Modal analysis of radiation and energy storage mechanisms on conducting scatterers

The manifestation of radiation and stored energy by electric currents on conducting bodies is studied via modal expansions. The novel modal expansions are based on the quadratic operators which map a current distribution to each quantity. Adaptations of the continuous forms of these operators into the Method of Moments is reviewed. The discrete modal expansions are studied on several example objects, leading to conclusions regarding the sparsity of the radiation mode spectrum. Analytic forms for the sparse radiation modes on electrically small objects are derived. Negative energy current distributions are studied using the energy storage modal expansions. The role of ground plane radiation on the determination of an embedded antenna’s Q factor is studied using radiation modes, giving a new perspective on the convergence behavior of this parameter with respect to ground plane size. Leveraging the invariance of radiation modes on small objects, an example procedure for the design of an embedded antenna array using radiation modes is presented.

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

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

[3]  Buon Kiong Lau,et al.  Tracking of characteristic modes through far-field pattern correlation , 2015, 2015 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting.

[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]  R.G. Vaughan,et al.  Antenna diversity in mobile communications , 1987, IEEE Transactions on Vehicular Technology.

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

[8]  Jordi Romeu Robert,et al.  Exact representation of antenna system diversity performance from input parameter description , 2003 .

[9]  Sung-Hoon Oh,et al.  Envelope Correlation Coefficient and Mean Effective Gain for Multiple Antennas in Different Use Cases , 2007 .

[10]  W. Stutzman,et al.  Spatial, polarization, and pattern diversity for wireless handheld terminals , 2001 .

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

[12]  Guy A. E. Vandenbosch,et al.  Radiators in Time Domain–Part II: Finite Pulses, Sinusoidal Regime and Q Factor , 2013, IEEE Transactions on Antennas and Propagation.

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

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

[15]  S.R. Best,et al.  The Significance of Ground-Plane Size and Antenna Location in Establishing the Performance of Ground-Plane-Dependent Antennas , 2009, IEEE Antennas and Propagation Magazine.

[16]  P. Hazdra,et al.  Comments to “Reactive Energies, Impedance, and Q Factor of Radiating Structures” by G. Vandenbosch , 2013 .

[17]  J. Bernhard,et al.  Classifying characteristic mode crossing avoidances with symmetry and energy coupling , 2016, 2016 IEEE International Symposium on Antennas and Propagation (APSURSI).

[18]  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.

[19]  David M. Pozar.  Antenna synthesis and optimization using weighted Inagaki modes , 1984 .

[20]  Guy A. E. Vandenbosch,et al.  Radiators in Time Domain–Part I: Electric, Magnetic, and Radiated Energies , 2013, IEEE Transactions on Antennas and Propagation.

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

[22]  R.G. Vaughan,et al.  Signals in mobile communications: A review , 1986, IEEE Transactions on Vehicular Technology.

[23]  U. Jakobus,et al.  A hybrid tracking algorithm for characteristic mode analysis , 2014, 2014 International Conference on Electromagnetics in Advanced Applications (ICEAA).

[24]  J. Remacle,et al.  Gmsh: A 3‐D finite element mesh generator with built‐in pre‐ and post‐processing facilities , 2009 .

[25]  S.R. Best,et al.  Low Q electrically small linear and elliptical polarized spherical dipole antennas , 2005, IEEE Transactions on Antennas and Propagation.

[26]  R. Rojas,et al.  Wideband Characteristic Mode Tracking , 2012, IEEE Transactions on Antennas and Propagation.

[27]  S.R. Best,et al.  A discussion on the quality factor of impedance matched electrically small wire antennas , 2005, IEEE Transactions on Antennas and Propagation.

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

[29]  Per-Olof Persson,et al.  A Simple Mesh Generator in MATLAB , 2004, SIAM Rev..

[30]  Q limits for arbitrary shape antennas using characteristic modes , 2012, 2012 6th European Conference on Antennas and Propagation (EUCAP).

[31]  Kin-Lu Wong,et al.  On the impedance bandwidth of a planar inverted-F antenna for mobile handsets , 2002 .

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

[33]  P. Wriggers.  Computational contact mechanics , 2012 .

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

[35]  R. Eisenschitz.  Matrix Algebra for Physicists , 1966 .

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

[37]  John L. Volakis,et al.  Computation of the $Q$ Limits for Arbitrary-Shaped Antennas Using Characteristic Modes , 2016, IEEE Transactions on Antennas and Propagation.

[38]  D. McNamara,et al.  Sub-structure characteristic mode concept for antenna shape synthesis , 2012 .

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

[40]  A. T. Arkko.  Effect of ground plane size on the free-space performance of a mobile handset PIFA antenna , 2003 .

[41]  J. T. Bernhard,et al.  Measuring electrically small antennas: Details and implications , 2009, 2009 IEEE International Workshop on Antenna Technology.

[42]  Xin-Qing Sheng,et al.  Essentials of Computational Electromagnetics , 2012 .

[43]  Miloslav Capek,et al.  Modal Analysis and Optimization of Radiating Planar Structures , 2014 .

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

[45]  N. Inagaki,et al.  Eigenfunctions of composite Hermitian operators with application to discrete and continuous radiating systems , 1982 .

[46]  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.

[47]  Jennifer T. Bernhard,et al.  Broadband Equivalent Circuit Models for Antenna Impedances and Fields Using Characteristic Modes , 2013, IEEE Transactions on Antennas and Propagation.

[48]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

[49]  M. Gustafsson.  Convex optimization for analysis of small antennas , 2013, 2013 7th European Conference on Antennas and Propagation (EuCAP).

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

[51]  Derek A. McNamara,et al.  Antenna Shape Synthesis Without Prior Specification of the Feedpoint Locations , 2014, IEEE Transactions on Antennas and Propagation.

[52]  R. Clarke.  A statistical theory of mobile-radio reception , 1968 .

[53]  Identifying radiation mechanisms on small conducting objects using radiation modes , 2015, 2015 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting.

[54]  J J Adams,et al.  A Modal Approach to Tuning and Bandwidth Enhancement of an Electrically Small Antenna , 2011, IEEE Transactions on Antennas and Propagation.

[55]  Jennifer T. Bernhard,et al.  Eigenvalue Crossing Avoidance in Characteristic Modes , 2016, IEEE Transactions on Antennas and Propagation.

[56]  Lukas Jelinek,et al.  On the Functional Relation Between Quality Factor and Fractional Bandwidth , 2014, IEEE Transactions on Antennas and Propagation.

[57]  Leigh Tesfatsion,et al.  Individual tracking of an eigenvalue and eigenvector of a parameterized matrix , 1981 .

[58]  Jennifer T. Bernhard,et al.  Design Guidelines Using Characteristic Mode Theory for Improving the Bandwidth of PIFAs , 2015, IEEE Transactions on Antennas and Propagation.

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

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

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

[62]  E. Y. Lam,et al.  Mobile-Phone Antenna Design , 2012, IEEE Antennas and Propagation Magazine.