Physical limitations of phased array antennas

TL;DR

This paper derives fundamental bounds on the Q-factor for narrow-band phased array antennas, providing insights into the trade-offs between bandwidth, element design, and performance metrics.

Contribution

It introduces a novel method to compute Q-factor bounds using quadratic optimization, applicable to arrays with ground planes and free space, aiding antenna design trade-offs.

Findings

Q-factor bounds depend on array geometry and environment

Trade-offs between Q-factor and efficiency, size, and polarization are quantified

Bounds guide optimal antenna element and array design choices

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.