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This paper provides analytical and graphical methods for the study, performance evaluation, and design of the modern carrier-based pulsewidth modulators (PWM's), which are widely employed in PWM voltage-source inverter (VSI) drives. Simple techniques for generating the modulation waves of the high-performance PWM methods are described. The two most important modulator characteristics-the current ripple and the switching losses-are analytically modeled. The graphical illustration of these often complex multivariable functions accelerate the learning process and help one understand the microscopic (per-carrier cycle) and macroscopic (per fundamental cycle) behavior of all the modern PWM methods. The analytical formulas and graphics are valuable educational tools. They also aid the design and implementation of the high-performance PWM methods.

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Abstract-This paper compares the many fault tolerant threephase ac motor drive topologies that have been proposed to provide output capacity for the inverter faults of switch short or open-circuits, phase-leg short-circuits, and single-phase open-circuits. Also included is a review of the respective control methods for fault tolerant inverters including two-phase and unipolar control methods. The output voltage and current space in terms of components is identified for each topology and fault. These quantities are then used to normalize the power capacity of each system during a fault to a standard inverter during normal operation. A silicon overrating cost factor is adopted as a metric to compare the relative switching device costs of the topologies compared to a standard three-phase inverter.Index Terms-Inverter faults, phase-leg short-circuits, silicon overrating cost factor (SOCF), single-phase open-circuits, three-phase inverter, three-phase ac motor drive topologies.