One-Dimensional Spectral Analysis of Complex PWM Waveforms Using Superposition

This paper takes a new look at the mechanisms underlying the double-edge pulse-width modulation (PWM) process. It presents a novel way of deriving equations for the spectrum of double-edge PWM using basic mathematical techniques. In the process the underlying nonlinearities that generate the PWM side-bands are identified. Unlike the classical double Fourier series approach, the proposed method of deriving the PWM spectrum does not require the construction of the so-called unit cell. The interaction between this new model of the pulse-width modulator and the regular sampling process is studied, and generalized equations for the Fourier transforms of regularly sampled PWM waveforms are derived. A general solution to the important question of what happens to the PWM spectrum when the PWM reference consists of a summation of signals is presented. It is shown that the addition of reference signals in the time domain results in a double convolution of the PWM sidebands in the frequency domain. As an application of this result, it is shown how new analytic equations for the harmonics of third-harmonic injection PWM and space vector modulation can easily be derived. Finally, the new theoretical results are benchmarked against results from the well-established double Fourier series method.