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D-CAP2 Frequency Response Model.pdf

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Application Report SLVA546 – January 2013 1 D-CAP2TM Frequency Response Model based on frequency domain analysis of Fixed On-Time with Bottom Detection having Ripple Injection Author: Toshiyuki (Rick) Zaitsu, Sales and Marketing, Power Technologist, TI-Japan Co-Author: Katsuya Goto, Takahiro Miyazaki, Digital Consumer Products, Junichi Yamamoto, Sales and Marketing, TI-Japan ABSTRACT Hysteretic control [2], which is basically non-linear control, has become an important control method due to its fast transient response. Normal hysteretic control requires a relatively high-ESR output capacitor. Adding ripple injection to hysteretic control allows the use of low-ESR ceramic output capacitors [3]-[6]. A “Fixed on-time with bottom detection having a ripple injection” control topology is shown in Figure 1. This topology, which is a type of hysteretic control, became popular due to pseudo fixed PWM frequency operation along with compatibility with low-ESR ceramic output capacitors. It is interesting that this control method behaves like linear control, showing similarity to a frequency response (bode-plot) of voltage mode control while keeping wide loop bandwidth, fbw. The frequency domain analysis of the “fixed on-time with bottom detection having ripple injection” is carried out [1] for the optimal DC-DC converter design based on the assumption of (a) Averaged model is applicable to a “small-signal analysis” for frequencies less than the switching frequency and, (b) injected ripple voltage is small compared to reference voltage. As a result, the comparator with ripple injection shows single zero (1st order lead system) characteristics. The open loop transfer function of the converter is expressed as equation (1). Figure 2 shows the approximated curve of the frequency response (bode-plot) based on equation (1). The phase increases up toward +90 degrees due to the single zero, and is a major contributor for the system stability wi
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