A new technique for phase only nulling with equispaced arrays

A number of accurate nulling algorithms are available for phased arrays which have full amplitude and phase control at each element. In many systems, it is essential that the nulls be formed quickly. We discuss an accurate closed form solution to this problem and its limitations. The technique preserves the general shape of the radiation pattern. We give a closed form technique for moving already existing nulls to desired null locations without significantly changing the amplitudes. Our method is based on the Schelkulnoff circle. First the array factor summation, with its explicit amplitudes and phases, is written as a product. The null positions are directly identified by the product roots. One root is changed to the desired null location. Moving a symmetric root will, to a large degree, compensate for the change in amplitudes of the expanded sum. The result is a pattern with a perfect null at the desired location and amplitudes similar to those of the original problem.