获取开关变换器小信号模型的阶跃响应法

Step-Response Method for Obtaining Small-Signal Models of Switching Power Converters

文章讨论从阶跃响应波形中获取开关变换器小信号模型的方法。通过对处于稳态的变换器施加小信号阶跃扰动并将输出结果与原稳态输出作差,获得能正确反映该稳态工作点处小信号特性的阶跃响应波形;应用小信号激励和响应之间的线性关系可将阶跃响应波形换算为同一系统的斜坡响应波形;通过对斜坡响应波形等间隔采样并采用最小二乘法进行参数估计,可以拟合出系统的脉冲传递函数;由离散系统的脉冲传递函数可以导出连续系统小信号模型的解析表达式。文中给出建模过程和实例,测试结果与使用状态空间平均法所得结果的比较证明了该方法的有效性。

A small-signal modeling method for switching converters that use the step-response waveforms is discussed in this paper. The step-response waveforms can be obtained by disturbing a steady converter and finding the differences be- tween the disturbed- and undisturbed circuit. The step-response waveform can be converted to the ramp response waveform by the linear relationship between small-signal excitations and responses. By sampling the ramp response waveform at regu- lar intervals and using least squares method to the sampled data, the parameters of the impulse transfer function can be esti- mated. Finally, the continuous small-signal transfer function with analytical expressions can be easily transformed from the impulse transfer function. The detailed modeling process and several examples are presented in this paper, the validity of which is proved by comparisons between the results in this paper and those deduced by state-space averaging method.