Current research and the price of semiconductors are making Matrix Converter topologies more attractive and practically viable for many applications. One of the key benefits claimed for the matrix approach is the possibility of greater power density due to the absence of a DC link. To capitalise on this it is necessary to make the input filter small by having a sufficiently high switching frequency. In order to arrive at optimised solutions in terms of filtering, heatsinking and packaging, it is important to have accurate models to predict power circuit losses as a function of operating point and switching frequency. This aim of this thesis is to further the understanding of Matrix Converter current commutation with a focus on switching losses. The commutation process is analysed in detail and a complete loss model for Matrix Converter circuits is developed. The use of circuit simulation software in the prediction of switching losses is investigated and comparisons are made with experimentally measured results. The loss model is used to compare Matrix Converter losses with a functionally equivalent sinusoidal front end inverter. A review of soft switching techniques for Matrix Converter circuits is given. A new auxiliary resonant soft switching Matrix Converter is presented which overcomes many of the problems of the previously proposed circuits. The design, construction and testing of a 6kW prototype soft switching Matrix Converter is presented to evaluate the feasibility of the topology.