The imperative for small aviation engines lies in the pursuit of heightened power-to-weight ratios and thermal efficiencies. Relying solely on piston engines and gas turbines is insufficient to concurrently meet these evolving performance demands. This paper introduces the concept of a combined cycle aviation engine (CCAE), amalgamating the cycle modes of piston engines and gas turbines. The CCAE achieves flexible control over turbine operating states and engine performance through the adjustment of the energy distribution between these two cycles. The air diversion strategy (α) and the burner's fuel supply strategy (λb) are identified as the key determinants of system performance. To comprehensively investigate the impact of α and λb on CCAE's performance, this paper constructs a theoretical model, a simulation model, and a test bench. The simulation model's accuracy is validated through test data, and the air-fuel ratio range for burner stable combustion is explored. The simulation results indicate a reduction of 50 % in the fluctuation of turbine speed within a single cycle. Under high-altitude conditions, CCAE's intake mass flow rate, power, and efficiency are notably enhanced when compared to conventional turbocharged piston engines. These findings contribute valuable insights that can inform the application of CCAE within the aviation domain.