This paper introduces a mathematical design and analysis of three-phase inverters used in electric drive applications such as aerospace, electric vehicles, and pumping applications. Different wide bandgap (WBG) semiconductor technologies are considered in this analysis. Using SiC MOSFETs and Si IGBTs, two drive systems are developed in order to show the improvement in the efficiency of the inverter. The efficiency, total losses of the drive systems and the power losses of two inverters are computed and compared for both drive systems at the same operating condition. The drive system with SiC MOSFET shows much better performance compared to the drive system with Si IGBT. The SiC MOSFET system provides a 59.39%, 86.13%, and 29.76% lower conduction losses, switching losses and drive’s total losses, respectively, compared to the Si IGBT system. The efficiency of the SiC MOSFET system is 2.46%pu higher than the efficiency of the Si IGBT drive system. Moreover, this paper introduces a detailed analysis for the dc-link voltage and current ripples in three-phase inverters. Furthermore, the minimal dc-link capacitor needed to deal with the ripple current and voltage is investigated. Finally, the performance of the drive with Si IGBT is experimentally tested under different operating speeds and loads.