Recirculating energy recovery linacs are a promising technology for being able to deliver high power particle beams (~GW) while only requiring low power (~kW) RF sources. This is achieved by decelerating the used bunches and using the energy they deposit in the accelerating structures to accelerate new bunches. We present studies of the impact of the bunch train filling pattern on the performance of the accelerating RF system. We perform RF beam loading simulations under various noise levels and beam loading phases with different linac topologies. We also present a mathematical description of the RF system during the beam loading, which can identify optimal beam filling patterns under different conditions. The results of these studies have major implications for design constraints for future energy recovery linacs, by providing a quantitative metric for different machine designs and topologies.