On bandwidth bounds for periodic antenna elements with a ground plane

In this paper, we compare two different bandwidth bounds on array antennas with a ground plane. The first of these bounds is based on the fact that the antenna can be seen as a passive system, which implies that its response can be described in terms of a Herglotz function. This passivity-based bandwidth bound is closely related to a sum rule for lossless arrays over the ground plane. The second bound is a recently developed Q-factor based bound, valid for resonant structures. In this paper, it is shown that this latter bound strongly depends on the allowed shape and the electrical size of the element within the unit cell. It also depends on the size of the unit cell, corresponding to the interelement spacing. The Q-factor bound provides a sharper bound when the structure is resonant.