Antenna Current Optimization using MATLAB and CVX

Antenna current optimization is a tool that offers many possibilities in antenna technology. Optimal currents are determined in the antenna design region and used for physical understanding, as a priori estimates of the possibilities todesign antennas, physical bounds and as figures of merits for antenna designs. Antenna current optimization is particularly useful for small antennas and antennas that are constrained by their electrical size. The initial non-convex antenna design optimization problem is reformulated as a convex optimizationproblem expressed in the currents on the antenna. This convex optimization problem is solved efficiently at a computational cost comparable to a Method of Moments (MoM) solution of the same geometry. In this paper a tutorial description of antenna current optimization is presented. Stored energies and their relation to the impedance matrix in MoM is reviewed. The convex optimization problems are solved using MATLAB and CVX. MoM data isincluded together with MATLAB and CVX codes to optimize the antenna current for strip dipoles and planar rectangles. Codes and numerical results for maximization of the gain to Q-factor quotient and minimization of the Q-factor for prescribed radiated fields are provided. (Less)

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

[2]  Andrew Lewis,et al.  An Investigation of the Performance Limits of Small, Planar Antennas Using Optimisation , 2015, ICCS.

[3]  K. Nikoskinen,et al.  The Parametric Optimization of Wire Dipole Antennas , 2011, IEEE Transactions on Antennas and Propagation.

[4]  W. Geyi.  Stored Energies and Radiation Q , 2014, IEEE Transactions on Antennas and Propagation.

[5]  Jonas Friden,et al.  Antenna Current Optimization for Lossy Media With Near-Field Constraints , 2015, IEEE Antennas and Wireless Propagation Letters.

[6]  S..  A Re-Examination of the Fundamental Limits on the Radiation Q of Electrically Small Antennas , 2008 .

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

[8]  Mats Gustafsson.  Physical bounds on antennas of arbitrary shape , 2011, 2011 Loughborough Antennas & Propagation Conference.

[9]  Mats Gustafsson.  Efficiency and Q for small antennas using Pareto optimality , 2013, 2013 IEEE Antennas and Propagation Society International Symposium (APSURSI).

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

[11]  L. J. Chu,et al.  Physical limitations of omnidirectional antennas , 1948 .

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

[13]  Raino A. E. Mäkinen,et al.  Introduction to shape optimization - theory, approximation, and computation , 2003, Advances in design and control.

[14]  S. Best,et al.  Electrically Small Resonant Planar Antennas: Optimizing the quality factor and bandwidth. , 2015, IEEE Antennas and Propagation Magazine.

[15]  R. Fletcher.  Practical Methods of Optimization , 1988 .

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

[17]  W. Geyi.  A method for the evaluation of small antenna Q , 2003 .

[18]  Buon Kiong Lau,et al.  Design of Orthogonal MIMO Handset Antennas Based on Characteristic Mode Manipulation at Frequency Bands Below 1 GHz , 2014, IEEE Transactions on Antennas and Propagation.

[19]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

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

[21]  T.H. O'Donnell,et al.  An Impedance-Matched 2-Element Superdirective Array , 2008, IEEE Antennas and Wireless Propagation Letters.

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

[23]  Chi-Chih Chen,et al.  Small Antennas:Miniaturization Techniques & Applications , 2009 .

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

[25]  Roger F. Harrington,et al.  Control of radar scattering by reactive loading , 1972 .

[26]  Eddie Wadbro,et al.  Topology Optimization of Metallic Antennas , 2014, IEEE Transactions on Antennas and Propagation.

[27]  Anja K. Skrivervik,et al.  PCS antenna design: the challenge of miniaturization , 2001 .

[28]  Harry L. Van Trees,et al.  Optimum Array Processing , 2002 .

[29]  J. Bladel,et al.  Electromagnetic Fields , 1985 .

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

[31]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

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

[33]  M. Cabedo-Fabres,et al.  The Theory of Characteristic Modes Revisited: A Contribution to the Design of Antennas for Modern Applications , 2007, IEEE Antennas and Propagation Magazine.

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

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

[36]  C. Balanis.  Antenna theory , 1982 .

[37]  Tai Tsun Wu,et al.  Highly directive current distributions: General theory , 1998 .

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

[39]  H. Wheeler,et al.  Simple relations derived fom a phased-array antenna made of an infinite current sheet , 1965 .

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

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

[42]  Lev Osherovich.  The Q factor , 2009 .

[43]  D. Luenberger.  Optimization by Vector Space Methods , 1968 .

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

[45]  Mats Gustafsson,et al.  Absorption efficiency and physical bounds on antennas , 2010 .

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

[47]  R. Fano.  Theoretical limitations on the broadband matching of arbitrary impedances , 1950 .

[48]  O. Breinbjerg,et al.  Superdirective Magnetic Dipole Array as a First-Order Probe for Spherical Near-Field Antenna Measurements , 2012, IEEE Transactions on Antennas and Propagation.

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

[50]  D. Kajfez,et al.  Invariant Definitions of the Unloaded Q Factor (Short Paper) , 1986 .

[51]  Slawomir Koziel,et al.  Antenna Design by Simulation-Driven Optimization , 2014 .

[52]  Guy A E Vandenbosch.  Simple Procedure to Derive Lower Bounds for Radiation $Q$ of Electrically Small Devices of Arbitrary Topology , 2011, IEEE Transactions on Antennas and Propagation.

[53]  Mats Gustafsson,et al.  Minimum Q for Lossy and Lossless Electrically Small Dipole Antennas , 2013 .

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

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

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

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

[58]  R. Fante.  Quality factor of general ideal antennas , 1969 .

[59]  A. Yaghjian,et al.  Lower Bounds on the Q of Electrically Small Dipole Antennas , 2010, IEEE Transactions on Antennas and Propagation.

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

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

[62]  Chao-Fu Wang,et al.  Characteristic Modes: Theory and Applications in Antenna Engineering , 2015 .

[63]  Mats Gustafsson,et al.  Stored energies in electric and magnetic current densities for small antennas , 2014, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[64]  M. Uzsoky,et al.  Theory of super-directive linear arrays , 1956 .

[65]  M. Gustafsson,et al.  Physical limitations on antennas of arbitrary shape , 2007, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[66]  S.R. Best,et al.  Limitations in Relating Quality Factor to Bandwidth in a Double Resonance Small Antenna , 2007, IEEE Antennas and Wireless Propagation Letters.

[67]  R. King.  Electromagnetic waves and antennas above and below the surface of the earth , 1979 .

[68]  Ole Sigmund,et al.  Topology Optimization of Sub-Wavelength Antennas , 2011, IEEE Transactions on Antennas and Propagation.

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