A New Approach to Theoretical Analysis of Harmonic Content of PWM Waveforms of Single- and Multiple-Frequency Modulators

This paper presents a new approach to the spectral analysis of a carrier-based pulse width modulation (PWM) signal with continuous modulating function, and natural or regular sampling. The method is based on 1-D Fourier series and an expansion of the implicitly defined functions of the pulse edge angles of a PWM signal to power series. Expressions for the individual harmonics are given in closed form, allowing direct the calculation of the harmonic components, and can readily be implemented by a computer software package, such as MATLAB. Similarly, analytical expressions for the edges of the naturally sampled output PWM signal are determined. Cases of single- and multiple-modulation wave are analyzed in detail. As modulation of the half-bridge, single-phase inverter and the resulting spectrum constitute the basic building block from which the spectrum content of modulated multiphase, multilevel converters can readily be discerned, the spectrum of harmonics of the output PWM signal of an ideal half-bridge, single-phase inverter is analyzed. The method is evaluated and validated by comparing the spectrum obtained using the present method with those obtained by applying double Fourier series or by direct numerical procedure.