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

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 sin...

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Main Authors: Cox, Stephen M., Yu, Jun, Goh, Wang Ling, Tan, Meng Tong
Format: Article
Published: Oxford University Press 2016
Subjects:
Online Access:https://eprints.nottingham.ac.uk/38819/
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author Cox, Stephen M.
Yu, Jun
Goh, Wang Ling
Tan, Meng Tong
author_facet Cox, Stephen M.
Yu, Jun
Goh, Wang Ling
Tan, Meng Tong
author_sort Cox, Stephen M.
building Nottingham Research Data Repository
collection Online Access
description 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.
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spelling nottingham-388192020-05-04T18:24:27Z https://eprints.nottingham.ac.uk/38819/ Analysis of a hysteresis-controlled self-oscillating class-D amplifier Cox, Stephen M. Yu, Jun Goh, Wang Ling Tan, Meng Tong 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. Oxford University Press 2016-12-26 Article PeerReviewed Cox, Stephen M., Yu, Jun, Goh, Wang Ling and Tan, Meng Tong (2016) Analysis of a hysteresis-controlled self-oscillating class-D amplifier. IMA Journal of Applied Mathematics, 82 (2). pp. 355-370. ISSN 1464-3634 Class-D amplifier Mathematical model Astable integrating modulator Hysteresis-controlled Self-oscillating modulator Hysteresis comparator http://imamat.oxfordjournals.org/content/early/2016/12/25/imamat.hxw053 doi:10.1093/imamat/hxw053 doi:10.1093/imamat/hxw053
spellingShingle Class-D amplifier
Mathematical model
Astable integrating modulator
Hysteresis-controlled Self-oscillating modulator
Hysteresis comparator
Cox, Stephen M.
Yu, Jun
Goh, Wang Ling
Tan, Meng Tong
Analysis of a hysteresis-controlled self-oscillating class-D amplifier
title Analysis of a hysteresis-controlled self-oscillating class-D amplifier
title_full Analysis of a hysteresis-controlled self-oscillating class-D amplifier
title_fullStr Analysis of a hysteresis-controlled self-oscillating class-D amplifier
title_full_unstemmed Analysis of a hysteresis-controlled self-oscillating class-D amplifier
title_short Analysis of a hysteresis-controlled self-oscillating class-D amplifier
title_sort analysis of a hysteresis-controlled self-oscillating class-d amplifier
topic Class-D amplifier
Mathematical model
Astable integrating modulator
Hysteresis-controlled Self-oscillating modulator
Hysteresis comparator
url https://eprints.nottingham.ac.uk/38819/
https://eprints.nottingham.ac.uk/38819/
https://eprints.nottingham.ac.uk/38819/