TPS546D24A: Cout on Calculator

Nathan Adams2 

Cell B38 - Output Capacitance to meet specified ripple uses an equation that does not consider the multi-phase ripple cancellation.  It is looking at the per-phase inductor ripple current and reflecting that into a ripple voltage.  In that way it is based on total Cout, but is significantly higher that what would be needed in a multi-phase configuration due to inductor current ripple cancellation.

In a multi-phase converter, the net current into the output capacitance is the sum of all inductor currents, but while one inductor's current is rising, some, or all of the other phases inductor currents are falling.

For Duty Cycles less than 1/N, where N is the number of phases, the net output ripple current is Ipk-pk * 1/N * (1-N*D)

Yes, that number drops to 0 at D = 1/N.  In theory, a multi-phase converter operating at D = 1/N does not need any output capacitance, since the AC currents of all of the phases will sum to zero.  In practice, small errors or offsets in the AC ripples have proven this theory to be impractical with real hardware.