An integrated approach to PWM through 3-dimensional visualization

This paper presents an approach to pulse-width modulation based on a 3D representation to facilitate analysis and design. The modulation process can be studied from a unified perspective. A mathematical and geometric framework is established to show that the behavior of a system follows a trajectory inscribed inside a cube. The cube corners represent available switch states. The basic equations governing the pulse width modulation (PWM) process are derived in the proposed three dimensional space. The 3D curve representing a PWM process is used to yield some of its general characteristics. It is shown how basic harmonic behavior can be approximated from this 3D trajectory. A few modulation schemes are compared using this new approach with emphasis on space vector modulation. Finally, this approach is used to design a modulation scheme for the overmodulation range with reduced harmonic distortion.