Affine transformation and its application to antenna arrays

The application of affine transformations to antenna arrays is discussed in this paper. Arrays related by this transformation can define a pattern invariant group. Thus, pattern functions of many arrays of a general type can be written down immediately from that of a simple type which is affine-equlvalent: for example, the pattern of an elliptical array from that of a circular one, the pattern of a periodic array with parallelogram or parallelepiped cells from that of a conventional one with square or cubic cells. This method also leads to an optimum design for the cophasal periodic arrays in the sense that the number of elements is a minimum under the condition that there are no grating lobes in the visible region for any given scanning range. For example, in the case of full scan, the number of elements can be reduced by 13.4 percent and 29.3 percent from those of conventional two- and three-dimensional arrays, respectively.