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A CO₂ cycle shows large throttling loss during the expansion process. The application of an expander into the CO₂ cycle can reduce the throttling loss and then improve system performance. In this study, the performance of a trans critical CO₂ cycle with an expander was analytically investigated in order to improve the cooling performance of the system. The expander was applied to the single-stage and two-stage compression cycles. The performance was analyzed with the variations of compressor frequency, outdoor temperature, and expander efficiency. The single-stage and two-stage compression cycles with the expander showed COP improvement of 25% and 32%, respectively, over the single-stage cycle with an EEV.