Physical Limitations of Phased Array Antennas
Journal article, 2021

In this paper, the bounds on the Q-factor, a quantity inversely proportional to bandwidth, are derived and investigated for narrow-band phased array antennas. Arrays in free space and above a ground plane are considered. The Q-factor bound is determined by solving a minimization problem over the electric current density. The support of these current densities is on an element-enclosing region, and the bound holds for lossless antenna elements enclosed in this region. The Q-factor minimization problem is formulated as a quadratically constrained quadratic optimization problem that is solved either by a semi-definite relaxation or an eigenvalue-based method. We illustrate numerically how these bounds can be used to determine trade-off relations between the Q-factor and other design specifications: element form-factor, size, efficiency, scanning capabilities, and polarization purity.




electromagnetic radiation

Q factor

Floquet expansions

current distribution

Energy storage

antenna theory

optimization methods

Current density


periodic structures

Phased arrays


Andrei Osipov

Chalmers, Electrical Engineering, Signal Processing and Biomedical Engineering, Signal Processing

Royal Institute of Technology (KTH)

Jari Matti Hannula

Royal Institute of Technology (KTH)

Patricia Naccachian

American University of Beirut

B. L.G. Jonsson

Royal Institute of Technology (KTH)

IEEE Transactions on Antennas and Propagation

0018-926X (ISSN)

Vol. In Press

Subject Categories

Computational Mathematics

Control Engineering

Discrete Mathematics



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Latest update

5/4/2021 2