In this paper, a new control method is proposed for three-phase to single-phase cycloconverters for synthesizing the desired output voltage from balanced and unbalanced input voltages. The theoretical analysis of the proposed control method is given for both of the conventional topologies of three-phase to single-phase cycloconverters. Using the proposed control method, the maximum output/input voltage transfer ratios are 0.5 and 1.5 for conventional cycloconverters that consist of three and six bidirectional switches, respectively. The proposed control method has no limitation on frequency conversion and is independent of the load. In other words, using the proposed control method, the three-phase to single-phase cycloconverter can operate as a generalized transformer. Using the proposed control method, the low order harmonics are not generated in the input and output quantities. As a result, the size of the required filters is decreased. The proposed control method can be easily extended to three-phase to n-phase cycloconverters based on the same principle of the operation. The simulation and experimental results verify the operation and performance of the proposed control method. (C) 2011 Elsevier Ltd. All rights reserved.