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This study considers the maximum modulation index of a direct torque control (DTC)-based converter. The maximum modulation index and maximum output voltage of the circular flux trajectory DTC method are analytically derived, and the result is validated by measurements. It is found out that the maximum modulation index of a DTC converter with a circular flux trajectory is slightly lower than the limit of the overmodulation range 1. The analysis is based on a new method of modelling the DTC output voltage with continuous analytical functions.