Computational Tools for Antenna Analysis and Design

Many engineers and scientists prevalently use computational tools in electromagnetics, which is also the predominant case for antennas. The ever-increasing number of applications and technologies that employ antennas create a constant demand to improve and extend existing tools and develop new ones. This dissertation investigates computational tools for antenna analysis and design. Antenna current optimization is used to determine the theoretical performance bounds on antennas above a ground plane. The results add insight to the performance of patch antennas and can thereby benefit antenna designers. Moreover, the limits are used to design antennas in method of moments (MoM) and genetic algorithm (GA) solvers. The matrices used to compute characteristic modes, that is a generalized eigenvalue problem, are analyzed. Numerical issues of the calculation are circumvented, and the computational complexity is decreased with the use of spherical vector waves. A macro basis function (MBF) and adaptive cross approximation (ACA) algorithm framework is employed to simulate vast endfire arrays. Convex optimization is used to synthesize endfire patterns with improved matching performance. Furthermore, the performance of two techniques that are used in the MBF method to model interconnected arrays is investigated in the endfire mode. (Less)

[1]  Wee Ser,et al.  Robust Beampattern Synthesis for Antenna Arrays With Mutual Coupling Effect , 2011, IEEE Transactions on Antennas and Propagation.

[2]  G. Vecchi,et al.  Analysis of Large Complex Structures With the Synthetic-Functions Approach , 2007, IEEE Transactions on Antennas and Propagation.

[3]  A. Polimeridis,et al.  On the Direct Evaluation of Weakly Singular Integrals in Galerkin Mixed Potential Integral Equation Formulations , 2008, IEEE Transactions on Antennas and Propagation.

[4]  Sergey N. Makarov,et al.  Antenna and EM Modeling with MATLAB , 2002 .

[5]  S. Best,et al.  Impedance, bandwidth, and Q of antennas , 2005 .

[6]  Matthew N. O. Sadiku,et al.  Numerical Techniques in Electromagnetics with MATLAB , 1992 .

[7]  Optimal Realizations of Passive Structures , 2014, IEEE Transactions on Antennas and Propagation.

[8]  W. W. Hansen,et al.  A New Principle in Directional Antenna Design , 1938, Proceedings of the Institute of Radio Engineers.

[9]  S. Schelkunoff A mathematical theory of linear arrays , 1943 .

[10]  Mats Gustafsson,et al.  Antenna Bandwidth Optimization With Single Frequency Simulation , 2014, IEEE Transactions on Antennas and Propagation.

[11]  Mats Gustafsson,et al.  Q factors for antennas in dispersive media , 2014, 1408.6834.

[12]  S. Nordebo,et al.  Optimal Antenna Currents for Q, Superdirectivity, and Radiation Patterns Using Convex Optimization , 2013, IEEE Transactions on Antennas and Propagation.

[13]  R. Mittra,et al.  Fast Analysis of Large Antenna Arrays Using the Characteristic Basis Function Method and the Adaptive Cross Approximation Algorithm , 2008, IEEE Transactions on Antennas and Propagation.

[14]  R. Harrington Time-Harmonic Electromagnetic Fields , 1961 .

[15]  D. Tayli,et al.  A Comparison of Macro Basis Function Methods for Interconnected Endfire Antenna Arrays , 2017, IEEE Antennas and Wireless Propagation Letters.

[16]  James Demmel,et al.  IEEE Standard for Floating-Point Arithmetic , 2008 .

[17]  R. Harrington,et al.  Computation of characteristic modes for conducting bodies , 1971 .

[18]  B. L. G. Jonsson,et al.  Physical Bounds and Optimal Currents on Antennas , 2012, IEEE Transactions on Antennas and Propagation.

[19]  E. Dufort,et al.  Pattern synthesis based on adaptive array theory , 1989 .

[20]  J. H. Wilkinson The algebraic eigenvalue problem , 1966 .

[21]  S. Nordebo,et al.  Characterization of MIMO Antennas Using Spherical Vector Waves , 2006, IEEE Transactions on Antennas and Propagation.

[22]  R. Mittra,et al.  Computational Methods for Electromagnetics , 1997 .

[23]  Alan Jeffrey,et al.  Handbook of mathematical formulas and integrals , 1995 .

[24]  Mats Gustafsson,et al.  Antenna Q and Stored Energy Expressed in the Fields, Currents, and Input Impedance , 2015, IEEE Transactions on Antennas and Propagation.

[25]  Doruk Tayli,et al.  On the issue of simulating very large endfire arrays with complex antenna geometries , 2016, 2016 URSI International Symposium on Electromagnetic Theory (EMTS).

[26]  Mats Gustafsson,et al.  Physical bounds of antennas , 2015 .

[27]  Jacob J. Adams,et al.  Systematic Shape Optimization of Symmetric MIMO Antennas Using Characteristic Modes , 2016, IEEE Transactions on Antennas and Propagation.

[28]  Roger F. Harrington,et al.  The Method of Moments in Electromagnetics , 1987 .

[29]  M. Gustafsson,et al.  Multiband Antenna ${Q}$ Optimization Using Stored Energy Expressions , 2014, IEEE Antennas and Wireless Propagation Letters.

[30]  O. Brune Synthesis of a finite two-terminal network whose driving-point impedance is a prescribed function of frequency , 1931 .

[31]  R. Garbacz,et al.  A generalized expansion for radiated and scattered fields , 1971 .

[32]  Juan R. Mosig,et al.  A Dynamical Radiation Model for Microstrip Structures , 1982 .

[33]  Leon S. Lasdon,et al.  Optimization Theory of Large Systems , 1970 .

[34]  W. Geyi Physical limitations of antenna , 2003 .

[35]  Raj Mittra,et al.  Application of Trapezoidal-Shaped Characteristic Basis Functions to Arrays of Electrically Interconnected Antenna Elements , 2007, 2007 International Conference on Electromagnetics in Advanced Applications.

[36]  A. Karlsson,et al.  Physical limitations of antennas in a lossy medium , 2004, IEEE Transactions on Antennas and Propagation.

[37]  Y. Lo,et al.  Optimization of directivity and signal-to-noise ratio of an arbitrary antenna array , 1966 .

[38]  Lukas Jelinek,et al.  Optimal Currents on Arbitrarily Shaped Surfaces , 2016, IEEE Transactions on Antennas and Propagation.

[39]  Mats Gustafsson,et al.  Validating the Characteristic Modes Solvers , 2017, IEEE Transactions on Antennas and Propagation.

[40]  Omar Wing,et al.  Classical Circuit Theory , 2008 .

[41]  Z. Yu,et al.  Beampattern Synthesis for Linear and Planar Arrays With Antenna Selection by Convex Optimization , 2010, IEEE Transactions on Antennas and Propagation.

[42]  Y. Rahmat-Samii,et al.  Particle swarm optimization in electromagnetics , 2004, IEEE Transactions on Antennas and Propagation.

[43]  Mats Gustafsson,et al.  State‐space models and stored electromagnetic energy for antennas in dispersive and heterogeneous media , 2017 .

[44]  Mats Gustafsson,et al.  Stored Electromagnetic Energy and Antenna Q , 2012, 1211.5521.

[45]  Dehai Zhang,et al.  PMM-GA METHOD TO SYNTHESIZE QUASI-OPTICAL FREQUENCY SELECTIVE SURFACE ON SiO2 SUBSTRATE , 2013 .

[46]  Walton C. Gibson,et al.  The Method of Moments in Electromagnetics , 2007 .

[47]  H. Shigesawa,et al.  Multiband single-layer frequency selective surface designed by combination of genetic algorithm and geometry-refinement technique , 2004, IEEE Transactions on Antennas and Propagation.

[48]  J. R. Mosig,et al.  On the Direct Evaluation of Surface Integral Equation Impedance Matrix Elements Involving Point Singularities , 2011, IEEE Antennas and Wireless Propagation Letters.

[49]  Gene H. Golub,et al.  Matrix computations , 1983 .

[50]  Nikos D. Sidiropoulos,et al.  Convex Optimization-Based Beamforming , 2010, IEEE Signal Processing Magazine.

[51]  M. John,et al.  Wideband Printed Monopole Design Using a Genetic Algorithm , 2007, IEEE Antennas and Wireless Propagation Letters.

[52]  Stephen P. Boyd,et al.  Graph Implementations for Nonsmooth Convex Programs , 2008, Recent Advances in Learning and Control.

[53]  D. Wilton,et al.  Electromagnetic scattering by surfaces of arbitrary shape , 1980 .

[54]  Juan R. Mosig,et al.  Complete semi-analytical treatment of weakly singular integrals on planar triangles via the direct evaluation method , 2010 .

[55]  Panos M. Pardalos,et al.  Introduction to Global Optimization , 2000, Introduction to Global Optimization.

[56]  L. J. Chu Physical Limitations of Omni‐Directional Antennas , 1948 .

[57]  R. Harrington,et al.  Theory of characteristic modes for conducting bodies , 1971 .

[58]  Wen Geyi Foundations of Applied Electrodynamics , 2010 .

[59]  D. A. Dunavant High degree efficient symmetrical Gaussian quadrature rules for the triangle , 1985 .

[60]  Y. Rahmat-Samii,et al.  Multiport characteristics of a wide-band cavity backed annular patch antenna for multipolarization operations , 2005, IEEE Transactions on Antennas and Propagation.

[61]  Guy A. E. Vandenbosch,et al.  Energy Stored by Radiating Systems , 2017, IEEE Access.

[62]  Weng Cho Chew,et al.  Integral Equation Methods for Electromagnetic and Elastic Waves , 2007, Synthesis Lectures on Computational Electromagnetics.

[63]  P. Hazdra,et al.  A Method for the Evaluation of Radiation Q Based on Modal Approach , 2012, IEEE Transactions on Antennas and Propagation.

[64]  Yahya Rahmat-Samii,et al.  Electromagnetic Optimization by Genetic Algorithms , 1999 .

[65]  Kristopher L. Kuhlman,et al.  mpmath: a Python library for arbitrary-precision floating-point arithmetic , 2017 .

[66]  Arto Hujanen,et al.  Limitations for the Radiation Q of a Small Antenna Enclosed in a Spheroidal Volume: Axial Polarisation , 2001 .

[67]  Dick den Hertog,et al.  Interior Point Approach to Linear, Quadratic and Convex Programming: Algorithms and Complexity , 1994 .

[68]  Shambhu Nath Jha,et al.  Fast Full-Wave Synthesis of Printed Antenna Arrays Including Mutual Coupling , 2016, IEEE Transactions on Antennas and Propagation.

[69]  P. Waterman Matrix formulation of electromagnetic scattering , 1965 .

[70]  L. Dagum,et al.  OpenMP: an industry standard API for shared-memory programming , 1998 .

[71]  D.J. Bekers,et al.  Eigencurrent analysis of resonant behavior in finite antenna arrays , 2006, IEEE Transactions on Microwave Theory and Techniques.

[72]  Raj Mittra,et al.  Macro Basis Function Framework for Solving Maxwell’s Equations in Surface Integral Equation Form , 2014 .

[73]  Mats Gustafsson,et al.  Bandwidth, Q factor, and resonance models of antennas , 2005 .

[74]  Gerhard Kristensson,et al.  Scattering of Electromagnetic Waves by Obstacles , 2016 .

[75]  Stephen J. Wright,et al.  Numerical Optimization (Springer Series in Operations Research and Financial Engineering) , 2000 .

[76]  Chao-Fu Wang,et al.  Electrically Small UAV Antenna Design Using Characteristic Modes , 2014, IEEE Transactions on Antennas and Propagation.

[77]  Ronold W. P. King,et al.  The theory of endfire arrays , 1964 .

[78]  C.L. Dolph,et al.  A Current Distribution for Broadside Arrays Which Optimizes the Relationship between Beam Width and Side-Lobe Level , 1946, Proceedings of the IRE.

[79]  David V. Thiel,et al.  An Investigation Into the Gustafsson Limit for Small Planar Antennas Using Optimization , 2013, IEEE Transactions on Antennas and Propagation.

[80]  F. Venneri,et al.  Use of the Simultaneous Diagonalization Technique in the Ax̄ = λBx̄ Eigenproblem Applied to the Computation of the Characteristic Modes , 2003 .

[81]  R. Collin,et al.  Evaluation of antenna Q , 1964 .

[82]  Y. Rahmat-Samii,et al.  Genetic algorithms and method of moments (GA/MOM) for the design of integrated antennas , 1999 .

[83]  P. Waterman,et al.  SYMMETRY, UNITARITY, AND GEOMETRY IN ELECTROMAGNETIC SCATTERING. , 1971 .

[84]  G. Thiele,et al.  Antenna theory and design , 1981 .

[85]  Mats Gustafsson,et al.  Minimization of Antenna Quality Factor , 2017, IEEE Transactions on Antennas and Propagation.

[86]  D. Pozar Microwave Engineering , 1990 .

[87]  Paolo Rocca,et al.  Compressive Sensing in Electromagnetics - A Review , 2015, IEEE Antennas and Propagation Magazine.

[88]  Lukas Jelinek,et al.  The Measurable Q Factor and Observable Energies of Radiating Structures , 2014, IEEE Transactions on Antennas and Propagation.

[89]  Mario Bebendorf,et al.  Approximation of boundary element matrices , 2000, Numerische Mathematik.

[90]  Mats Gustafsson,et al.  Antenna Current Optimization using MATLAB and CVX , 2016 .

[91]  Mats Gustafsson,et al.  Accurate and Efficient Evaluation of Characteristic Modes , 2018, IEEE Transactions on Antennas and Propagation.

[92]  M.A. Khayat,et al.  Numerical evaluation of singular and near-singular potential Integrals , 2005, IEEE Transactions on Antennas and Propagation.

[93]  H. Steyskal,et al.  Broad-band fragmented aperture phased array element design using genetic algorithms , 2005, IEEE Transactions on Antennas and Propagation.

[94]  Thomas F. Eibert,et al.  On the calculation of potential integrals for linear source distributions on triangular domains , 1995 .

[95]  M. Vouvakis,et al.  The adaptive cross approximation algorithm for accelerated method of moments computations of EMC problems , 2005, IEEE Transactions on Electromagnetic Compatibility.

[96]  Ronald F. Boisvert,et al.  NIST Handbook of Mathematical Functions , 2010 .

[97]  Philip E. Gill,et al.  Practical optimization , 1981 .

[98]  Douglas H. Werner,et al.  Genetic Algorithms in Electromagnetics , 2007 .

[99]  M. Gustafsson,et al.  Illustrations of New Physical Bounds on Linearly Polarized Antennas , 2009, IEEE Transactions on Antennas and Propagation.

[100]  Roger F. Harrington,et al.  Field computation by moment methods , 1968 .

[101]  Lukas Jelinek,et al.  Stored electromagnetic energy and quality factor of radiating structures , 2014, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[102]  Lukas Jelinek,et al.  Optimal Composition of Modal Currents for Minimal Quality Factor $Q$ , 2016, IEEE Transactions on Antennas and Propagation.

[103]  David M. Pour Considerations for Millimeter Wave Printed Antennas , 1983 .

[104]  David M. Pozar,et al.  New results for minimum Q, maximum gain, and polarization properties of electrically small arbitrary antennas , 2009, 2009 3rd European Conference on Antennas and Propagation.

[105]  Guy A. E. Vandenbosch Reply to "Comments on 'Reactive energies, impedance, and Q factor of radiating structures'" , 2013 .

[106]  H.A. Wheeler,et al.  Fundamental Limitations of Small Antennas , 1947, Proceedings of the IRE.

[107]  Stephen P. Boyd,et al.  Antenna array pattern synthesis via convex optimization , 1997, IEEE Trans. Signal Process..

[108]  Mats Gustafsson,et al.  Physical bounds on small antennas as convex optimization problems , 2012 .

[109]  R. Mittra,et al.  Characteristic basis function method: A new technique for efficient solution of method of moments matrix equations , 2003 .

[110]  C. J. Reddy,et al.  Characteristic Mode Analysis: Putting Physics back into Simulation , 2015, IEEE Antennas and Propagation Magazine.

[111]  A. Monorchio,et al.  An Iteration-Free MoM Approach Based on Excitation Independent Characteristic Basis Functions for Solving Large Multiscale Electromagnetic Scattering Problems , 2008, IEEE Transactions on Antennas and Propagation.

[112]  M. Gustafsson,et al.  Physical Bounds for Antennas Above a Ground Plane , 2016, IEEE Antennas and Wireless Propagation Letters.

[113]  Jennifer T. Bernhard,et al.  Radiation and Energy Storage Current Modes on Conducting Structures , 2015, IEEE Transactions on Antennas and Propagation.

[114]  H. Thal New Radiation$Q$Limits for Spherical Wire Antennas , 2006, IEEE Transactions on Antennas and Propagation.

[115]  G. T. Timmer,et al.  Stochastic global optimization methods part I: Clustering methods , 1987, Math. Program..