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The synthesis of electrically large, aperiodic planar arrays with equi-amplitude excitations plays an increasingly relevant role in satellite applications. Unfortunately, for such a kind of synthesis problems, local optimization procedures may be ineffective, whereas global optimization procedures involve a severe computational effort. To circumvent these problems, a new deterministic approach for fast design of aperiodic concentric ring arrays is proposed. The method exploits easily obtained optimal continuous planar solutions, accounts for the geometric properties of the array element and allows, once the central geometry of the array (that is, at least the most internal ring) is fixed, to compute in a deterministic, iterative, very fast way the whole geometry of the density-tapered concentric ring array. Numerical examples show the effectiveness of the method, which provides in a few seconds layouts of hundreds of elements able to produce directivity patterns that satisfy realistic satellite project requirements.