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Recently, RF energy transfer has been introduced as an alternative method for powering sensor nodes in wireless sensor networks (WSNs). However, RF energy transfer-based sensor networks have a problem of unfairness among sensor nodes due to the significant difference between their energy harvesting rates according to their positions. To overcome this problem, the energy adaptive MAC protocol, called EA-MAC, has been proposed in our previous work , which adaptively manages the duty cycle of sensor nodes according to the amount of their harvested energy as well as the contention time of sensor nodes considering fairness among them. However,  does not provide an analytical model to get the throughput and fairness of EA-MAC. In this paper, we provide an analytical model that can accurately evaluate the performance of EA-MAC and verify the validity of the model by comparing analytical results with simulation results.