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This paper presents analytical techniques for the determination of the expressions for the modulation signals used in the carrier-based sinusoidal and generalized discontinuous pulse-width modulation schemes for two-level, three-phase voltage source inverters. The proposed modulation schemes are applicable to inverters generating balanced or unbalanced phase voltages. Some results presented in this paper analytically generalize the several expressions for the modulation signals already reported in the literature and new ones are set forth for generating unbalanced three-phase voltages. Confirmatory experimental and simulation results are provided to illustrate the analyses.