A second-order class-D audio amplifier

Cox, Stephen M.; Tan, M.T.; Yu, J.

Abstract

Class-D audio amplifiers are particularly efficient, and this efficiency has led to their ubiquity in a wide range of modern electronic appliances. Their output takes the form of a high-frequency square wave whose duty cycle (ratio of on-time to off-time) is modulated at low frequency according to the audio signal. A mathematical model is developed here for a second-order class-D amplifier design (i.e., containing one second-order integrator) with negative feedback. We derive exact expressions for the dominant distortion terms, corresponding to a general audio input signal, and confirm these predictions with simulations. We also show how the observed phenomenon of “pulse skipping” arises from an instability of the analytical solution upon which the distortion calculations are based, and we provide predictions of the circumstances under which pulse skipping will take place, based on a stability analysis. These predictions are confirmed by simulations.

Citation

Cox, S. M., Tan, M., & Yu, J. (2011). A second-order class-D audio amplifier. SIAM Journal on Applied Mathematics, 71(1), https://doi.org/10.1137/100788367

• Journal Article Type: Article
• Publication Date: Jan 1, 2011
• Deposit Date: Feb 9, 2013
• Publicly Available Date: Feb 9, 2013
• 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: 71
• Issue: 1
• DOI: https://doi.org/10.1137/100788367
• Public URL: https://nottingham-repository.worktribe.com/output/1010535
• Publisher URL: http://dx.doi.org/10.1137/100788367
• Additional Information: (c) SIAM