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A guide to mutual coupling between various types of antennas in arrays such as wires, apertures and microstrip patches or antennas co-sited on platforms
Mutual Coupling Between Antennas explores the theoretical underpinnings of mutual coupling, offers an up-to-date description of the physical effects of mutual coupling for a variety of antennas, and contains techniques for analysing and assessing its effects. The book puts the topic in historical context, presents an integral equation approach, includes the current techniques, measurement methods, and discusses the most recent advances in the field.
With contributions from noted experts on the topic, the book reviews practical aspects of mutual coupling and examines applications that clearly demonstrate where the performance is impacted both positively and negatively. Mutual Coupling Between Antennas contains information on how mutual coupling can be analysed with a wide range of methods from direct computer software using discrete methods, to integral equations and Greens function methods as well as approximate asymptotic methods. This important text:
Written for antenna engineers, technical specialists, researchers and students, Mutual Coupling Between Antennas is the first book to examine mutual coupling between various types of antennas including wires, horns, microstrip patches, MIMO antennas, co-sited antennas and arrays in planar or conformal configurations.
Trevor S. Bird, PhD, is Principal Antengenuity, Distinguished Visiting Professor University of Technology, Sydney, and Adjunct Professor Macquarie University, Australia.
Preface and acknowledgements
List of Contributors
Notation
Chapter 1 Introduction (Trevor S. Bird)
1.1 Aims and scope
1.2 Historical Perspective
1.3 Overview of Text
1.4 References
Chapter 2 Basics of Antenna Mutual Coupling (Trevor S. Bird)
2.1 Introduction
2.2 Electromagnetic Field Quantities
2.2.1 Definitions
2.2.2 Field representations in source-free region
2.3 Mutual coupling between elementary sources
2.3.1 Radiation
2.3.2 Generalized infinitesimal current elements
2.3.3 Mutual coupling between infinitesimal current elements
2.4 Network Representation of Mutual Coupling
2.4.1 Extension to combination of elements
2.4.2 Mutual impedance and admittance formulation
2.4.3 Scattering matrix representation
2.5 Radiation from Antennas in the Presence of Mutual Coupling
2.5.1 Far-field radiation
2.5.2 Magnetic current only
2.5.3 Electric current only
2.6 Conclusion
2.7 References
Chapter 3 Methods in the Analysis of Mutual Coupling in Antennas (Trevor S. Bird)
3.1 Introduction
3.2 Mutual Coupling in Antennas with Continuous Sources
3.2.1 Impedance and admittance with continuous sources
3.2.2 Reaction
3.2.3 Definition of circuit quantities
3.3 On Finite and Infinite Arrays
3.3.1 Finite array analysis by element-by-element method
3.3.2 Infinite periodic array analysis
3.4 Integral Equation Methods Used in Coupling
3.4.1 Introduction
3.4.2 Greens function methods
3.4.2.1 Free-space Green’s function for harmonic sources
3.4.2.2 Free-space Green’s function for transient sources
3.4.2.3 Fields with sources
3.4.3 Solution by weighted residuals
3.5 Other Methods in Coupling Analysis
3.5.1 Unit cell analysis in periodic structure method
3.5.2 Mode matching methods
3.5.3 Moment methods
3.5.4 Method of characteristic modes
3.5.5 Arrays of minimum scattering antennas
3.6 Practical Aspects of Numerical Methods in Mutual Coupling Analysis
3.6.1 Introduction
3.6.2 Numerical quadrature
3.6.3 Matrix inversion
3.7 Conclusion
3.8 References
Chapter 4 Mutual Coupling in Arrays of Wire Antennas (Trevor S. Bird)
4.1 Introduction
4.2 Formulation of the Problem
4.2.1 Moment method
4.2.2 Moment method solution for the dipole
4.3 Mutual Impedance
4.4 Arrays of Wire Antennas
4.4.1 Full-wave dipole above a perfect ground
4.4.2 The Yagi-Uda array
4.5 Asymptotic Approximations to Mutual Impedance
4.6 Concluding Remarks
4.7 References
Chapter 5 Arrays of Planar Aperture Antennas (Trevor S. Bird)
5.1 Introduction
5.2 Mutual Coupling in Waveguide and Horn arrays
5.2.1 Integral equation formulation
5.2.2 Modelling of profiled horns and mode matching
5.2.3 Asymptotic approximation of mutual admittance
5.3 Coupling in Rectangular Waveguides and Horns
5.3.1 Self-admittance of TE10 mode
5.3.2 Example of mutual coupling between different-size waveguides
5.3.3 Application to horns
5.3.4 Waveguide-fed slot arrays
5.3.5 Asymptotic approximation of coupling in rectangular apertures
5.4 Coupling in Arrays of Coaxial Waveguides and Horns
5.4.1 Self-admittance of TE11 mode in coaxial waveguide
5.4.2 TEM mode coupling in coaxial waveguide
5.4.3 Asymptotic approximation of coupling in coaxial waveguide apertures
5.4.4 Coaxial and circular aperture array examples
5.5 Mutual coupling between apertures with general cross sections
5.5.1 Elliptical apertures
5.5.2 General apertures
5.6 Coupling in Apertures Loaded with Dielectrics and Metamaterials
5.6.1 Dielectric-loaded apertures
5.6.2 Metamaterial-loaded apertures
5.7 Concluding remarks
5.8 References
Chapter 6 Arrays of Microstrip Patch Antennas (Trevor S. Bird)
6.1 Introduction
6.2 Representation of Mutual coupling Between Patch Antennas
6.2.1 E-current model of coupling
6.2.2 Cavity model (H-model) of coupling
6.2.3 Full-wave solution
6.3 Applications of Microstrip Arrays
6.3.1 Mutual Coupling Between Microstrip Patches
6.3.2 Steering by Switching Parasitic Elements
6.3.3 A Metasurface From Microstrip Patches
6.4 Conclusion
6.5 References
Chapter 7 Mutual Coupling Between Antennas on Conformal Surfaces (Trevor S. Bird)
7.1 Introduction
7.2 Mutual Admittance of Apertures on Slowly Curving Surfaces
7.2.1 Greens Function Formulation for Curved Surfaces
7.2.2 The Cylinder
7.2.3 The Sphere
7.3 Asymptotic Solution for Fields Near Convex Surfaces
7.3.1 Review of literature for convex surfaces
7.3.2 Asymptotic solution for the surface fields
7.4 Mutual Coupling of Apertures in a Cylinder
7.4.1 Closed Form Expressions for Mutual Coupling Between Rectangular Waveguides in a Cylinder
7.4.2 Expressions for Mutual Coupling Between Circular Waveguides in a Sphere
7.4.3 Mutual Coupling Between Microstrip Patches on a Cylinder
7.5 Extension of Canonical Solution to Large Convex Surfaces with Slowly Varying Curvature
7.6 Applications of Coupling on Curved Surfaces
7.6.1 Mutual Coupling in a Waveguide Array on a Cylinder
7.6.2 Mutual Coupling Between Monopoles on a Cylinder
7.6.2 Mutual Coupling Between Waveguides on an Ellipsoid
7.7 Conclusion
7.8 References
Chapter 8 Mutual Coupling Between Co-sited Antennas and Antennas on Large Structures (Derek McNamara and Eqab Almajali)
8.1 Preliminaries and Assumptions
8.1.1 The problem at hand
8.1.2 Course adopted
8.2 Full-Wave CEM Modelling View of a Single Antenna
8.3 Full-Wave CEM Modelling View of Coupled Antennas in the Presence of a Host Platform
8.3.1 Field point of view
8.3.2 Two-port network parameter point of view
8.4 Useful Expressions for Coupling in the Presence of a Host Platform
8.4.1 Motivation
8.4.2 Reciprocity and reaction theorems revisited
8.4.3 Generalized reaction theorem
8.4.4 Expressions for mutual impedance and open circuit voltage
8.4.5 Power coupling
8.5 Supplementary Comments on CEM Modelling Method
8.6 Reduced Complexity Antenna Electromagnetic Model
8.7.1 Necessity for simplified antenna model
8.7.2 Huygen’s box model
8.7.3 Spherical wave expansion model
8.7.4 Infinitesimal dipole model
8.7.5 Planar aperture model
8.7.6 Point source models
8.8 CEM Modelling of Coupled Antennas on a Platform – Pragmatic Approaches
8.8.1 Necessity
8.8.2 Limited descriptive list of pragmatic approaches
8.9 Co-Sited Antenna Coupling Computation Examples
8.10 Concluding Remarks
8.11 References
Chapter 9 Mutual Coupling and Multiple Input Multiple Output (MIMO) Communications (Karl F. Warnick)
9.1 Introduction
9.2 Previous work on mutual coupling and MIMO
9.3 Basics of MIMO communications
9.3.1 MIMO channel capacity
9.3.2 Eigenchannels and the water-filling solution
9.3.3 Eigenchannels in MIMO systems and beamforming arrays
9.3.4 Reference planes and the intrinsic channel matrix
9.4 Mutual coupling and MIMO transmitting
9.4.1 Radiated electric field and embedded element patterns
9.4.2 Pattern overlap matrix, conservation of energy, and mutual coupling
9.4.3 Gain and directivity in the overlap matrix formulation
9.4.4 Overlap matrix for isotropic radiators
9.4.5 Mutual coupling for closely spaced elements, superdirectivity, and Q-factor bounds
9.4.6 EEPs, mutual coupling, and minimum scattering antennas
9.4.7 Mutual coupling and interactions between elements
9.4.8 Transmitter power constraint
9.4.9 Impedance matching at the transmitter
9.5 Mutual coupling and MIMO receiving arrays
9.5.1 Receive array signal and noise model
9.5.2 Receive array Thévenin equivalent network
9.5.3 Loaded receive array output voltages
9.5.4 External noise and loss noise
9.5.5 Signal correlation matrix
9.5.6 Signal correlation in a rich multipath environment
9.5.7 Mutual coupling, noise matching, and equivalent receiver noise
9.6 Conclusion
9.7 References
Chapter 10 Mutual Coupling in Beamforming and Interferometric Antennas (Hoi Shun Antony Lui and Trevor S. Bird)
10.1 Introduction
10.2 The Array Manifold
10.3 Direction-of-Arrival (DOA) Algorithms
10.3.1 Matrix Pencil Method for DOA Estimation
10.4 Maximum Gain Design for Single and Multiple beams
10.4.1 Penalty Function Optimization of Array Parameters
10.4.2 Method of Successive Projections
10.4.3 Comparison of Penalty Functions and Successive Projections
10.5 Direction-of-Arrival (DOA) Estimation
10.5.1 No Coupling Situation
10.5.1.1 Cramer-Rao Lower Bound
10.5.1.2 Four-element linear arrays with Different Apertures (2 Incoming Signals)
10.5.1.3 Fixed Aperture ULAs with Different Numbers of Elements (2 Incoming Signals)
10.5.1.4 Fixed Aperture ULAs with Different Number of Elements (3 Incoming Signals)
10.5.2 Perturbation due to Mutual Coupling
10.5.2.1 Eight-element linear arrays with Different Apertures (3 Incoming Signals)
(a) DOA estimation under the effect of mutual coupling
(b) Compensation using Conventional Mutual Impedance
(c) Compensation using Receiving Mutual Impedance
10.5.2.2 Fixed Array Aperture with Different Numbers of Elements (2 Incoming Signals)
10.6 Conclusion
10.7 References
Chapter 11 Techniques for Minimizing Mutual Coupling Effects in Arrays (Hoi Shun Antony Lui and Trevor S. Bird)
11.1 Introduction
11.2 Mutual Coupling in Transmitting and Receiving Arrays
11.2.1 The Mutual Coupling Path
11.2.2 Moment Method Analysis
11.3 Typical Methods for Minimizing Mutual Coupling
11.3.1Aperture Field Taper
11.3.2Electromagnetic Fences
11.3.3Other Approaches to Compensation
11.4 Techniques for Practical Mutual Coupling Compensation
11.4.1 Conventional Mutual Impedance Method
11.4.2 Full-Wave Method
11.4.3 Receiving Mutual Impedance Method
11.4.3.1 Determination of the receiving mutual impedance
11.4.3.2 Comparison between different mutual impedances and direction-finding applications
11.4.4 Calibration Method
11.4.5 Compensation through beamforming network
11.4.6 Compensation in the Aperture
11.5 Conclusion
11.6 References
Chapter 12 Noise Performance in the Presence of Mutual Coupling (Christophe Craeye, Jean Cavillot, and Eloy de Lera Acedo)
12.1 Generalities About Noise in Receiving Arrays
12.2 Coupling of Noise Originating from LNAs
12.3 Coupling of Noise Originating from Lossy Antenna Arrays
12.4 Coupling of Noise Originating from the Far-field Environment
12.5 Conclusion
12.6 References
Chapter 13 Methods for Analyzing Mutual Coupling in Large Arrays
(Christophe Craeye and Ha Bui Van)
13.1 Goals of Numerical Mutual Coupling Analysis
13.2 Periodic Method of Moments
13.3 Iterative Solution Techniques
13.4 Macro Basis Functions
13.5 Pattern Transformations
13.6 Optimization
13.7 Conclusion
13.8 References
Chapter 14 Measurement of Mutual Coupling Effects
(Alpha O. Bah and Trevor S. Bird)
14.1 Introduction
14.2 Instrumentation
14.3 Basic Measurement of Static Element Coupling and Radiation
14.3.1 Measurement of coupling coefficients
14.3.2 Measurement of element radiation
14.3.3 Measurement of gain
14.4 Measurement of Active Element Coupling and Array Radiation
14.4.1 Measurement of active element patterns
14.4.2 Measurement of array radiation patterns
14.4.2.1 Pattern multiplication method
14.4.2.2 The unit excitation active element pattern method
14.4.2.3 The hybrid active element pattern method
14.4.2.4 The average active element pattern method
14.4.3 Measurement of input mismatch and coupling
14.4.3.1 Mutual coupling coefficient method
14.4.3.2 Directional coupler method
14.4.3.3 Power divider method
14.4.4 Measurement of gain
14.5 Conclusion
14.6 References
Appendices
APPENDIX A: Useful Identities (Trevor S. Bird)
APPENDIX B: Bessel and Hankel Functions (Trevor S. Bird)
APPENDIX C: Properties of Hankel Transform Functions (Trevor S. Bird)
APPENDIX D: Properties of Surface Fock Functions (Trevor S. Bird)
APPENDIX E: Four Parameter Noise Representation of an Amplifier (Christophe Craeye, Jean Cavillot, and Eloy de Lera Acedo)
APPENDIX F: Equivalent Noise Currents (Christophe Craeye, Jean Cavillot, and Eloy de Lera Acedo)
APPENDIX G: Basic Reciprocity Result (Christophe Craeye, Jean Cavillot, and Eloy de Lera Acedo)
APPENDIX H: On the Extended Admittance Matrix (Christophe Craeye and Ha Bui Van)
Index
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