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This paper describes the various common converters and illustrates the working principle of single phase matrix converter that shows a single topology capable of performing all function required in basic converter. An algorithm is developed that enables a single-phase matrix converter (SPMC) to perform functions of a generalised single phase power electronics converter such as acting as a frequency changer, rectifier, inverter and chopper. This reduces the need for new converter hardware. The algorithm is implemented on computer simulation software Orcad Capture CIS version 9.1. Simulation results are presented for all five types of converters with a control input variable that decides the 1) type of converter and 2) type of output waveform. The simulated results verify the working and operation of a generalised converter based on SPMC.