Design and analysis of ripple-based controllers for buck converters based on discrete modeling and Floquet theory

Abstract

Ripple-based controls can strongly reduce the required output capacitance in PowerSoC converter thanks to a very fast dynamic response. Unfortunately, these controls are prone to sub-harmonic oscillations and several parameters affect the stability of these systems. This paper derives and validates a simulation-based modeling and stability analysis of a closed-loop V 2 Ic control applied to a 5 MHz Buck converter using discrete modeling and Floquet theory to predict stability. This allows the derivation of sensitivity analysis to design robust systems. The work is extended to different V 2 architectures using the same methodology.

A New Multiple-Frequency Small-Signal Model for High-Bandwidth Computer V-Core Regulator Applications

“…By the same approach, the Fourier coefficient of the perturbed vc1(t) can be shown equaling to Therefore, (16) can be rewritten as (18). One can see from (18) that d(fm) consists of terms.…”

“…Average model has been used for many years in other applications [11]- [17], but it is accurate only for a design with low bandwidth/switching frequency ratio. There are other approaches [18]- [19] intending to deal with the same issue but are generally deviating from small-signal concept and hard to use for engineers. To increase the model accuracy for a high-ratio application, a two-frequency model was proposed and verified in [20].…”

Bifurcation Mechanism and Stabilization of V2C Controlled Buck Converter

“…The sub-harmonic oscillation behavior is illustrated and the slope compensation is introduced to control it [17]. The sub-harmonic oscillation of the power regulator affected by the ESR of the output capacitor has been investigated in [18], however, the influences of voltage feedback coefficient on stability property is not considered, nor did control method of stabilizing the converter system is addressed. The mechanism of bifurcation and chaos belong to the V 2 C controlled buck converter are still open problems.…”

Comparison of the behavior of voltage mode, V² and V²I<inf>c</inf> control of a buck converter for a very fast and robust dynamic response

“…The dynamic behavior of power converters can be accurately modeled by means of Discrete Modeling together with Floquet theory [11]. Not only a discrete model of the form of Xk+i = f(xk) can be derived but the whole time-domain waveform can be reconstructed.…”

“…Not only a discrete model of the form of Xk+i = f(xk) can be derived but the whole time-domain waveform can be reconstructed. The stability of the power converter can be analyzed by means of the Floquet theory which is able to predict sub-harmonic oscillations [11]. The major advantages of these techniques are the accuracy, the simplicity of including parasitic elements and the extension of the methodology to other controls.…”