Reflection properties of two-layer dipole arrays

The mutual impedance method for determining the reflection from a loaded dipole array is extended to the case of two parallel planar dipole arrays. The dipole arrays are illuminated by a plane wave with arbitrary incidence angle in either the - or -plane. The specular reflection coefficient obtained is shown, with proper design, to have a more narrow stop band with steeper skirts and a flatter top than that for a single array. The near-field coupling is included in the analysis, and the criteria for the validity of a simple transmission line solution are given. For close spacings the near fields may cause the reflection coefficient curve to: 1) not reach unity reflection; 2) attain unity reflection at one frequency; or 3) attain unity reflection at two frequencies, with a shallow dip between. The type of resonance curve obtained depends on the spatial arrangement of the two arrays. The evaluation of the mutual impedance sums is greatly simplified by certain impedance relationships that are presented. Calculated and measured reflection curves for various array separations are included.