Useful approximations for the directivity and beamwidth of large scanning Dolph-Chebyshev arrays

Approximate but accurate formulas are presented in a closed form that makes possible an easy examination and computation of directivity and beamwidth for large scanning Dolph-Chebyshev arrays. Array length, number of elements, spacing of the elements, sidelobe level, and angle of scan are parameters. Element spacings less than λ/2 are included. Comparisons between exact and approximate theory are presented in a graphical form that illustrates the lower limits of array size for which the approximations are valid. The maximum directivity for Chebyshev arrays is in principle limited, regardless of array size. Values of maximum directivity, and the particular array designs required to achieve them, are given for several fixed array lengths. The directivity-beamwidth product is evaluated over a wide range of sidelobe levels and array lengths, and the region over which this product is essentially constant is specified. In the interests of achieving joint minimization of beamwidth and maximization of directivity, the particular Chebyshev design such that the directivity-beamwidth ratio is maximized is determined.