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**Harvard**

Kildal, P., Martini, E. och Maci, S. (2017) *Degrees of Freedom and Maximum Directivity of Antennas: A bound on maximum directivity of nonsuperreactive antennas*.

** BibTeX **

@article{

Kildal2017,

author={Kildal, Per-Simon and Martini, Enrica and Maci, Stefano},

title={Degrees of Freedom and Maximum Directivity of Antennas: A bound on maximum directivity of nonsuperreactive antennas},

journal={IEEE Antennas and Propagation Magazine},

issn={10459243},

volume={59},

issue={4},

pages={16-25},

abstract={We derive a general fundamental directivity limitation formula that applies to nonsuperreactive antennas of any size that fit within a minimum sphere of any given radius rmin. The derivation is done by using a new concept: the degrees of freedom (DoF) of the field radiated by arbitrary sources within the minimum sphere must be twice the maximum directivity. The formula converges to the known bound of the directivity for large rmin. For small spheres, it becomes equal to three, i.e., 4.8 dBi, which is the directivity of the Huygens source. The transition region between these two limiting cases is determined by counting the most significant spherical modes at the surface of the minimum sphere. This is not trivial, because spherical modes have a gradual cutoff when their order approaches krmin. Therefore, we use a weighted summation where the weighting factor is inversely proportional to the radiation-Q of the modes. This extends the DoF from a discrete to continuous function of the minimum sphere radius. The final maximum directivity is similar to a previously published heuristic limit. The formulas are compared to results for measured antennas with large directivity and superdirectivity. },

year={2017},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 252194

A1 Kildal, Per-Simon

A1 Martini, Enrica

A1 Maci, Stefano

T1 Degrees of Freedom and Maximum Directivity of Antennas: A bound on maximum directivity of nonsuperreactive antennas

YR 2017

JF IEEE Antennas and Propagation Magazine

SN 10459243

VO 59

IS 4

SP 16

OP 25

AB We derive a general fundamental directivity limitation formula that applies to nonsuperreactive antennas of any size that fit within a minimum sphere of any given radius rmin. The derivation is done by using a new concept: the degrees of freedom (DoF) of the field radiated by arbitrary sources within the minimum sphere must be twice the maximum directivity. The formula converges to the known bound of the directivity for large rmin. For small spheres, it becomes equal to three, i.e., 4.8 dBi, which is the directivity of the Huygens source. The transition region between these two limiting cases is determined by counting the most significant spherical modes at the surface of the minimum sphere. This is not trivial, because spherical modes have a gradual cutoff when their order approaches krmin. Therefore, we use a weighted summation where the weighting factor is inversely proportional to the radiation-Q of the modes. This extends the DoF from a discrete to continuous function of the minimum sphere radius. The final maximum directivity is similar to a previously published heuristic limit. The formulas are compared to results for measured antennas with large directivity and superdirectivity.

LA eng

DO 10.1109/MAP.2017.2706659

LK http://dx.doi.org/10.1109/MAP.2017.2706659

OL 30