Transmitarrays antennas (TAs) can be seen as the planar counterpart of optical lenses. They are composed of thin radiating elements (unit cells) which introduce different local phase shifts on an incident electromagnetic wave, emitted by a primary source, and re-radiate it. By properly designing the unit cells and their distribution in the TA, the properties of the incident wave, e.g. wavefront and polarization, as well as the pattern of the radiated field can be tailored. Moreover, TAs are suited to low-cost multilayer fabrication processes, e.g. printed circuit board (PCB) technology, and can achieve electronic reconfiguration embedding diodes. Therefore, TAs are natural and cost-effective candidates for applications requiring to steer and shape the antenna beam, such as satellite communications (Satcom) and future terrestrial wireless networks. For instance, satellite antennas radiate contoured beams to cover specific Earth regions, whereas Satcom ground terminals and mobile base stations require very directive beams compliant with prescribed radiation masks. In many cases, the amplitude of the field impinging on the TA is fixed and the TA phase profile, i.e. the spatial distribution of the phase-shifting elements, is the only parameter that can be designed to generate the desired radiation pattern. Thus, versatile, efficient and robust phase-only synthesis methods are essential. Closed-form expressions for the phase profile can be derived only in a few cases and for specific targeted far-field patterns. On the other hand, synthesis approaches based on global optimization techniques, such as genetic algorithms, are general purpose but their convergence and accuracy is often poor, despite the long computation time. In this thesis, a mathematical approach for the phase-only synthesis of TAs using convex optimization is developed to solve diverse pattern shaping problems. The use of convex optimization ensures a good compromise between the generality, robustness and computational cost of the method.First, a model for the analysis of the TA is presented. It accurately predicts the antenna radiation pattern using the equivalence theorem and includes the impact of the spillover, i.e. the direct radiation from the TA feed. Then, the TA synthesis is formulated in terms of the far-field intensity pattern computed by the model. The phase-only synthesis problem is inherently non-convex. However, a sequential convex optimization procedure relying on proper relaxations is proposed to approximately solve it. The accuracy of these sub-optimal solutions is discussed and methods to enhance it are compared. The procedure is successfully applied to synthesize relatively large TAs, with symmetrical and non-symmetrical phase profiles, radiating either focused-beam or shaped-beam patterns, with challenging mask constraints.Finally, three millimeter-wave TAs, comprising different sets of unit cells, are designed using the synthesis procedure. The good agreement between the predicted radiation patterns and those obtained from full-wave simulations of the antennas demonstrates the precision and versatility of the proposed tool, within its range of validity. / Transmitarray antennas (TAs) är en typ av antenna som konsiderades som optiska lenser motparten. Transmitterray antennas (TAs) are a type of antenna that is considered as optical lenses counterpart.De är sammansatta av tunna strålande element eller unit cell (UCs) som introducerar olika lokala fasförskjutningar på en inkommande elektromagnetisk våg och stråla ut den igen. They are composed of thin radiating elements or unit cells (UCs) that introduce different local phase shifts on an incoming electromagnetic wave and radiate it out again.Den här vågen kommer från en primär elektromagnetisk källa. This wave comes from a primary electromagnetic source.Syftet med detta examensarbete är att bestämma hur man ska UC placera för att skapa en önskad utgångsstråle.This master thesis aim is to determine how to place the UC in order to create a desired output beam.TAs är biliga att bygga och kan också vara elektroniska omkonfigurerbara med hjälp av dioder. TAs are cheap to produce and can also be electronically reconfigurable using diodes. TAs används i Satcom-domänen eller för att designa ny hög hastighet nätverk (6G).TAs are used in the Satcom domain or to design new high-speed network (6G). När man skapar en antenn, kan man stämma fas och amplitud av kompositerna för att skapa en önskad utgångsstråle. På TAs är det lite svårare.When someone create an antenna, one can tune phase and amplitude of the composants to create a desired output beam. For TAs it is a little bit more difficult.Faktiskt kan man stämma endast fas i TA- arkitektur. In fact, one can only tune the phase in the TA architecture. Så behöver vi speciell designprocedur som kallas: fassyntesSo, we need special design procedure called: phase-only synthesis.Konvex optimering är en bra kompromiss mellan metodens generalitet och uträkningstimeConvex optimization is a good compromise between generality and computation time.Här presenterar vi en fassyntes metod på skapa TAs som utstrålar en önskad stråle. Here we present a phase-only synthesis method in order to create TAs which radiate a precise beam. Metoden är baserade på konvex optimering.