Research Repository

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Analysis of Low-Frequency-Oscillations in Single-Phase AC Systems by LTP Theory (2018)
Conference Proceeding
Salis, V., Costabeber, A., Zanchetta, P., & Cox, S. (2018). Analysis of Low-Frequency-Oscillations in Single-Phase AC Systems by LTP Theory. In 2018 20th European Conference on Power Electronics and Applications (EPE'18 ECCE Europe)

The paper presents the analysis of a single-phase active rectifier, with DC constant power load, affected by Low-Frequency Oscillation (LFO) behaviour. Conventional LTI analysis tools might fail to reveal the LFO phenomenon, whereas the LTP (Linear T... Read More

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, doi:10.1016/j.physd.2018.01.012. ISSN 0167-2789

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

Stability boundary analysis in single-phase grid-connected inverters with PLL by LTP theory (2017)
Journal Article
Salis, V., Costabeber, A., Cox, S. M., Zanchetta, P., & Formentini, A. (2018). Stability boundary analysis in single-phase grid-connected inverters with PLL by LTP theory. IEEE Transactions on Power Electronics, 33(5), doi:10.1109/TPEL.2017.2714860. ISSN 0885-8993

Stability analysis of power converters in AC net¬works is complex due to the non-linear nature of the conversion systems. Whereas interactions of converters in DC networks can be studied by linearising about the operating point, the extension of the... Read More

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), doi:10.1109/TPEL.2017.2666720. ISSN 0885-8993

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

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), doi:10.1093/imamat/hxw053. ISSN 0272-4960

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

Stability analysis of single-phase grid-feeding inverters with PLL using Harmonic Linearisation and Linear Time Periodic (LTP) theory (2016)
Conference Proceeding
Salis, V., Costabeber, A., Zanchetta, P., & Cox, S. M. (2016). Stability analysis of single-phase grid-feeding inverters with PLL using Harmonic Linearisation and Linear Time Periodic (LTP) theory

A general method for the stability analysis of power converters is presented in this paper. The method is based on Harmonic Linearisation and Linear Time Periodic (LTP) analysis techniques and a single-phase grid-feeding inverter with PLL is consider... Read More

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), doi:10.1137/140966897. ISSN 1536-0040

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

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), doi:10.1093/imamat/hxt006. ISSN 0272-4960

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

Intrinsic distortion of a fully differential BD-modulated Class-D amplifier with analog feedback (2013)
Journal Article
Class-D amplifier with analog feedback. IEEE Transactions on Circuits and Systems I: Regular Papers, 60(1), doi:10.1109/TCSI.2012.2215713. ISSN 1549-8328

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

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), doi:10.1109/TPEL.2011.2171196. ISSN 0885-8993

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

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, doi:10.1007/s10665-009-9325-8. ISSN 0022-0833

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

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), doi:10.1137/080718863. ISSN 0036-1399

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

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, doi:10.1063/1.3210777. ISSN 1070-6631

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

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), doi:10.1063/1.2789970. ISSN 1070-6631

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