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Enric Rodríguez Vilamitjana

Ph.D. Thesis title:
Design-oriented model for predicting and controlling fast-scale instabilities in switching converters. Application to advanced power management integrated circuits 


Enric Rodríguez Vilamitjana



Dr. Eduard Alarcón /Abdelali El Aroudi

Reading day:

28th February 2011 


Trends in battery-operated portable applications require further miniaturization and eventually on-chip integration of power processing circuits along with their optimum power management control circuits, considered as key components in on-chip power subsystems which have a high impact upon the overall system in terms of size and efficiency.


On-chip power management subsystems, both in regulation and more sophisticated functionalities as wideband tracking, are ideally based on power switching converters, paradigm of high efficiency circuits. These subsystems, due to their nonlinear switched dynamic nature, can exhibit various instabilities which are mainly classified as slow-scale and fast-scale instabilities, the latter also known as subharmonic oscillations. The prediction of slow-scale instabilities can be carried out by conventional averaged dynamic models, which are derived form a simple mathematical circuit analysis and have a clear design-oriented standpoint, but due to their averaged nature, they fail to predict fast-scale instabilities. Alternatively, the prediction of the overall stability boundaries within the complete design space, encompassing fast-scale subharmonic oscillations, has hitherto been addressed from an analytic standpoint based on the discrete-time model, which are based on complex analysis that yields accurate prediction results but lacks of a circuit standpoint and hence are not aligned with a design-oriented use.


In this thesis the effect of different system parameters upon the stability boundaries is explored, demonstrating that trends towards integration, namely the reduction of reactive component size or a decrease of the relative switching frequency compared to the converter natural dynamics leads to the exhibition of fast-scale instabilities. As far as characterization is concerned, a two-fold approach has been considered both exploring the complete parameter design space of the switching regulator and categorizing it in terms of which type of nonlinear dynamic performance the circuit exhibits (design space characterization), as well as providing a novel characterization of the electrical behaviour for the different dynamic modes in terms of electrical performance metrics connatural to a power processing circuit, such as voltage ripple, average switching frequency and spectra (electrical characterization).


With the aim of having a design-oriented circuit-based model for predicting subharmonic instabilities, the thesis proposes a novel approach based on considering the ripple component at the PWM modulator input as an index to predict the fast-scale stability boundary -in the particular case of a voltage-mode buck converter in continuous conduction mode, a representative case of widespread use in battery-operated applications-. This ripple-based instability index has been validated both from the instantaneous nonlinear dynamic state equations solved numerically as well as through  experimental prototypes. Finally a bridge between the ripple-based index approach and the discrete-time model is established though relating the ripple and the control signal slope at the switching instant. The approach has been extended to the discontinuous conduction-mode and to current-mode control, demonstrating the general purpose of the ripple-based fast-scale instability prediction approach. A design-oriented comprehensive frequency domain model able to concurrently predict both slow scale and fast scale instabilities through the combined application of averaged models and the ripple-based approach closes this part.


Complementarily to the prediction of fast-scale stability boundary, fast-scale instability controllers or chaos controllers are studied, first revisiting the operating principle of already existing delay-based controllers, afterwards proposing and analyzing simpler implementation-friendly chaos controllers. Under the integrated power management perspective, the thesis extends them taking into account other power processor metrics such as output ripple or transient response, thereby proposing a novel controller that, apart from improving fast-scale stability boundary, allows reducing reactive components size and the output voltage ripple.


Finally, the thesis tackles the fast-scale instabilities in more advanced topologies and functionalities, which are representative of advanced power management circuits. First, for a multilevel converter, demonstrating that its inherent lower ripple behaviour makes it less prone to exhibit fast-scale instabilities and hence a better candidate to integration, and second for a wideband switching power amplifier, exploring its nonlinear dynamic phenomena and demonstrating that in the case of a single-tone modulation with a frequency close to the filter and switching frequencies, the fast scale stability boundary condition for regulation application is a sufficient condition to guarantee stability over the entire reference period for tracking applications.