A major challenge for aircraft fuel cell propulsion systems is to ensure that the air properties on the cathode side remain within a narrow, suitable envelope throughout the flight. The components must maintain almost constant temperature, pressure and humidity levels under widely varying ambient conditions. The choice of components must take into account the aviation-specific requirements for weight and waste heat. In this numerical study, we investigate a novel cathode air supply system for a hydrogen fuel cell propulsion system which replaces the state-of-the-art electrical components used to drive the compressor in the cathode air supply system with a hydrogen-fuelled micro gas turbine.