A general analytical method for determining the theoretical harmonic components of carrier based PWM strategies

The analysis of pulse width modulation schemes for switched power converters has been a major research area for several decades, and considerable effort has gone into attempting to develop analysis techniques which allow one scheme to be evaluated against another for various fundamental and carrier frequencies and at different modulation depths. Except for a limited number of analytical solutions developed for specific modulation strategies, this analysis is generally done by digital simulation of the switched waveform and subsequent FFT or performance index calculation. This approach can require substantial computing capacity, and also has a significant potential for inaccuracies caused by subtle programming errors, which may cause erroneous comparisons to be made between different PWM schemes under particular operating conditions when the performance differences are slight. This paper presents a general method for determining the theoretical harmonic components of all major known variations of PWM. The method identifies appropriate inner and outer integral limits of the double Fourier integral solution of the switched waveform to suit each modulation strategy, and then solves this double integral using Jacobi-Anger expansions to establish closed form solutions. The method is applicable irrespective of the pulse ratio between the carrier and the fundamental, and the computational requirements are essentially constant irrespective of the absolute value of the carrier frequency.