A generalized time domain pulse width modulation spectrum calculation method

Pulse width modulation is a widely used technique for both DC to DC and DC to AC voltage conversion, with most modern-day DC and AC drives control systems exploiting this method. This paper presents a simple and versatile time domain method to determine the spectrum of a pulse width modulated converter output voltage for an arbitrary modulation signal waveform, an arbitrary number of output voltage levels and an arbitrary modulation method. Integration boundaries can be set in a simple and straightforward way in time domain using basic algebra and analytic trigonometry, even for complex modulation signal waveforms, or accounting for various nonlinearities. The proposed method and its constraints were elaborated, and the method was demonstrated on two examples: single- and double-edge naturally sampled two-level pulse width modulation.