Activated carbon-ammonia multi-stage adsorption refrigeration cycle was analyzed in this article, which realized deep-freezing for evaporating temperature under -18 degrees C with heating source temperature much lower than 100 degrees C. Cycle mathematical models for single, two and three-stage cycles were established on the basis of thorough thermodynamic analysis. According to simulation results of thermodynamic evaluation indicators such as COP (coefficient of performance), exergetic efficiency and cycle entropy production, multi-stage cycle adapts to high condensing temperature, low evaporating temperature and low heating source temperature well. Proposed cycle with selected working pair can theoretically work under very severe conditions, such as -25 degrees C evaporating temperature, 40 degrees C condensing temperature, and 70 degrees C heating source temperature, but under these working conditions it has the drawback of low cycle adsorption quantity. It was found that both COP and exergetic efficiency are of great reference value in the choice of cycle, whereas entropy production is not so useful for cycle stage selection. Finally, the application boundary conditions of single-stage, two-stage, and three-stage cycles were summarized as tables according to the simulation results, which provides reference for choosing optimal cycle under different conditions. (c) 2016 Elsevier Ltd. All rights reserved.