Compact analytical solutions for determining the spectral characteristics of multicarrier-based multilevel PWM

Multilevel pulsewidth modulation (PWM) has become very important in high-power applications in recent years. Many different types of topology and control strategy have been developed to cater for the increasing need. One of the major concerns of the control strategy is to reduce the undesirable harmonics in order to improve the performance and efficiency. This paper presents the derivation of analytical solutions for determining the spectral characteristics of the multicarrier-based multilevel sinusoidal PWM. By decomposing the multilevel PWM into a series of sub-PWM and followed by using double Fourier series analysis, compact analytical solutions for any level with any carrier phase disposition have been obtained. Closed-form solutions have also been derived for double-sided multilevel PWM under certain specific carrier phase settings. The analytical solutions have been cross verified extensively with simulations and the results match with each other very well. It is shown that the proposed analytical solutions are by far the most compact reported in the literature.