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 (omega(upper) < (1/3)omega(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.