<p>  </p> <p>This thesis introduces a 2.4 GHz hybrid 3-dB coupler with improved out-of-band rejection by incorporating a setup of transverse transmission lines, extensions, and open-circuit stubs at each of the coupler branches. To achieve matching at the design frequency, the <em>ABCD</em> matrix of the above-mentioned setup is calculated and associated to that of a 90° transmission line, leading to exact analytical equations for the impedances and electrical lengths. Simulated coupler design shows a return loss and isolation better than –27 dB as well as an in-band and out-of-band transmission losses better than –4 dB and –25 dB, respectively.</p> <p>The resulting design is applied to a 4×4 Butler matrix, which consists of other components; namely, crossovers, phase shifters and phase matchers. After designing and validating each of these components, they are integrated in the Butler matrix. To validate the radiation (i.e., beamforming) patterns, a microstrip patch antenna array is also designed and verified. The overall network (i.e., Butler matrix, antenna array) is simulated and parameters including phase-differences and 2D and 3D radiation patterns are validated. These electrical parameters are also measured for the fabricated Butler matrix. Based on the 2D and 3D radiation patterns, beamforming is obtained at ±10° and ±30°.</p> <p>Beamforming has applications in many different areas. Some applications like tracking and localization, satellite communication, high power beam-steering, and harmonic radar are also referenced in this thesis.</p>