Naturally sampled triangle carrier PWM bandwidth limit and output spectrum

This paper first presents a general theory predicting harmonic components in naturally sampled pulse width modulation (PWM) output signals, so that any input signal with a Fourier series representation may be handled. This theory provides a basis for the mathematical analysis of PWM systems, such as converters transmitting a main signal and a broadband of feedback or feedforward signals. Ultimately, the results of this theory are applied to the concrete problem of determining reasonable conditions on the carrier frequency such that an input consisting of a main signal and a bandwidth of small feedback or feedforward signals may be recovered through active filtering or similar methods, and conditions similar to the Nyquist theorem are derived. This research has been based on the premise that the results obtained will provide valuable insight into the general behaviour of PWM systems, and provide a supporting theory for concrete systems utilizing signals of this kind, such as PWM converters whose purpose is to ensure a dominant sinusoidal waveform along with a broadband frequency channel for small feedback signals.