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A third-order class-D amplifier with and without ripple compensation (2018)
Journal Article
Cox, S. M., & du Toit Mouton, H. (2018). A third-order class-D amplifier with and without ripple compensation. Physica D: Nonlinear Phenomena, 372, https://doi.org/10.1016/j.physd.2018.01.012

We analyse the nonlinear behaviour of a third-order class-D amplifier, and demonstrate the remarkable effectiveness of the recently introduced ripple compensation (RC) technique in reducing the audio distortion of the device. The amplifier converts a... Read More about A third-order class-D amplifier with and without ripple compensation.

Small-signal analysis of naturally-sampled single-edge PWM control loops (2017)
Journal Article
Mouton, T., Cox, S., McGrath, B., Risbo, L., & Putzeys, B. (2017). Small-signal analysis of naturally-sampled single-edge PWM control loops. IEEE Transactions on Power Electronics, 33(1), 51-64. https://doi.org/10.1109/TPEL.2017.2666720

This paper presents a simple method to analyse the behaviour of feedback loops that contain a naturally-sampled single-edge pulse-width modulator. A small-signal model is derived by means of simple geometric arguments. It is shown how this small-sign... Read More about Small-signal analysis of naturally-sampled single-edge PWM control loops.

Analysis of a hysteresis-controlled self-oscillating class-D amplifier (2016)
Journal Article
Cox, S. M., Yu, J., Goh, W. L., & Tan, M. T. (in press). Analysis of a hysteresis-controlled self-oscillating class-D amplifier. IMA Journal of Applied Mathematics, 82(2), https://doi.org/10.1093/imamat/hxw053

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... Read More about Analysis of a hysteresis-controlled self-oscillating class-D amplifier.

Ripple compensation for a class-D amplifier (2015)
Journal Article
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

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-fr... Read More about Ripple compensation for a class-D amplifier.

Orientation-Dependent Pinning and Homoclinic Snaking on a Planar Lattice (2015)
Journal Article
Dean, A. D., Matthews, P. C., Cox, S. M., & King, J. R. (2015). Orientation-Dependent Pinning and Homoclinic Snaking on a Planar Lattice. SIAM Journal on Applied Dynamical Systems, 14(1), 481-521. https://doi.org/10.1137/140966897

We study homoclinic snaking of one-dimensional, localized states on two-dimensional, bistable lattices via the method of exponential asymptotics. Within a narrow region of parameter space, fronts connecting the two stable states are pinned to the und... Read More about Orientation-Dependent Pinning and Homoclinic Snaking on a Planar Lattice.

Dead-time effects on the voltage spectrum of a PWM inverter (2013)
Journal Article
Moore, D. C., Odavic, M., & Cox, S. M. (2014). Dead-time effects on the voltage spectrum of a PWM inverter. IMA Journal of Applied Mathematics, 79(6), https://doi.org/10.1093/imamat/hxt006

An inverter converts a direct-current power supply to an alternating-current power supply. This con- version is achieved by switching the output between the inputs at high frequency. The resulting output voltage may be described by a high-frequency t... Read More about Dead-time effects on the voltage spectrum of a PWM inverter.

Intrinsic distortion of a fully differential BD-modulated Class-D amplifier with analog feedback (2013)
Journal Article
Cox, S. M., Yu, J., Goh, W., & Tan, M. (2013). Intrinsic distortion of a fully differential BD-modulated Class-D amplifier with analog feedback. IEEE Transactions on Circuits and Systems I: Regular Papers, 60(1), https://doi.org/10.1109/TCSI.2012.2215713

This paper presents a mathematical analysis of a fully differential BD-modulated Class-D amplifier with analog feedback, i.e., one having a bridge-tied-load output configuration with negative feedback and ternary PWM signal. Notwithstanding the highl... Read More about Intrinsic distortion of a fully differential BD-modulated Class-D amplifier with analog feedback.

Time-domain analysis of intermodulation distortion of closed-loop Class D amplifiers (2012)
Journal Article
Yu, J., Tan, M., Cox, S. M., & Goh, W. (2012). Time-domain analysis of intermodulation distortion of closed-loop Class D amplifiers. IEEE Transactions on Power Electronics, 27(5), https://doi.org/10.1109/TPEL.2011.2171196

This paper presents a time-domain analysis of the intermodulation distortion (IMD) of a closed-loop Class D amplifier with either 1st-order or 2nd-order loop filter. The derived expression for the IMD indicates that there exist significant 3rd-order... Read More about Time-domain analysis of intermodulation distortion of closed-loop Class D amplifiers.

A second-order class-D audio amplifier (2011)
Journal Article
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

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-... Read More about A second-order class-D audio amplifier.

Voltage and current spectra for matrix power converters (2009)
Journal Article
Cox, S. M., & Creagh, S. C. (2009). Voltage and current spectra for matrix power converters. SIAM Journal on Applied Mathematics, 69(5), https://doi.org/10.1137/080718863

Matrix power converters are used for transforming one alternating-current power supply to another, with different peak voltage and frequency. There are three input lines, with sinusoidally varying voltages which are 120? out of phase one from another... Read More about Voltage and current spectra for matrix power converters.

Nonlinear development of matrix-converter instabilities (2009)
Journal Article
Cox, S. M., & Clare, J. C. (2009). Nonlinear development of matrix-converter instabilities. Journal of Engineering Mathematics, https://doi.org/10.1007/s10665-009-9325-8

Matrix converters convert a three-phase alternating-current power supply to a power supply of a different peak voltage and frequency, and are an emerging technology in a wide variety of applications. However, they are susceptible to an instability,... Read More about Nonlinear development of matrix-converter instabilities.

Large Rayleigh number thermal convection: heat flux predictions and strongly nonlinear solutions (2009)
Journal Article
Chini, G. P., & Cox, S. M. (2009). Large Rayleigh number thermal convection: heat flux predictions and strongly nonlinear solutions. Physics of Fluids, 21, https://doi.org/10.1063/1.3210777

We investigate the structure of strongly nonlinear Rayleigh–Bénard convection cells in the asymptotic limit of large Rayleigh number and fixed, moderate Prandtl number. Unlike the flows analyzed in prior theoretical studies of infinite Prandtl number... Read More about Large Rayleigh number thermal convection: heat flux predictions and strongly nonlinear solutions.

A mixer design for the pigtail braid (2008)
Journal Article
Binder, B. J., & Cox, S. M. (2008). A mixer design for the pigtail braid. Fluid Dynamics Research, 40(1), 34-44. https://doi.org/10.1016/j.fluiddyn.2006.09.001

The stirring of a body of viscous fluid using multiple stirring rods is known to be particularly effective when the rods trace out a path corresponding to a nontrivial mathematical braid. The optimal braid is the so-called "pigtail braid", in which t... Read More about A mixer design for the pigtail braid.

Conditional moment closure for chemical reactions in laminar chaotic flows (2007)
Journal Article
Vikhansky, A., & Cox, S. M. (2007). Conditional moment closure for chemical reactions in laminar chaotic flows. AIChE Journal, 53(1),

We implement conditional moment closure (CMC) for simulation of chemical reactions in laminar chaotic flows. The CMC approach predicts the expected concentration of reactive species, conditional upon the concentration of a corresponding nonreactive s... Read More about Conditional moment closure for chemical reactions in laminar chaotic flows.

Two-dimensional Stokes flow driven by elliptical paddles (2007)
Journal Article
Cox, S. M., & Finn, M. D. (2007). Two-dimensional Stokes flow driven by elliptical paddles. Physics of Fluids, 19(11), https://doi.org/10.1063/1.2789970

A fast and accurate numerical technique is developed for solving the biharmonic equation in a multiply connected domain, in two dimensions. We apply the technique to the computation of slow viscous flow (Stokes flow) driven by multiple stirring rods.... Read More about Two-dimensional Stokes flow driven by elliptical paddles.

Persistent localized states for a chaotically mixed bistable reaction (2006)
Journal Article
Cox, S. M. (2006). Persistent localized states for a chaotically mixed bistable reaction. Physical Review E, 74(5),

We describe the evolution of a bistable chemical reaction in a closed two-dimensional chaotic laminar flow, from a localized initial disturbance. When the fluid mixing is sufficiently slow, the disturbance may spread and eventually occupy the entire... Read More about Persistent localized states for a chaotically mixed bistable reaction.

Class-D audio amplifiers with negative feedback (2006)
Journal Article
Cox, S. M., & Candy, B. H. (2006). Class-D audio amplifiers with negative feedback. SIAM Journal on Applied Mathematics, 66(2),

There are many different designs for audio amplifiers. Class-D, or switching, amplifiers generate their output signal in the form of a high-frequency square wave of variable duty cycle (ratio of on time to off time). The square-wave nature of the ou... Read More about Class-D audio amplifiers with negative feedback.

A bistable reaction-diffusion system in a stretching flow (2006)
Journal Article
Cox, S. M., & Gottwald, G. A. (2006). A bistable reaction-diffusion system in a stretching flow. Physica D: Nonlinear Phenomena, 216(2),

We examine the evolution of a bistable reaction in a one-dimensional stretching flow, as a model for chaotic advection. We derive two reduced systems of ordinary differential equations (ODEs) for the dynamics of the governing advection-reaction-diffu... Read More about A bistable reaction-diffusion system in a stretching flow.

Reduced models of chemical reaction in chaotic flows (2006)
Journal Article
Vikhansky, A., & Cox, S. M. (2006). Reduced models of chemical reaction in chaotic flows. Physics of Fluids, 18(3), https://doi.org/10.1063/1.2182373

We describe and evaluate two reduced models for nonlinear chemical reactions in a chaotic laminar flow. Each model involves two separate steps to compute the chemical composition at a given location and time. The “manifold tracking model” first track... Read More about Reduced models of chemical reaction in chaotic flows.

Chaotic mixing of a competitive-consecutive reaction (2004)
Journal Article
Cox, S. M. (2004). Chaotic mixing of a competitive-consecutive reaction. Physica D: Nonlinear Phenomena, 199(3-4), 369-386. https://doi.org/10.1016/j.physd.2004.08.030

The evolution of a competitive-consecutive chemical reaction is computed numerically in a two-dimensional chaotic fluid flow with initially segregated reactants. Results from numerical simulations are used to evaluate a variety of reduced models c... Read More about Chaotic mixing of a competitive-consecutive reaction.