恒定导通时间控制Buck变换器电感和负载电阻的稳定性机理

恒定导通时间(constant on-time,COT)控制Buck变换器的稳定性不仅受输出电容等效串联电阻(equivalent series resistance,ESR)的影响,还受电感和负载电阻的影响。为了研究电感和负载电阻的稳定性机理,建立了COT控制Buck变换器的分段线性模型。利用分岔图、特征根轨迹研究了输出电容ESR较小时COT控制Buck变换器随电感和负载电阻变化时的动力学特性。结果表明,随着电感减小或负载电阻增大,Buck变换器由阵发混沌状态经边界碰撞分岔进入到稳定的电感电流断续导电模式(discontinuous conduction mode,DCM)周期1状态。进一步,推导了确保变换器稳定工作的电感和负载电阻的临界表达式。最后,数值仿真和理论分析得到了实验结果的验证。研究结果可以有效地指导COT控制Buck变换器的电路参数设计。

Stability Mechanism of Inductance and Load Resistance in Constant On-Time Controlled Buck Converter

The stability of constant on-time (COT) controlled buck converter is not related to equivalent series resistance (ESR) of output capacitor, but also is greatly affected by variation of inductance and load resistance. To investigate the stability mechanism of inductance and load resistance, a piecewise smooth continuous model of the COT controlled buck converter is established. With variation of inductance and load resistance, the dynamical characteristics of the COT controlled buck converter with small output capacitor ESR are then studied by bifurcation diagrams and loci of eigenvalues. The results indicate that with the decrease of inductance or the increase of load resistance, the COT controlled buck converter enters stable period-1 state with inductor current discontinuous conduction mode (DCM) from intermittency chaos via border-collision bifurcation. Furthermore, the critical inductance and load resistance to ensure the converter operate in stable state is derived. Finally, the correctness of the numerical simulations and theoretical analyses is verified by the experimental results. The studying results in this paper can provide a guideline for the parameter design of the COT controlled buck converter.