Finite periodic structure approach to large scanning array problems

There are two conventional techniques dealing with mutual coupling problems for antenna arrays. The "element-by-element" method is useful for small to moderate size arrays. The "infinite periodic structure" method deals with one cell of infinite periodic structures, including all the mutual coupling effects. It cannot, however, include edge effects, current tapers, and nonuniform spacings. A new technique called the "finite periodic structure" method, is presented and applied to represent the active impedance of an array, it involves two operations. The first is to convert the discrete array problem into a series of continuous aperture problems by the use of Poisson's sum formula. The second is to use spatial Fourier transforms to represent the impedance in a form similar to the infinite periodic structure approach. The active impedance is then given by a convolution integral involving the infinite periodic structure solution and the Fourier transform of the equivalent aperture distribution of the current over the entire area of the array. The formulation is particularly useful for large finite arrays, and edge effects, current tapers, and nonuniform spacings can also be included in the general formulation. Although the general formulation is valid for both the free and forced modes of excitation, the forced excitation problem is discussed to illustrate the method.