Radiation Impedance of a Dipole in an Infinite Planar Phased Array

Abstract

The radiation impedance of a dipole in an infinite array phased for any angle of radiation is calculated. The calculation is made by means of plane wave expansions and gives a very simple result. The radiation resistance is the product of the broadside resistance times a scanning factor which is unity on broadside and changes the resistance as the beam is scanned. The scanning factor is identified as the product of the element pattern and a factor equal to the ratio of the broadside aperture to the projected aperture. The radiation reactance is also calculated and consists of a leading term due to reflection of the wave fronts from the ground plane plus an infinite series of higher order‐terms contributed by the cutoff wave. Results are plotted for the variation of radiation resistance and reactance with changes in radiation angle. A comparison is also made between results calculated by the method of plane wave expansions and those obtained from the method employing mutual impedance coefficients.