Complex Behavior of Switching Power Converters

Tse, Chi Kong

doi:10.1201/9780203494554

Cited by 412 publications

(154 citation statements)

References 26 publications

Supporting

Mentioning

152

Contrasting

Order By: Relevance

“…As is evident from Figure 5, this instability occurs, as we demonstrate below, on the short time scale of the switching [10,11,16], so it cannot be captured by the analysis of section 3, which accommodates only variations on the audio time scale. We thus turn next to an analysis of the difference equations (2.12), (2.14), (2.15), and (2.16).…”

Section: In Each Case S(t) Is Given By (412) With Frequency 5khz (mentioning

confidence: 99%

A Second-Order Class-D Audio Amplifier

Cox¹,

Tan²,

Yu³

2011

SIAM J. Appl. Math.

View full text Add to dashboard Cite

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.Key words. class-D amplifier, mathematical model, pulse skipping, total harmonic distortion AMS subject classifications. 34E10, 37N20 DOI. 10.1137/1007883671. Introduction. Class-D amplifiers are used widely in modern electronic devices, such as laptops, mobile phones, and hearing aids, because they are particularly efficient. Their output takes the form of a high-frequency square wave whose switching times are modulated in such a way that the low-frequency components of the output correspond to the intended audio signal. The high-frequency switching components of the output are filtered out.For an open-loop class-D amplifier (i.e., a class-D amplifier without feedback), it is readily shown that no distortion is introduced into the audio range of the output signal by the pulse-width modulation (PWM) process [4,6,12,14]. However, due to nonidealities in practical designs (e.g., output-stage noise, component variation, or distortion in the carrier signal that drives the switching), it is desirable in practice to add a negative feedback loop to the design, but this inevitably introduces some distortion into the audio components of the output (see, for example, [15]). In this paper, we develop a mathematical model for a second-order class-D amplifier, in which a loop filter is configured as a second-order integrator. (For the purpose of our analysis, this second-order integrator is modeled as two first-order integrators connected in series.) We have previously derived similar models for first-order class-D amplifier designs [6], but the presentation here is more systematic and is extended to allow consideration of the stability of the analytical solutions that we develop; the question of their stability proves to be essential in explaining the observed behavior of the amplifier. A further motivation for the design considered here is that the secondorder integrator is now becoming much more prevalent than its first-order counterpart in state-of-art audio amplifier design, as it provides higher loop gain, which allows it to better overcome the nonlinearities inhe...

show abstract

Section: In Each Case S(t) Is Given By (412) With Frequency 5khz (mentioning

confidence: 99%

A Second-Order Class-D Audio Amplifier

Cox¹,

Tan²,

Yu³

2011

SIAM J. Appl. Math.

View full text Add to dashboard Cite

show abstract

“…This implies that it may be possible to study this behaviour of the converter using the so-called nonlinear "averaged model" . However, this model cannot fully unfold the complete dynamics of the system, as a) it ignores the fast scale phenomena induced by the switching [2] and b) in some converters (like the buck converter) the averaged model cannot even locate the existence of a saddle node bifurcation. Therefore it is imperative to validate the averaged model prior to any usage for the analysis and design of suitable control laws.…”

Section: Bifurcation Analysismentioning

confidence: 99%

“…It is an interesting control problem with special characteristics and challenges, such as hard state and control constraints, the need for a fast and accurate static and dynamic performance, robustness to unpredictable but bounded supply voltage and load variations, low complexity of implementation and corresponding low-cost hardware. The basic challenge is that switched-mode converters are highly nonlinear systems [1,2,3] hybrid in nature, since they involve high-frequency switching among two different modes of operation.…”

Section: Introductionmentioning

confidence: 99%

Robust constrained stabilization of boost DC–DC converters through bifurcation analysis

Yfoulis

Giaouris

Stergiopoulos

et al. 2015

Control Engineering Practice

View full text Add to dashboard Cite

This paper proposes a new methodology for designing robust affine state-feedback control laws, so that wide-range safe and efficient operation of switched-mode DC-DC boost converters is guaranteed. Several undesirable nonlinear phenomena such as unstable attractors and subharmonic oscillations are avoided through bifurcation analysis based on the bilinear averaged model of the converter. The control design procedure also relies on constrained stabilization principles and the generation of safety domains using piecewise linear Lyapunov functions, so that robustness to supply voltage and output load variations is ensured, while input saturation is avoided and additional state constraints are also respected. The technique has been numerically and experimentally validated.

show abstract

“…The origin of these maps lies in the representation of temporal evolutions that are inherently discrete as well as the analysis of oscillations in continuous dynamical systems via the Poincar e section. Among the extensive list of examples, it can be mentioned the population models in Biology, [1][2][3] the cardiac activity models in Medicine, [4][5][6] the structure markets in Economics, 7,8 the impact systems in Mechanics, 9,10 the modulated lasers in Physics, [11][12][13] the power converters in Electronics, 14,15 etc. In many of these applications, quadratic maps have played an important role in the description of the detected dynamical scenarios.…”

Section: Introductionmentioning

confidence: 99%

Exact period-four solutions of a family of n-dimensional quadratic maps via harmonic balance and Gröbner bases

D’Amico

Calandrini

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

Analytical solutions of the period-four orbits exhibited by a classical family of n-dimensional quadratic maps are presented. Exact expressions are obtained by applying harmonic balance and Gröbner bases to a single-input single-output representation of the system. A detailed study of a generalized scalar quadratic map and a well-known delayed logistic model is included for illustration. In the former example, conditions for the existence of bistability phenomenon are also introduced.

show abstract

Complex Behavior of Switching Power Converters

Cited by 412 publications

References 26 publications

A Second-Order Class-D Audio Amplifier

A Second-Order Class-D Audio Amplifier

Robust constrained stabilization of boost DC–DC converters through bifurcation analysis

Exact period-four solutions of a family of n-dimensional quadratic maps via harmonic balance and Gröbner bases

Contact Info

Product

Resources

About