Saving space on board, reducing costs and improving the antenna performances are tasks of outmost importance in the field of satellite communication. In this work it is shown how a non-uniformly spaced, direct radiating array designed according to the so called ‘sunflower’ law is able to satisfy stringent requirements with a reduced number of active chains, all employing amplifiers working at the same, optimised, operation point. The aim of this PhD thesis is to identify several array configurations characterized by a reduced complexity and cost when compared with conventional arrays or to reflector configurations. These arrays must satisfy stringent requirements of a GEOstationary satellite communication mission, especially in terms of a minimum directivity to be guaranteed in several spot beam areas and sidelobe levels to be kept below an assigned value. The dissertation starts with the discussion of the pattern characteristics of regularly spaced array. Since regularly spaced arrays do not allow pattern shaping without making use of an amplitude distribution, non-uniformly spaced arrays are introduced and their pattern behaviour is discussed at length. These arrays are proven to offer the freedom for shaping the pattern according to the imposed requirements and, at the same time, avoid the occurrence of grating lobes. Several innovative techniques for designing this particular class of arrays are proposed and compared. Among them, the sunflower positioning technique is chosen as the best candidate to deterministically design non-uniform planar arrays with really low sidelobe levels and a good rotational symmetry of the radiation patterns. This simple technique is based on the application of two separate laws for finding the radial and angular element positions. The first one comes directly from the relation established in the thesis between the amplitude distribution law and the density distribution one. Regarding the angular positioning law, the concept of optimal angular spreading, inherited from the natural world, is applied to the sunflower array antenna in order to guarantee the sparsity of the element positions both in the radial and angular coordinates.This angular sparsity is achieved by ensuring that each element of the array is placed at a different angular position. The sunflower synthesis technique is then generalized for employing differently sized sub-arrays in the same aperture. Two different options are presented, in which the sub-arrays composing the sunflower array have the same amplitude or the same power. In the first one, the planar aperture is divided into convex cells associated with the spatial locations obtained by means of the sunflower positioning. These cells are then filled with the best fitting (regular) sub-arrays. In this sense, several shapes are experimented with, ranging from circular ones to some that present clear technological advantages. In the latter case, the selected sub-arrays may induce a slight alteration of the rigorous sunflower placement. However, the easier technological implementation makes them the preferred choice for the design of the large planar array that is able to satisfy the satellite mission requirements. In order to physically validate the positioning principle of the sunflower array antenna, a demonstrator at a scaled frequency has been manufactured and measured. Four different sub-arrays are assembled starting from a standard 4x4 square, circularly polarized tile, and their radiation patterns are superimposed in order to compute the total array radiated pattern. Measurements and simulated results are shown to be in very good agreement. The dissertation attests the sunflower placement technique as an innovative, successful, deterministic method for designing large arrays. This technique can be complemented with a modular sub-array design, the combination of the two yielding an effective instrument for implementing highly demanding antennas, such as those required by satellite communication applications.