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TPS53315 with ceramic capacitors: datasheet error and lack of a parameter to design

Other Parts Discussed in Thread: TPS53315

Hello forum members!

I am experiencing problems to design a power stage with TPS53315 DCDC regulator with ceramic output capacitors.

in the Adaptive ON TIME DCAP control section on page 18 is written:
"The adaptive on-time control adjusts the on-time to be inversely proportional to the input voltage
and proportional to the output voltage" and then the following equation is the opposite: Ton proportional Vin and inversely proportional to Vout. As far as I remember in a Buck converter the aim is to maintain the Vout proportional to the Ton/Switching period.

Furthermore in equation (10) at page 23 the DUTY factor is needed to perform the computation of Vinj_sw. The duty factor is not defined in the datasheet (hopefully it should be D=Ton/Tsw) but can be ideally calculated using the wrong formulae at page 18, which I already mentioned, but only if it is Ton/Tsw=Vout/Vin where Tsw is the switching period or 1/fsw. 

Can anybody give me a hint?