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In this paper, a dv/dt filter is designed for the modular multilevel converters (MMCs) based variable frequency motor drives. This concept utilizes the inherent arm inductors of the MMC as a part of the output low-pass filter, thus eliminating the need for an add-on inductor. Particularly, a mathematical model is proposed to optimize the filter loss and volume for a given dv/dt requirements. It turns out that with SiC-MOSFET-based high switching frequency operation, the dv/dt filter improves the output power quality and alleviates the voltage stress in motor drive applications. For applications with various requirements on filter volume and loss, weighted-sum optimal solutions are presented. Simulation results based on a seven-level MMC are provided to validate the theoretical analysis.