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TPS51120: Limiting the delay of MOSFETs used in the TPS51120.

Part Number: TPS51120

Maybe I made the wrong choice of development tools / software, change it and ask again.

(I have the same question here. -> e2e.ti.com/.../835739)

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I am considering a MOSFET controlled by TPS51120.
Are there any limits on MOSFET delay parameters (rise time (tr), turn-on delay time (td (on)), fall time (tf), turn-off delay time (td (off))?
I am thinking of selecting a FET using the following parameters: Can I use (1) and (2) below?

(1) TOSHIBA TPN2R903PL (tr = 4.7ns, td (on) = 12ns, tf = 8.2ns, td (off) = 30ns)
(2) TOSHIBA TPCA8045-H (tr = 4.6ns, td (on) = 15ns, tf = 11ns, td (off) = 67ns)