Extension of Hannan’s Limit: Evaluation and Enhancement of Beam-Scanning Performance of Planar Phased Arrays

For a large-scale array, its realized gain is always smaller than the summation of the element gains in isolation, which is the well-known gain paradox proposed by Hannan. To explain the paradox, embedded element efficiency (EEE) was defined to indicate whether the array elements are being fully utilized, and Hannan’s limit was introduced to provide a fundamental upper bound of the EEE. In this paper, Hannan’s limit is extended to assess the beam-scanning capability of a phased array, which can provide a fundamental upper bound of the EEE corresponding to different scanning angles. In addition, the methods for enhancing the EEE of a large-scale array to approach Hannan’s limit are discussed, including selecting an appropriate power pattern for the array element and efficiently decoupling the array elements. For verification, a planar large-scale wide-angle scanning array utilizing a hybrid decoupling strategy is designed in this paper. The proposed decoupling structure improves the isolation between adjacent array elements in both the E-plane and H-plane by approximately 18.3 dB. The beam-scanning range in the E-plane and H-plane can reach ±65° and ±60°. During beam scanning, the realized gain of the array can be improved by approximately 0.74 dB. After decoupling, the EEE of the 8 × 8 wide-angle scanning array can be improved by approximately 12.64% on average during beam scanning, which is closer to Hannan’s limit.