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In this paper, by adopting the superposition of terms with unequalcoefficients, some useful closed-form formulas for the class of large planararrays are presented for predicting the directivities of radiated beams.Despite the applied simplifying assumptions, the provided formulas may be usedfor designing a large multiple-beam planar array with a specified powerpattern. Several illustrative examples are presented which are numericallydemonstrate by the MATLAB software. The applicability of the proposed synthesismethod verified by the achieved conformity between the simulations andtheoretical predictions. Furthermore, the impact of quantization and arraydimensions on the performance of power controlling as well as the limitationson the maximum scan angle are investigated. It is believed that the proposedstraightforward approach for array synthesis provides a new opportunity forvarious applications such as multiple-target radar systems and beamformingarray antenna.

Some useful approximations for calculation of directivities of multibeam power patterns of large planar arrays