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AC-AC converters (e.g. matrix converters) are mostly semiconductor solutions for applications where intermediate energy storage is eliminated. This paper summarizes the research done and being carried out at the University of Minnesota for applications in motor drives and power-electronic transformers with advanced features. This paper presents a carrier-based modulation method for matrix converters and its application during for both input unbalance and output over-modulation. Various topologies of matrix converter are described for both drives and power-electronic transformers. These topologies have some inherent benefits like common-mode voltage elimination across the bearings of the motor/generator and controllable power factor at the input side. Some of the described technologies require open-ended machines as load and thereby some advantages like enhanced output voltage (1.5 times the output of normal three terminal load) are achieved. 