Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - On Methods to Determine Bounds on the $Q$ -Factor for a Given Directivity
AU - Jonsson, B.L.G.
AU - Shi, Shuai
AU - Wang, Lei
AU - Ferrero, Fabien
AU - Lizzi, Leonardo
PY - 2017/11/30
Y1 - 2017/11/30
N2 - 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.
AB - 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.
U2 - 10.1109/TAP.2017.2748383
DO - 10.1109/TAP.2017.2748383
M3 - Journal article
VL - 65
SP - 5686
EP - 5696
JO - IEEE Transactions on Antennas and Propagation
JF - IEEE Transactions on Antennas and Propagation
SN - 0018-926X
IS - 11
ER -