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It is known that the optimal carrier based approach for modulating a multilevel converter is to use a phase disposition (PD) carrier arrangement with a common mode offset added to the reference waveforms to centre the implicitly selected space vectors. However, this strategy does not fully utilize all available voltage levels at lower modulation depths, with an odd level system only using odd voltage levels and an even level system only using even voltage levels as the modulation depth varies. Recent work has suggested that this is not the harmonically optimal approach at reduced modulation depths. This paper shows how up to a 40% reduction in harmonic distortion can be achieved if all available voltage levels are used throughout the linear modulation range. The improvement is achieved by adding a simple (1/2) carrier magnitude common mode dc offset in key modulation regions, which allows the converter to use all available voltage levels. The paper uses analytical spectral decomposition and harmonic flux trajectory analysis to propose a theoretical basis for this improvement, and to determine the precise points at which the (1/2) carrier magnitude offset should be added to achieve the harmonic improvement.