Optimal antenna currents using convex optimization Gustafsson, Mats 2012 Link to publication Citation for published version (APA): Gustafsson, M. (2012). Optimal antenna currents using convex optimization. 1-1. Abstract from The Radio and Antenna Days of the Indian Ocean, Mauritius. General rights Unless other specific re-use rights are stated the following general rights apply: Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal Read more about Creative commons licenses: https://creativecommons.org/licenses/ Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.
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LUND UNIVERSITY
PO Box 117221 00 Lund+46 46-222 00 00
Optimal antenna currents using convex optimization
Gustafsson, Mats
2012
Link to publication
Citation for published version (APA):Gustafsson, M. (2012). Optimal antenna currents using convex optimization. 1-1. Abstract from The Radio andAntenna Days of the Indian Ocean, Mauritius.
General rightsUnless other specific re-use rights are stated the following general rights apply:Copyright and moral rights for the publications made accessible in the public portal are retained by the authorsand/or other copyright owners and it is a condition of accessing publications that users recognise and abide by thelegal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private studyor research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal
Read more about Creative commons licenses: https://creativecommons.org/licenses/Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will removeaccess to the work immediately and investigate your claim.
Optimal antenna currents using convex optimizationMats Gustafsson
Dept. Electrical and Information Technology Lund University, Box 118, SE-221 00 Lund, Sweden,e-mail: [email protected]
Design of small antennas is challenging because of the high Q-factor (low bandwidth), low efficiency, andoften low radiation resistance [1]. The fundamental trade-off between performance and size of the designvolume is expressed by physical bounds. Chu computed bounds on the Q-factor, Q, from the stored andradiated energies outside a sphere that circumscribes the antenna, see [1] for an overview. The bounds weregeneralized to arbitrary shaped antennas in [2, 3].
In [4], optimal currents and physical bounds on D/Q are formulated as an optimization problem usingthe expressions for the stored energies presented by Vandenbosch [5]. Here, convex optimization [6] is usedto determine optimal current distributions on arbitrary shaped antennas for minimum Q, maximal G/Q,superdirective antennas, and antennas with prescribed radiated fields [4, 7]. This generalizes the physicalbounds in [1, 2, 3] in many ways. We also show how losses and antennas embedded in perfectly electricconducting structures can be included in the bounds. The new results are for arbitrary shaped structuresbut restricted to antenna structures composed of metallic or dielectric materials. Moreover, we restrictthe size of the antenna structure to approximately half a wavelength to obtain positive semidefinite energyexpressions, see [4]. This restricts the presented results to Q � 1 that coincides with the size restrictionon the antennas considered here. Convex optimization is used in many areas [6] and it has e.g., been usedextensively to determine array patterns. The formulation as a convex optimization problem is advantageousas it has a well-developed theory [6] and there are efficient solvers. The theoretical results are illustratedwith numerical simulations for antennas confined to planar rectangles.
References
[1] J. Volakis, C. C. Chen, and K. Fujimoto. Small Antennas: Miniaturization Techniques & Applications.McGraw-Hill, New York, 2010.
[2] M. Gustafsson, C. Sohl, and G. Kristensson. Physical limitations on antennas of arbitrary shape. Proc.R. Soc. A, 463:2589–2607, 2007.
[3] M. Gustafsson, C. Sohl, and G. Kristensson. Illustrations of new physical bounds on linearly polarizedantennas. IEEE Trans. Antennas Propagat., 57(5):1319–1327, May 2009.
[4] Mats Gustafsson, Marius Cismasu, and B. Lars G. Jonsson. Physical bounds and optimal currents onantennas. IEEE Trans. Antennas Propagat., 60(6):2672–2681, 2012.
[5] G. A. E. Vandenbosch. Reactive energies, impedance, and Q factor of radiating structures. IEEE Trans.Antennas Propagat., 58(4):1112–1127, 2010.
[6] S. P. Boyd and L. Vandenberghe. Convex optimization. Cambridge Univ Pr, 2004.
[7] Mats Gustafsson and Sven Nordebo. Antenna currents for optimal Q, superdirectivity, and radiationpatterns using convex optimization. (LUTEDX/(TEAT-7216)/1–21/(2016)), 2012.
