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According to this application note from Texas Instruments, in the design of the output filter for a multiphase buck converter there are basically two ways of choosing the output capacitor. The first and most common is to use the condition of output voltage ripple, i.e., to apply the following expressions $$C = \frac{\Delta i_L}{8\times f_{sw}\times\Delta v_o}$$ The second is to use the transient response using the expressions shown in the figure below. enter image description here My question is related to the second method. For me to obtain the transient response, I need to insert the controller, but for me to design the controller I need the value of output capacitance to obtain the converter's transfer function. So my question is, am I correct to think that way? If not, what value of capacitor should I use first? The one that comes from the output voltage ripple condition?

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Think of these two values as lower limits for the value of the output capacitance.

Note that the second method does not require you to specify the transient settling time. The calculation is for the additional charge to be supplied by the output capacitor to maintain a constant voltage. You would need an output capacitor higher than all the three values i.e., voltage ripple, undershoot and overshoot. Once you finalize this capacitance, you can proceed with designing your controller.

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