优化带前馈电容的内置补偿-dc-dc转换器的瞬态响应资料.pdf

优化带前馈电容的内置补偿 DC-DC转换器的瞬态响应 Brian Butterfi eldPMP – 便携式电源 摘要 本应用报告阐述了如何选择内置补偿 dc-dc 电源的前馈电容值(Cff)以实现最优化的 瞬态响应应用报告的论述顺序提供了指向性，通过增加转换器的带宽，同时保 持足够的相位裕量以实现瞬态响应的优化本文档旨在辅助所有希望优化其内置 补偿 dc-dc 转换器运转时的瞬态响应的电源设计人员 简介 内置补偿 dc-dc 转换器尽可能的减少了设计人员必须选取的外部元件数量，从而节省了设计及调试流程的耗 时此类简化也从根本上制约了设计人员对转换器的瞬态响应进行优化的能力尽管如此，对于某些内置 补偿转换器而言，在反馈网络中采用前馈电容仍然是推荐的优化方式本文仅提供一般性的指南以辅助选 1 优化带前馈电容的内置补偿DC-DC转换器的瞬态响应 目录 1 简介 1 2 带或不带前馈电容的反馈网络 2 3 结论 11 4 参考文献 11 图表目录 1 两个偏置电阻所组成的、用于设定输出电压的反馈网络 2 2 标准反馈分压器的传递函数 2 3 带附加前馈电容的反馈网络 3 4 带前馈电容的标准反馈分压器传递函数 3 5 不带前馈电容的内置补偿转换器 4 6 Tip see the following Equation 1 and Equation 2. Increasing the value of Cff shifts the zero and pole in Equation 1 to lower frequencies, and decreasing the value Cff shifts the zero and pole to higher frequencies. The gain at dc is set by R1 and R2. The following equations calculate the pole, zero, and the dc gain of the feedback network as is shown in Figure 4. Equation 1 calculates the zero frequency based on the feedforward capacitor value and the top bias resistor, R1. fz is shown on the plot in Figure 4. Equation 2 calculates the pole frequency based on the feedforward capacitor value and both top and bottom bias resistors, R1 and R2. fp is shown in on the plot in Figure 4. Figure 4. Standard Feedback Divider With Feedfoward Capacitor Transfer Function To optimize transient response, a Cff value is chosen such that the gain and phase boost of the feedback increases the bandwidth of the converter, while still maintaining an acceptable phase margin. In general, larger values of Cff provide greater bandwidth improvements. However, if Cff is too large, the feedforward capacitor causes the loop gain to crossover too high in frequency and the Cff phase boost contribution is insufficient, resulting in unacceptable phase margin or instability. Recommended limitations of Cff is discussed later in this document. SLVA289–January 2008Optimizing Transient Response of Internally Compensated dc-dc Converters With Feedforward Capacitor3 Submit Documentation Feedback R1 470�k� C1 10�pF R2 180�k� VFB VOUTConverter fz� 1 2� � R1 � Cff (1) fp 1 2Cff 1 R2 1 R1 = x + () � (2) The�transfer�function�is�plotted�as: 40 20 -10 -20 Gc(f) c(f)� 1-10 -3 0.010.11101001-10 3 1-10 4 f/kHz 30 10 0 fp fz Feedback Network With and Without the Feedforward Capacitor Figure 3. Feedback Network With Addition of Feedforward Capacitor Although Cff introduces a gain boost after its zero frequency, loop phase boost is at a maximum between the zero and pole frequencies; see the following Equation 1 and Equation 2. Increasing the value of Cff shifts the zero and pole in Equation 1 to lower frequencies, and decreasing the value Cff shifts the zero and pole to higher frequencies. The gain at dc is set by R1 and R2. The following equations calculate the pole, zero, and the dc gain of the feedback network as is shown in Figure 4. Equation 1 calculates the zero frequency based on the feedforward capacitor value and the top bias resistor, R1. fz is shown on the plot in Figure 4. Equation 2 calculates the pole frequency based on the feedforward capacitor value and both top and bottom bias resistors, R1 and R2. fp is shown in on the plot in Figure 4. Figure 4. Standard Feedback Divider With Feedfoward Capacitor Transfer Function To optimize transient response, a Cff value is chosen such that the gain and phase boost of the feedback increases the bandwidth of the converter, while still maintaining an acceptable phase margin. In general, larger values of Cff provide greater bandwidth improvements. However, if Cff is too large, the feedforward capacitor causes the loop gain to crossover too high in frequency and the Cff phase boost contribution is insufficient, resulting in unacceptable phase margin or instability. Recommended limitations of Cff is discussed later in this document. SLVA289–January 2008Optimizing Transient Response of Internally Compensated dc-dc Converters With Feedforward Capacitor3 Submit Documentation Feedback 图. 带附加前馈电容的反馈网络 Cff 在零点频率之后引入了一个增益增量，而环路相位增量的最大值则介于零点与极点频率之间；敬请参见 下方的公式 1 及公式 2。

增加 Cff 的值将使零点和极点向低频偏移，如公式 1 所示，降低 Cff 的值则使得零点 和极点向高频偏移直流增益由 R1 及 R2 确定下列公式可用于计算如图 4 所示反馈网络的极点、零点及 直流增益 公式 1 基于反馈电容值及上偏压电阻 R1 计算零点频率fz 如图 4 的曲线图所示 公式 2 基于反馈电容值及上、下方的偏压电阻（R1 及 R2）计算极点频率 Fp 如图 4 的曲线图所示 为优化瞬态响应，Cff 值是必须进行选择的，反馈的增益及相位增量在增大转换器带宽的同时，仍保持了可 接受的相位裕量一般来说，较大的 Cff 值提供了更大的带宽改善然而，若 Cff 值过大，前 馈电容将导 致环路频域的增益穿越至太高的值，而 Cff 相位增量的上涨则不够充分，导致相位裕量超过了可接受范围或 不稳定Cff 推荐的极限值将在本文档后续部分讨论 图 . 带前馈电容的标准反馈分压器传递函数 优化带前馈电容的内置补偿DC-DC转换器的瞬态响应 带或不带前馈电容的反馈网络 2.1Feedforward Capacitor Value Optimization Process 2.2Determining the Crossover Frequency Open Feedback Network With and Without the Feedforward Capacitor The following process outlines a step-by-step procedure for optimizing the feedforward capacitor. 1. Determine the crossover frequency of an internally compensated dc-dc converter with an unpopulated feedforward capacitor (f_nocff). In certain circumstance, this can be calculated, but for this application report, this op。