Matching Bandwidth Limits for Arrays Backed by a Conducting Ground Plane

Matching bandwidth limits are developed for antenna arrays backed by a perfect electrically conducting (PEC) ground plane. We model a general array in the long wavelength limit as a thin PEC-backed slab and use Fano's method to determine a limit for the frequency integral of the reflection coefficient. This yields a simple expression for the maximum bandwidth of the array under TE or TM excitation, subject to a specified tolerance for mismatch and efficiency. The limit also depends on the array's thickness, scan angle, and static permeability. The special case of a thin planar radiating sheet placed above a ground plane is also considered, which has a maximum impedance bandwidth of 8.3:1 at broadside when no materials are used (VSWR ≤ 2:1). Previous empirical approximations for the minimum height of a wideband array and maximum bandwidth of a tightly coupled dipole array (TCDA) are compared with the theoretical limits and found to be in good agreement.