Properties of a phased array of rectangular waveguides with thin walls

The radiation impedance of an infinite array of open rectangular waveguides has been calculated by a function-theoretic method forHplane and quasi-Eplane beam scanning directions. The mutual coupling between columns has also been obtained. The amplitudes of the coupling coefficients decay asymptotically asr^{-3/2}while the phase difference between successive coupling coefficients approaches that to be expected from free space wave propagation. This asymptotic behavior is independent of waveguide dimensions for both planes of scan. It is similar to the asymptotic behavior of a line-source-excited wave propagating over a lossy surface. This suggests that the interface between an array and free space may in general be treated as such a surface. The coupling coefficients are used to determine the properties of an array, which has a finite number of active elements surrounded by an infinite passive array. Also, the edge effect due to the finiteness of an array is evaluated.