This paper mainly investigated a looped tube refrigerator driven by a three-stage travelling wave thermoacoustic engine (later simply called as thermacoustic engine-refrigerator system). The onset and steady operation features of this coupling thermoacoustic system are analyzed through the network model developed by the author's research group and the DeltaEC code, which is widely used in the thermacoustic research field. For power electronic thermal management utilizing low grade energy, a small scale three-stage travelling wave thermoacoustic engine-refrigerator system is designed. The onset features, steady performances and acoustic field features are analyzed in depth according to the simulation results. The analysis start with an investigation on the parametric sensitivity, followed by the description on the scaling and coupling impacts of this engine-refrigerator system on the onset temperature difference. The scaling impact is determined from the comparison results between a small scale and a large scale system, while the coupling impact is derived from the simulation of a refrigerator system and a simple engine system. The simulation results are also compared with the experimental data in publication, and the comparison demonstrated a desirable agreement. The main findings from this research work would provide some physical insights on the design and operating principles for the development of multi-stage thermoacoustic systems. (C) 2016 Elsevier Ltd. All rights reserved.