This article focuses on a modular multilevel converter (MMC) based on GaN transistors designed for use in aeronautical applications, as opposed to its conventional use in terrestrial power distribution networks. The converter controls a variable-frequency permanent magnet generator and is responsible for generating an 800 V DC electrical network on board the aircraft. Strict weight and volume constraints play a decisive role in the design of the system in this context. This article proposes a pre-sizing method to inform the selection of arm inductance and module capacitance values, considering the specific requirements of the case study. An experimental GaN MMC was designed and built based on the pre-sizing results in order to validate theoretical results. This study is part of the MOTECH project, which focuses on the design of technologies for hybridization systems in turbofans. The project is supported by the French Civil Aviation Authority (DGAC).