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A nonlinear time‐varying map of a buck power‐switching amplifier for wide band tracking applications

A nonlinear time‐varying map of a buck power‐switching amplifier for wide band tracking applications Purpose – The purpose of this paper is to characterize the nonlinear dynamical behaviour of a buck‐based power‐switching amplifier controlled by fixed frequency and pulse width modulation with a proportional‐integral compensator. The system has two forcing frequencies and one natural frequency and therefore it is characterized by three different scales of time. When the frequencies are far one from the other, quasi‐static approximation can be used. However, as the switching and the modulating frequencies become closer, this approximation is not valid and the results based on it lead to erroneous conclusions about the dynamics of the system. Design/methodology/approach – A discrete time approach is used to reveal the interesting nonlinear phenomena that the system can exhibit. From numerical simulations using the switched model, it is shown that the system can present period‐doubling bifurcation at the fast scale (switching frequency). Findings – An exact solution discrete‐time model is derived, able to predict accurately the nonlinear dynamical behaviour of the system. Originality/value – The discrete time model is obtained without making quasi‐static approximation. The exact switched model is used to validate the discrete‐time model obtained. Finally, the effect of the switching frequency instabilities on the output voltage spectrum has been explored. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering Emerald Publishing

A nonlinear time‐varying map of a buck power‐switching amplifier for wide band tracking applications

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Publisher
Emerald Publishing
Copyright
Copyright © 2010 Emerald Group Publishing Limited. All rights reserved.
ISSN
0332-1649
DOI
10.1108/03321641011007984
Publisher site
See Article on Publisher Site

Abstract

Purpose – The purpose of this paper is to characterize the nonlinear dynamical behaviour of a buck‐based power‐switching amplifier controlled by fixed frequency and pulse width modulation with a proportional‐integral compensator. The system has two forcing frequencies and one natural frequency and therefore it is characterized by three different scales of time. When the frequencies are far one from the other, quasi‐static approximation can be used. However, as the switching and the modulating frequencies become closer, this approximation is not valid and the results based on it lead to erroneous conclusions about the dynamics of the system. Design/methodology/approach – A discrete time approach is used to reveal the interesting nonlinear phenomena that the system can exhibit. From numerical simulations using the switched model, it is shown that the system can present period‐doubling bifurcation at the fast scale (switching frequency). Findings – An exact solution discrete‐time model is derived, able to predict accurately the nonlinear dynamical behaviour of the system. Originality/value – The discrete time model is obtained without making quasi‐static approximation. The exact switched model is used to validate the discrete‐time model obtained. Finally, the effect of the switching frequency instabilities on the output voltage spectrum has been explored.

Journal

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic EngineeringEmerald Publishing

Published: Jan 1, 2010

Keywords: Tracking; Switching systems; Amplifiers; Modelling; Simulation; Discrete control systems

References