An algorithm is developed that enables a single-phase matrix converter (SPMC) to perform functions of a generalized 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 first on computer simulation software Orcad Capture CIS version 9.1. Simulation results are presented for 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 generalized converter based on SPMC. Simulated results are verified with experimental results. Hardware design is obtained using readily available ICs and other components. The trigger circuit has been tested qualitatively by observing waveforms on CRO. The operation of the proposed system has been found to be satisfactory.