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A second-order class-D audio amplifier

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


Stephen M. Cox

M.T. Tan

J. Yu


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.


Cox, S. M., Tan, M., & Yu, J. (2011). A second-order class-D audio amplifier. SIAM Journal on Applied Mathematics, 71(1),

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 0036-1399
Publisher Society for Industrial and Applied Mathematics
Peer Reviewed Peer Reviewed
Volume 71
Issue 1
Public URL
Publisher URL
Additional Information (c) SIAM


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