The supercritical carbon dioxide (S-CO₂) Brayton cycle is a new type of power generation technology with broad application prospects. This paper takes the supercritical carbon dioxide simple Brayton cycle with recuperation as the research object, and takes the nuclear power plant as the application background. The system cycle model and the efficiency model of the key components is discussed in detail. Based on this model, the influence of various engineering factors on the efficiency of the Brayton cycle and the volume of the system has been discussed. The analysis results show that the sensitivity of cycle efficiency and system volume to parameters such as temperature, pressure, turbomachinery efficiency and regenerator design differs obviously, and the most effective method to reduce the system volume is increasing the turbine inlet temperature. It is necessary to establish a complete system analysis model to optimize the design of the S-CO₂ system.