Duplex Stirling refrigerators are the alternative cycles to the conventional vapor refrigeration cycles with their high efficient, low noise, and low emission characteristics. It consists of a Stirling heat engine and a Stirling refrigerator in a mono-block construction that operates by a power piston. In this particular study, the effect of imperfect regeneration on the performance of the duplex Stirling refrigerator is determined analytically while helium is the working fluid. The polytropic heat transfer processes are chosen instead of isothermal processes to get a more realistic approach. Various temperature and compression ratios are taken into account for the refrigerator side of the duplex system and the required compression ratio of the heat engine is determined by using the work equality constraint. The combined effects of the regenerator effectiveness, temperature and compression ratios on the performance of the duplex system are assessed. The results of the parametric analysis are presented in terms of heat removal from the refrigerated space, coefficient of performance of the refrigerator side, work consumed by the system, heat addition to the engine side, thermal efficiency and overall system performance. (c) 2020 Elsevier Ltd. All rights reserved.