Abstract
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.
Highlights
O NE of the most important antenna design parameters is the impedance bandwidth, for which an antenna satisfies its design criteria
A class of tools addressing this problem are the fundamental bounds, and they have been instrumental for determining optimal performance for small antennas [1]–[3]
The proposed optimization methods efficiently solve the originally nonconvex problems of Q-factor minimization and determine an optimal current density corresponding to the minimum value
Summary
O NE of the most important antenna design parameters is the impedance bandwidth, for which an antenna satisfies its design criteria. We use the Q-factor [4], [5] to determine the bounds for narrowband phased array antennas in free space and above a ground plane. A different approach was considered by Tomasic and Steyskal [43], [44] They proposed a lower bound for the Q-factor of a 1-D array of infinitely long cylinders in free space and above the ground plane. LUDVIG-OSIPOV et al.: PHYSICAL LIMITATIONS OF PHASED ARRAY ANTENNAS dominant cylindrical mode and they express the stored energies in terms of field densities in a unit cell (the fields of the propagating Floquet mode are excluded from stored energies) This approach can be seen as a periodic-structures counterpart of Collin and Rothschild’s method [26].
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