The Quality Factor of the Folded Cylindrical Helix

Abstract

Any electrically small antenna can be impedance matched at any single frequency using a number of well known techniques. Once the small antenna is impedance matched, the primary characteristics of interest are its radiation efficiency, its operating bandwidth and to a lesser extent, its radiation patterns. The bandwidth of the small antenna is often quantified using the antenna's quality factor (Q) since fundamental lower bounds for Q are defined in terms of the antenna's occupied volume. The lower bound on Q, also known as the Chu-limit, is defined in terms of the spherical volume occupied by the antenna. However, many small antenna designs are constrained to fit within volumes other than a sphere. To address this issue, Gustafsson et al derived lower bounds for antennas of arbitrary shape with a specific focus on cylindrical and planar shaped antennas. In this paper we consider the quality factor of the folded cylindrical helix, an antenna design that effectively utilizes the available cylindrical volume. We compare its Q to the Gustaffson limit as a function of length-to-diameter ratio, while maintaining a fixed value of ka, and show that it’s Q is at or above Gustafsson’s lower bound for cylindrical shaped antennas.