Analysis of a hysteresis-controlled self-oscillating class-D amplifier

Abstract

This paper gives the first systematic perturbation analysis of the audio distortion and mean switching period for a self-oscillating class-D amplifier. Explicit expressions are given for all the principal components of audio distortion, for a general audio input signal; the specific example of a sinusoidal input is also discussed in some detail, yielding an explicit closed-form expression for the total harmonic distortion (THD). A class-D amplifier works by converting a low-frequency audio input signal to a high-frequency train of rectangular pulses, whose widths are slowly modulated according to the audio signal. The audiofrequency components of the pulse-train are designed to agree with those of the audio signal. In many varieties of class-D amplifier, the pulse-train is generated using a carrier wave of fixed frequency, well above the audio range. In other varieties, as here, there is no such fixed-frequency clock, and the local frequency of the pulse-train varies in response to the audio input. Such self-oscillating designs pose a particular challenge for comprehensive mathematical modelling; we show that in order to properly account for the local frequency variations, a warped-time transformation is necessary. The systematic nature of our calculation means it can potentially be applied to a range of other self-oscillating topologies. Our results for a general input allow ready calculation of distortion diagnostics such as the intermodulation distortion (IMD), which prior analyses, based on sinusoidal input, cannot provide.