Regarding LTM4649 and LTM4622, I'd like to know Vout start-up time(t1) after reaching RUN pin ON threshold and Vout turn-off time(t2) after falling RUN pin OFF threshold.
Regarding this delay, when the RUN threshold is reached INTVCC gets enabled and once it reaches its UVLO threshold it waits for a number of clock cycles before switching starts. For practical values of soft-start cap you will find that the SS voltage will reach tens of mV (ie 50mV) before you see switching begin and Vout ramp up. You can also look into this in more detail with LTSpice simulations for these parts.
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