A Flux pump (FP) is a high current generating device for powering superconducting magnets. Based on their operating mechanism, they can be broadly classified into two types: dynamo FP and rectifier FP. In this paper we built the circuit models of various rectifier FP topologies, which uses DC field controlled HTS switches for the rectification purpose. The topologies are listed as: (i) half-wave retifier FP with a series resistance, (ii) half-wave rectifier FP with two switches, (iii) fullwave rectifier FP with four switches and (iv) full-wave rectifier FP with two switches. All these topologies are built within the MATLAB/Simscape platform using the predefined Ic(B) look up tables. The results show the flux pumping phenomena for various topologies using the input sinusoidal current controlled source. The modelling results from the half-wave rectifier FP model with two switches are verified against the experimental results. A feedback controlled switching methodology of the applied field switch for maximised operating efficiency is proposed for the first time in this paper. The maximum efficiency values achieved for various topologies are tabulated for comparison purpose. This models presented in this paper helps to understand the rectifier FP operating mechanism and also to optimise the FP design for the appropriate load characteristics.