Minimizing the use of transceivers is an effective approach for achieving minimum energy consumption in convergent access networks. While synchronizing downstream transmissions can minimize the use of transceivers and reduce the number of switches of these components, incurring in less consumed energy. In this paper, we propose the synchronization of downstream traffic to reduce the consumed energy in a fixed-mobile access network. Specifically, we present a novel synchronized integrated downstream bandwidth allocation scheme for saving energy. EPON are considered for the fixed part of the network and wireless technologies for the integration are WiMAX, LTE and LTE_Advanced. Simulation results verify the proposed model and highlight the advantages of our scheme