New design method for derivation of the amplitude distributions of an uniformly spaced n-element linear antenna array

In this work, a linear array that is formed by placing elements along a straight line is considered to shape the beam and control the level of the side lobes by adjusting the amplitudes of the current in the array. The total radiated field, |E| is produced by using the Nth Bernstein polynomial, BN(f;x). So that the well-known linear arrays and rest unrealized ones that uses the current distribution excitations for the required radiation, can be obtained as special cases from an unified analytical procedure by changing fk coefficients in the Bernstein polynomial. The connection between arrays and Bernstein polynomial is established by considering current excitation symmetrical for obtaining real-valued array function, and by choosing an appropriate transformation between x and Ψ to make the array function and polynomial identical. By this new method, both broadside ( maximum radiation at θ = π/2) and end-fire (maximum radiation at θ = 0) type arrays can obtain by adjusting the current excitations. Also, to control and change the directivity function at a given Ψ point is possible and one can set the maximum lobe amplitude for a given N and by the time can change the other lobes position and amplitude.