Journal
IEEE TRANSACTIONS ON POWER ELECTRONICS
Volume 27, Issue 4, Pages 2116-2128Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TPEL.2011.2169283
Keywords
Carrier-based pulse width modulation (PWM) strategies; Carson's rule; closed-form solutions; digital simulation; double Fourier integral; pulse width modulation (PWM); regular sampling
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This paper provides a new look at the mechanisms underlying pulse width modulation (PWM). A simple approach to analyze the behavior of a single-sided pulse width modulator is presented. By using elementary methods, the pulse-width-modulated waveform is written as the sum of two sawtooth functions and the original modulating waveform. Simply applying the well-known Fourier series expansion of the sawtooth function, an equivalent model of the pulse width modulator, which shows that it is in essence a sequence of phase modulators, is derived. This model provides a clear understanding of the nonlinearities involved in the PWM process. It is shown how the superposition of modulating waveforms in the time-domain translates into the convolution of the sidebands in the frequency domain. Finally, the interaction of the pulse width modulator and a sample-and-hold register is studied and a general expression for the Fourier transform of a regular-sampled PWM waveform is derived. The analysis applies to periodic as well as aperiodic modulating waveforms.
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