Regenerated air (reverse Brayton) cycle has unique potentials in heat pump applications compared to conventional vapor-compression cycles. To better understand the regenerated air heat pump cycle characteristics, a thermodynamic model with new equivalent parameters was developed in this paper. Equivalent temperature ratio and equivalent isentropic efficiency of expander were introduced to represent the effect of regenerator, which made the regenerated air cycle in the same mathematical expressions as the basic air cycle and created an easy way to prove some important features that regenerated air cycle inherits from the basic one. Moreover, we proved in theory that the regenerator does not always improve the air cycle efficiency. Larger temperature ratio and lower effectiveness of regenerator could make the regenerated air cycle even worse than the basic air cycle. Lastly, we found that only under certain conditions the cycle could get remarkable benefits from a well-sized regenerator. These results would enable further study of the regenerated air cycle from a different perspective. (C) 2015 Elsevier Ltd. All rights reserved.