This article presents an optimization process applied to the sizing of high power silicon carbide inverters. The case study is the design of an aeronautical converter. A gradient-based optimization method is chosen for its ability to explore a wide solution space with a large amount of constraints, what is the case during the pre-design phase. Many topologies are selected and associated models are developed. Among all these models, active and passive component design, and spectral analysis of voltages and currents, are presented. Optimization results, with the goal of minimizing the global mass of the converter, are provided. The different topologies are compared to find the best one for the selected case study. The relevance of the optimization result is evaluated with the study of the optimality of the solution. Finally, experimental results are compared to the optimization ones, which validates the good accuracy of analytical models.