Developing hybrid electric aircraft is propitious to reducing carbon dioxide emissions and fuel consumption. Combustion engines coupled with solid oxide fuel cells are proposed for aircraft propulsion systems, where the compressor is powered by fuel cells instead of turbines. The thermal cycle of the new engine is obviously different from that of conventional combustion engines and can be characterized in the temperature entropy diagram under some reasonable assumptions, which were analyzed and investigated. Performance parameters, such as the specific thrust, are derived and can be expressed by several fundamental thermal parameters. Three different cycles integrating Brayton cycles and SOFC are shown. The main conclusions are as follows: (1) The maximum operating pressure ratio of the Brayton cycles integrated with fuel cells is 32. The maximum thermal efficiency of the cycle at the lowest combustion temperature is 82.2%, while that of the BC is 65.1% at the high combustion temperature. (2) The new cycles can not work if the combustion temperature is lower than 1350 K. Otherwise, the fuel utilization will be too huge.