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arXiv · 1702.03234

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
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Abstract

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 has related the radius of a circumscribing sphere to the directivity, and bounds on the Q-factor has 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 semi-definite relaxation techniques (SDR). 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 non-convex constraints in antenna optimization such as tuning, losses, 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 EM-simulations of a parasitic element antenna with high directivity.

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B. L. G. Jonsson, Shuai Shi, Lei Wang, Fabien Ferrero, Leonardo Lizzi. 2017-02-10. On methods to determine bounds on the Q-factor for a given directivity. https://doi.org/10.1109/tap.2017.2748383

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