Conduction Loss in Buck SMPS FET

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Hello,

I am trying to calculate conduction losses in the upper FET of a synchronous buck converter.

I thought conduction losses in an SMPS FET were I^2.R
-where I = I(rms) in the FET



-but equation (2) on page 1 of the following….


AN-6005
https://www.fairchildsemi.com/an/AN/AN-6005.pdf

.......states that it is I(OUT)^2 . R(DS)ON . Vout/Vin (2)


……surely equation (2) cannot be right ?
 

Your Vout/Vin is the duty cycle factor, which you need because
the FET is only dissipating power during that fraction of the time.
 

but the RMS value has already taken that into account.
...there is no need to take the duty cycle into account again.
 

The calculation is assuming a constant Iout, commutated between two switches.
Sketch the waveform, perhaps you understand...
 

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