The Analysis of Circular Waveguide Phased Arrays

The requirements of modern radar and communication systems have stimulated considerable activity in the design and use of phased array antennas. To date, the design information required for their development has been obtained from the analysis of simplified array models and from experimental data. The great speed and storage capacity of present day digital computers, however, have now made it possible to solve the planar phased array boundary value problem veiy accurately. 1,2 A general formulation of the planar phased array boundaiy value problem may be found. A vector two dimensional integral equation * T h e work reported in this paper was supported by the U. S. Army Materiel C o m m a n d under contract DA-30-069-AMC-333(Y). 1903 1904 T H E BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1968 for the tangential aperture field (that is, the tangential field at the planar interface between the waveguides and free space) can then be derived. In its most general form the array elements are assumed to be arranged in a doubly periodic grid along two skewed (nonorthogonal) coordinates; and dielectric loading, covers, and plugs, as well as thin irises at the aperture plane, may be accounted for in the analysis. The possibility of multimode excitation of the array has also been included. The Ritz-Galerkin method is applied to obtain a solution for circular waveguide arrays. Numerical solutions for the reflection characteristics of dielectricfree planar arrays of circular waveguides hexagonally arranged in a conducting ground plane have been carried out.