Ripple compensation for a class-D amplifier

Cox, Stephen M.; du Toit Mouton, Hendrik

Abstract

This paper presents the first detailed mathematical analysis of the ripple compensation technique for reducing audio distortion in a class-D amplifier with negative feedback. The amplifier converts a relatively low-frequency audio signal to a high-frequency train of rectangular pulses whose widths are slowly modulated according to the audio signal (pulse-width modulation, PWM). Distortion manifests itself through unwanted audio-frequency harmonics that arise in the output due to nonlinearities inherent in the design. In this paper, we first develop a small-signal model, which describes the fate of small-amplitude perturbations to a constant input, and demonstrate how this traditional engineering tool may be extended to allow one to infer the most significant contributions to the full output in response to a general audio input. We then compute the audio output of the amplifier through a perturbation expansion based on the ratio between audio and switching frequencies. Our results explicitly demonstrate how the ripple compensation technique significantly linearizes the output, thereby reducing the distortion.

Citation

Cox, S. M., & du Toit Mouton, H. (2015). Ripple compensation for a class-D amplifier. SIAM Journal on Applied Mathematics, 75(4), https://doi.org/10.1137/140997695

• Journal Article Type: Article
• Acceptance Date: May 14, 2015
• Publication Date: Jul 14, 2015
• Deposit Date: Nov 12, 2015
• Publicly Available Date: Nov 12, 2015
• Journal: SIAM Journal on Applied Mathematics
• Print ISSN: 0036-1399
• Electronic ISSN: 1095-712X
• Publisher: Society for Industrial and Applied Mathematics
• Peer Reviewed: Peer Reviewed
• Volume: 75
• Issue: 4
• DOI: https://doi.org/10.1137/140997695
• Keywords: class-D amplifier, mathematical model, small-signal model, Apostol–Bernoulli functions, pulse-width modulation
• Public URL: https://nottingham-repository.worktribe.com/output/757028
• Publisher URL: http://epubs.siam.org/doi/10.1137/140997695
• Additional Information: First Published in SIAM Journal on Applied Mathematics in volume 75 number 4, 2015, published by the Society of Industrial and Applied Mathematics (SIAM). (c) 2015 Society for Industrial and Applied Mathematics.