Energy scarcity is an important problem in wireless communication networks. Radio frequency energy harvesting (RFEH) is a promising solution as an alternative energy source for low-power wireless nodes. In this paper, we target to obtain a finite-state Markov channel based Markov model of an RFEH wireless node powered with a finite capacity rechargeable battery. With this model, we combine the power model of the incoming radio frequency (RF) signal, the energy and traffic models of the node in a single Markov model. The range of the harvested energy is partitioned with the proposed method. The obtained steady-state distributions are applied to the Markov chain, which provides an energy model of the node including the impact of wireless channel. Based on the obtained fundamental RFEH model, energy harvesting models are extended to different scenarios by taking probabilistic structures of RF signal arrival and energy consumption event arrival processes into account. With the proposed methodology, RFEH communications systems can be realistically modeled and analyzed. Numerical studies show the effects of parameters on the performance of RFEH systems, and verify the developed models.