Gaussian approach versus Dolph-Chebyshev synthesis of pencil beams for linear antenna arrays

A very simple and fast method for the synthesis of pencil beams with linear antenna arrays of equally spaced elements is presented. The proposed procedure starts selecting the desired pencil beam as a Gaussian function. This is very convenient for two reasons: first, the continuous line-source distribution that exactly produces the desired pencil beam (i.e. the Fourier transform of it) is in turn a Gaussian function and is immediately calculated. Second, a suitable weighted sampling of this distribution gives the excitations of the array elements in closed form. Two numerical examples reveal the good performances of the proposed approach, also in comparison with the classical method by Dolph-Chebyshev. It is shown that the synthesised array factors well approximate the desired pencil beams in real time, in particular ensuring a very good behaviour in the side lobe regions. Furthermore, the ‘dynamic range ratio’ of the excitations, defined as the ratio between the maximum and the minimum amplitude of the excitations, is very low and close to unity when the array length is sufficiently small.