On methods to determine bounds on the Q-factor for a given directivity

B. L. G. Jonsson, Shuai Shi, Lei Wang, Fabien Ferrero, Leonardo Lizzi

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)


This paper revisit and extend the interesting case of bounds on the Q-factor for a given directivity for a small antenna of arbitrary shape. A higher directivity in a small antenna is closely connected with a narrow impedance bandwidth. The relation between bandwidth and a desired directivity is still not fully understood, not even for small antennas. Initial investigations in this direction have related the radius of a circumscribing sphere to the directivity, and bounds on the Q-factor have also been derived for a partial directivity in a given direction. In this paper, we derive lower bounds on the Q-factor for a total desired directivity for an arbitrarily shaped antenna in a given direction as a convex problem using semidefinite relaxation (SDR) techniques. We also show that the relaxed solution is also a solution of the original problem of determining the lower Q-factor bound for a total desired directivity. SDR can also be used to relax a class of other interesting nonconvex constraints in antenna optimization, such as tuning, losses, and front-to-back ratio. We compare two different new methods to determine the lowest Q-factor for arbitrary-shaped antennas for a given total directivity. We also compare our results with full electromagnetic simulations of a parasitic element antenna with high directivity.
Original languageEnglish
Pages (from-to)5686-5696
Number of pages11
JournalIEEE Transactions on Antennas and Propagation
Issue number11
Early online date1 Sept 2017
Publication statusPublished - Nov 2017


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