The bandwidth limitations of resonant, electrically small antennas that fully occupy a spherical volume are well defined by the inverse of the Chu-limit or the lower bound on quality factor. Recently, Gustafsson et al developed lower bounds for the Q of antennas of arbitrary shape. We have previously described antenna designs fully occupying a spherical volume and a cylindrical volume that exhibit Q's close to the Chu-limit and close to the Gustafsson limit, respectively.
In many applications, there is a requirement for electrically small planar antennas. It is understood that the Q of an electrically small planar antenna cannot approach the Q of a spherical or cylindrical antenna, where all have the same value of ka and fully occupy their respective total available volumes. Comparing the Q's of planar antennas to the lower bound for spherical or cylindrical antennas does not provide sufficient insight into how well the antenna performs relative to the theoretical performance that can be achieved in the planar shape. Recently, Gustafsson et al presented the limit on achievable Q for planar antennas as a function of their length-to-diameter ratio. In this paper, we present several designs for electrically small, thin planar antennas and compare their Q's to the Gustafsson limit.
