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The paper describes a new three-phase to single-phase matrix converter featuring unity input power factor, very low input total harmonic distortion, and soft-switching over the full power range, for high frequency induction heating applications. A variable output pulse density modulation scheme has been proposed for stable operation of the converter, with the notable feature of requiring no on-line calculations for the synthesis of three-phase input current system. Practical issues in realising the converter, viz. line frequency synchronisation and output current circulation, are described. Good agreement between simulation and experimental results confirm the benefits of the proposed converter.