tps53315 mode pin

OK, here is my take on this (which will probably have to e sufficient as I do not believe any of the original development team is available for comment).

Generally speaking for DCAP 3 control, the LC corner frequency of the output filter has to be placed in the vicinity of the internal ripple injection zero frequency.  The LC filter provide a second order pole with 180 deg. of phase inversion.  Without the ripple injection zero, that would result in near 0 deg. phase margin.  The ripple injection zero provides some phase boost, 45 degrees at the zero frequency increasing towards 90 degrees above it.  For TPS53515 (which is what you reference in your attachment), Table 3 shows "recommended" component values based on the VOUT listed in column 1 and 8 A output, 12V and 600 khz Fsw.  For these results the inductor value is calculated using the % ripple  current shown.  Equation 3 gives the nominal Cout required, so the minimum is chosen as somewhat less and the loop response ins measured to verify stable operation (they most likely tried and rejected other values).  The "maximum" value is just an arbitrarily large 30 x 100 uF (who will realistically use that?...no one).  All this is verified by measurement.  They suggest to use double the RC time constant for maximum output cap design, but that doesn't really matter for practical purposes as who would ever design such a circuit?  I think your best bet is to use use EQ 3 to choose your output cap, and if you must go lower use Table 3 as a guideline for minimum capacitance.  Remember, you absolutely need to verify the loop performance of YOUR design to ensure it meets the criteria as outlined in the datasheet pages 17 and 18.  Let me know if you have further questions.