Synthesis of equiripple sector antenna patterns

A tutorial description is given of a procedure for synthesizing equiripple approximations to a sector pattern which is constant over the coverage region and zero elsewhere. This procedure, which represents a generalization of Dolph-Chebyshev synthesis, can be used to synthesize both zero phase and minimum phase approximations (with the latter yielding a better approximation to the desired magnitude function). Theoretical considerations and comparisons of recently constructed arrays suggest that the synthesized patterns have maximum rolloff at the coverage region boundary given constraints on the maximum allowable deviations from the desired pattern and the number of array elements. Extension to synthesis of more complex desired functions is discussed.