On Methods to Determine Bounds on the Q -Factor for a Given Directivity

• Published in: IEEE transactions on antennas and propagation Vol. 65; no. 11; pp. 5686 - 5696
• Main Authors: Jonsson, B. L. G., Shi, Shuai, Wang, Lei, Ferrero, Fabien, Lizzi, Leonardo
• Format: Journal Article
• Language: English
• Published: IEEE 01.11.2017; Institute of Electrical and Electronics Engineers
• Subjects: Antenna Q; antenna radiation pattern; Antenna radiation patterns; antenna theory; Bandwidth; Convex functions; directional antennas; Directive antennas; Electromagnetism; Engineering Sciences; fundamental limitations; miniature antenna; Optimization; Q-factor; Q-factor; parasitic element antenna; convex programming; SDR techniques; directional antennas; arbitrary-shaped antennas; Optimization; miniature antenna; semidefinite relaxation; convex problem; impedance bandwidth; nonconvex constraints; antenna optimization; fundamental limitations; Bandwidth; Directive antennas; antenna theory; Convex functions; Antenna Q; electromagnetic simulations; antenna radiation pattern; Antenna radiation patterns
• ISSN: 0018-926X; 1558-2221; 1558-2221
• DOI: 10.1109/TAP.2017.2748383

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.