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In this paper, a new topology of a cascaded multilevel converter is proposed. The proposed topology is based on a cascaded connection of single-phase submultilevel converter units and full-bridge converters. Compared to the conventional multilevel converter, the number of dc voltage sources, switches, installation area, and converter cost is significantly reduced as the number of voltage steps increases. In order to calculate the magnitudes of the required dc voltage sources, three methods are proposed. Then, the structure of the proposed topology is optimized in order to utilize a minimum number of switches and dc voltage sources, and produce a high number of output voltage steps. The operation and performance of the proposed multilevel converter is verified by simulation results and compared with experimental results of a single-phase 49-level converter, too.