiators.

2.4.2 Higher-Order Phase Modes.

2.4.3 Directional Radiators.

2.5 Elevation Pattern.

2.6 Focused Beam Pattern.

References.

3 THE SHAPES OF CONFORMAL ANTENNAS.

3.1 Introduction.

3.2 360° Coverage.

3.2.1 360° Coverage Using Planar Surfaces.

3.2.2 360° Coverage Using a Curved Surface.

3.3 Hemispherical Coverage.

3.3.1 Introduction.

3.3.2 Hemispherical Coverage Using Planar Surfaces.

3.3.3 Half Sphere.

3.3.4 Cone.

3.3.5 Ellipsoid.

3.3.6 Paraboloid.

3.3.7 Comparing Shapes.

3.4 Multifaceted Surfaces.

3.5 References.

4 METHODS OF ANALYSIS.

4.1 Introduction.

4.2 The Problem.

4.3 Electrically Small Surfaces.

4.3.1 Introduction.

4.3.2 Modal Solutions.

4.3.2.1 Introduction.

4.3.2.2 The Circular Cylinder.

4.3.2.3 A Unit Cell Approach.

4.3.3 Integral Equations and the Method of Moments.

4.3.4 Finite Difference Time Domain Methods (FDTD).

4.3.4.1 Introduction.

4.3.4.2 Conformal or Contour-Patch (CP) FDTD.

4.3.4.3 FDTD in Global Curvilinear Coordinates.

4.3.4.4 FDTD in Cylindrical Coordinates.

4.3.5 Finite Element Method (FEM).

4.3.5.1 Introduction.

4.3.5.2 Hybrid FE-BI Method.

4.4 Electrically Large Surfaces.

4.4.1 Introduction.

4.4.2 High-Frequency Methods for PEC Surfaces.

4.4.3 High-Frequency Methods for Dielectric Coated Surfaces.

4.5 Two Examples.

4.5.1 Introduction.

4.5.2 The Aperture Antenna.

4.5.3 The Microstrip-Patch Antenna.

4.6 A Comparison of Analysis Methods.

Appendix 4A—Interpretation of the ray theory.

4A.1 Watson Transformation.

4A.2 Fock Substitution.

4A.3 SDP Integration.

4A.4 Surface Waves.

4A.5 Generalization.

References.

5 GEODESICS ON CURVED SURFACES.

5.1 Introduction.

5.1.1 Definition of a Surface and Related Parameters.

5.1.2 The Geodesic Equation.

5.1.3 Solving the Geodesic Equation and the Existence of Geodesics.

5.2 Singly Curved Surfaces.

5.3 Doubly Curved Surfaces.

5.3.1 Introduction.

5.3.2 The Cone.

5.3.3 Rotationally Symmetric Doubly Curved Surfaces.

5.3.4 Properties of Geodesics on Doubly Curved Surfaces.

5.3.5 Geodesic Splitting.

5.4 Arbitrarily Shaped Surfaces.

5.4.1 Hybrid surfaces.

5.4.2 Analytically Described Surfaces.

References.

6 ANTENNAS ON SINGLY CURVED SURFACES.

6.1 Introduction.

6.2 Aperture Antennas on Circular Cylinders.

6.2.1 Introduction.

6.2.2 Theory.

6.2.3 Mutual Coupling.

6.2.3.1 Isolated Mutual Coupling.

6.2.3.2 Cross Polarization Coupling.

6.2.3.3 Array mutual coupling.

6.2.4 Radiation Characteristics.

6.2.4.1 Isolated-Element Patterns.

6.2.4.2 Embedded-Element Patterns.

6.3 Aperture Antennas on General Convex Cylinders.

6.3.1 Introduction.

6.3.2 Mutual Coupling.

6.3.2.1 The Elliptic Cylinder.

6.3.2.2 The Parabolic Cylinder.

6.3.2.3 The Hyperbolic Cylinder.

6.3.3 Radiation Characteristics.

6.3.3.1 The Elliptic Cylinder.

6.3.3.2 End Effects.

6.4 Aperture Antennas on Faceted Cylinders.

6.4.1 Introduction.

6.4.2 Mutual Coupling.

6.4.3 Radiation Characteristics.

6.5 Aperture Antennas on Dielectric Coated Circular Cylinders.

6.5.1 Introduction.

6.5.2 Mutual Coupling.

6.5.2.1 Isolated Mutual Coupling.

6.5.2.2 Array Mutual Coupling.

6.5.3 Radiation Characteristics.

6.5.3.1 Isolated-Element Patterns.

6.5.3.2 Embedded-Element Patterns.

6.6 Microstrip-Patch Antennas on Coated Circular Cylinders.

6.6.1 Introduction.

6.6.2 Theory.

6.6.3 Mutual Coupling.

6.6.3.1 Single-Element Characteristics.

6.6.3.2 Isolated and Array Mutual Coupling.

6.6.4 Radiation Characteristics.

6.6.4.1 Isolated-Element Patterns.

6.6.4.2 Embedded-Element Patterns.

6.7 The Cone.

6.7.1 Introduction.

6.7.2 Mutual Coupling.

6.7.2.1 Aperture Antennas.

6.7.2.2 Microstrip-Patch Antennas.

6.7.3 Radiation Characteristics.

6.7.3.1 Aperture Antennas 248

6.7.3.2 Microstrip-Patch Antennas.

References.

7 ANTENNAS ON DOUBLY CURVED SURFACES.

7.1 Introduction.

7.2 Aperture Antennas.

7.2.1 Introduction.

7.2.2 Mutual Coupling.

7.2.2.1 Isolated Mutual Coupling.

7.2.2.2 Array Mutual Coupling.

7.2.3 Radiation Characteristics.

7.3 Microstrip-Patch Antennas.

7.3.1 Introduction.

7.3.2 Mutual Coupling.

7.3.2.1 Single-Element Characteristics.

7.3.2.2 Isolated Mutual Coupling.

7.3.3 Radiation Characteristics.

References.

8 CONFORMAL ARRAY CHARACTERISTICS.

8.1 Introduction.

8.2 Mechanical Considerations.

8.2.1 Array Shapes.

8.2.2 Element Distribution on a Curved Surface.

8.2.3 Multifacet Solutions.

8.2.4 Tile Architecture.

8.2.5 Static and Dynamic Stress.

8.2.6 Other Electromagnetic Considerations.

8.3 Radiation Patterns.

8.3.1 Introduction.

8.3.2 Grating Lobes.

8.3.3 Scan-Invariant Pattern.

8.3.4 Phase-Scanned Pattern.

8.3.5 A Simple Aperture Model for Microstrip Arrays.

8.4 Array Impedance.

8.4.1 Introduction.

8.4.2 Phase-Mode Impedance.

8.5 Polarization.

8.5.1 Polarization Definitions.

8.5.2 Cylindrical Arrays.

8.5.2.1 Dipole Elements.

8.5.2.2 Aperture elements.

8.5.3 Polarization in Doubly Curved Arrays.

8.5.3.1 A Paraboloidal Array.

8.5.4 Polarization Control.

8.6 Characteristics of Selected Conformal Arrays.

8.6.1 Nearly Planar Arrays.

8.6.2 Circular Arrays.

8.6.3 Cylindrical Arrays.

8.6.4 Conical Arrays.

8.6.5 Spherical Arrays.

8.6.6 Paraboloidal Arrays.

8.6.7 Ellipsoidal Arrays.

8.6.8 Other Shapes.

References.

9 BEAM FORMING.

9.1 Introduction.

9.2 A Note on Orthogonal Beams.

9.3 Analog Feed Systems.

9.3.1 Vector Transfer Matrix Systems.

9.3.2 Switch Matrix Systems.

9.3.3 Butler Matrix Feed Systems.

9.3.4 RF Lens Feed Systems.

9.3.4.1 The R-2R Lens Feed.

9.3.4.2 The R-kR Lens Feed.

9.3.4.3 Mode-Controlled Lenses.

9.3.4.4 The Luneburg Lens.

9.3.4.5 The Geodesic Lens.

9.3.4.6 The Dome Antenna.

9.4 Digital Beam Forming.

9.5 Adaptive Beam Forming.

9.5.1 Introduction.

9.5.2 The Sample Matrix Inversion Method.

9.5.3 An Adaptive Beam Forming Simulation Using a Circular Array.

9.6 Remarks on Feed Systems.

References.

10 CONFORMAL ARRAY PATTERN SYNTHESIS.

10.1 Introduction.

10.2 Shape Optimization.

10.3 Fourier Methods for Circular Ring Arrays.

10.4 Dolph-Chebysjev Pattern Synthesis.

10.4.1 Isotropic Elements.

10.4.2 Directive Elements.

10.5 An Aperture Projection Method.

10.6 The Method of Alternating Projections.

10.7 Adaptive Array Methods.

10.8 Least-Mean-Squares Methods (LMS).

10.9 Polarimetric Pattern Synthesis.

10.10 Other Optimization Methods.

10.11 A Synthesis Example Including Mutual Coupling.

10.12 A Comparison of Synthesis Methods.

References.

11 SCATTERING FROM CONFORMAL ARRAYS.

11.1 Introduction.

11.2 Definitions.

11.3 Radar Cross Section Analysis.

11.3.1 General.

11.3.2 Analysis Method for an Array on a Conducting Cylinder.

11.3.3 Analysis Method for an Array on a Conducting Cylinder with a Dielectric Coating.

11.4 Cylindrical Array.

11.4.1 Analysis and Experiment—Rectangular Grid.

11.4.2 Higher-Order Waveguide Modes.

11.4.3 Triangular Grid.

11.4.4 Conclusions from the PEC Conformal Array Analysis.

11.5 Cylindrical Array with Dielectric Coating.

11.5.1 Single Element with Dielectric Coating.

11.5.2 Array with Dielectric Coating.

11.6 Radiation and Scattering Trade-off.

11.6.1 Introduction.

11.6.2 Single-Element Results.

11.6.3 Array Results.

11.7 Discussion.

References.

Subject Index.

About the Authors.