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, or Class D amplifiers. Ultimately, the results of this theory are applied to two concrete problems, and conditions similar to the Nyquist theorem or Carson´s rule for FM modulation are derived for the cases of recovery of an input signal consisting of a main signal and a bandwidth of small feedback or feedforward signals and a bandlimited signal consisting of several harmonics of comparable magnitude. A rule of thumb, and conservative estimate of the bandwidth in both cases is one third of the carrier frequency (/spl omega//sub upper/<(1/3)/spl omega//sub c/). This research has been based on the premise that the results obtained will provide valuable insight into the general behavior 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.