Analysis and Control of Period Doubling Bifurcation in Buck Converters Using Harmonic Balance

Period doubling bifurcation in buck convertersis studied by using the harmonic balance method.A simple dynamic model of a buck converter in continuous conduction modeunder voltage mode or current mode controlis derived.This model consists of the feedback connection of a linear system and a nonlinear one.An exact harmonic balance analysis is usedto obtain a necessary and sufficient condition fora period doubling bifurcation to occur.If such a bifurcation occurs,the analysis also provides information on its exact location.Using the condition for bifurcation,a feedforward control is designed thateliminates a period doubling bifurcation.This results in a wider range of allowed source voltage,and also in improved output voltage regulation

Bifurcation Boundary Conditions for Switching DC-DC Converters Under Constant On-Time Control

Sampled-data analysis and harmonic balance analysis are applied to analyze switching DC-DC converters under constant on-time control. Design-oriented boundary conditions for the period-doubling bifurcation and the saddle-node bifurcation are derived. The required ramp slope to avoid the bifurcations and the assigned pole locations associated with the ramp are also derived. The derived boundary conditions are more general and accurate than those recently obtained. Those recently obtained boundary conditions become special cases under the general modeling approach presented in this paper. Different analyses give different perspectives on the system dynamics and complement each other. Under the sampled-data analysis, the boundary conditions are expressed in terms of signal slopes and the ramp slope. Under the harmonic balance analysis, the boundary conditions are expressed in terms of signal harmonics. The derived boundary conditions are useful for a designer to design a converter to avoid the occurrence of the period-doubling bifurcation and the saddle-node bifurcation.Comment: Submitted to International Journal of Circuit Theory and Applications on August 10, 2011; Manuscript ID: CTA-11-016

Unified model of voltage/current mode control to predict saddle-node bifurcation

A unified model of voltage mode control (VMC) and current mode control (CMC) is proposed to predict the saddle-node bifurcation (SNB). Exact SNB boundary conditions are derived, and can be further simplified in various forms for design purpose. Many approaches, including steady-state, sampled-data, average, harmonic balance, and loop gain analyses are applied to predict SNB. Each approach has its own merits and complement the other approaches.Comment: Submitted to International Journal of Circuit Theory and Applications on December 23, 2010; Manuscript ID: CTA-10-025

Closed-Form Critical Conditions of Subharmonic Oscillations for Buck Converters

A general critical condition of subharmonic oscillation in terms of the loop gain is derived. Many closed-form critical conditions for various control schemes in terms of converter parameters are also derived. Some previously known critical conditions become special cases in the generalized framework. Given an arbitrary control scheme, a systematic procedure is proposed to derive the critical condition for that control scheme. Different control schemes share similar forms of critical conditions. For example, both V2 control and voltage mode control have the same form of critical condition. A peculiar phenomenon in average current mode control where subharmonic oscillation occurs in a window value of pole can be explained by the derived critical condition. A ripple amplitude index to predict subharmonic oscillation proposed in the past research has limited application and is shown invalid for a converter with a large pole.Comment: Submitted to an IEEE Journal on Dec. 23, 2011, and resubmitted to IEEE Transactions on Circuits and Systems-I on Feb. 14, 2012. My current six papers in arXiv have a common reviewe

Sampled-Data and Harmonic Balance Analyses of Average Current-Mode Controlled Buck Converter

Dynamics and stability of average current-mode control of buck converters are analyzed by sampled-data and harmonic balance analyses. An exact sampled-data model is derived. A new continuous-time model "lifted" from the sampled-data model is also derived, and has frequency response matched with experimental data reported previously. Orbital stability is studied and it is found unrelated to the ripple size of the current-loop compensator output. An unstable window of the current-loop compensator pole is found by simulations, and it can be accurately predicted by sampled-data and harmonic balance analyses. A new S plot accurately predicting the subharmonic oscillation is proposed. The S plot assists pole assignment and shows the required ramp slope to avoid instability.Comment: Submitted to International Journal of Circuit Theory and Applications on August 9, 2011; Manuscript ID: CTA-11-016

Closed-Form Critical Conditions of Saddle-Node Bifurcations for Buck Converters

A general and exact critical condition of saddle-node bifurcation is derived in closed form for the buck converter. The critical condition is helpful for the converter designers to predict or prevent some jump instabilities or coexistence of multiple solutions associated with the saddle-node bifurcation. Some previously known critical conditions become special cases in this generalized framework. Given an arbitrary control scheme, a systematic procedure is proposed to derive the critical condition for that control scheme.Comment: Submitted to IEEE Transactions on Automatic Control on Jan. 9, 2012. Seven of my arXiv manuscripts have a common reviewe

Using Nyquist or Nyquist-Like Plot to Predict Three Typical Instabilities in DC-DC Converters

By transforming an exact stability condition, a new Nyquist-like plot is proposed to predict occurrences of three typical instabilities in DC-DC converters. The three instabilities are saddle-node bifurcation (coexistence of multiple solutions), period-doubling bifurcation (subharmonic oscillation), and Neimark bifurcation (quasi-periodic oscillation). In a single plot, it accurately predicts whether an instability occurs and what type the instability is. The plot is equivalent to the Nyquist plot, and it is a useful design tool to avoid these instabilities. Nine examples are used to illustrate the accuracy of this new plot to predict instabilities in the buck or boost converter with fixed or variable switching frequency.Comment: Submitted to an IEEE journal in 201