I read an article talking about the power switching loss formula, and I am curious about one thing.
How to use math to prove the 1/6 and 1/2 in these two waveforms? Could someone give me some idea?
I read an article talking about the power switching loss formula, and I am curious about one thing.
How to use math to prove the 1/6 and 1/2 in these two waveforms? Could someone give me some idea?
These expressions let you calculate the theoretical losses when a power switch turns on or off with overlapping current and voltage.
I have carried the calculations in my book for the two scenarios and the turn-off sequence in particular. The calculation is quite simple and involves an integral to average the instantaneous power \$p(t)\$ over a switching period. The below figure shows you a real shot taken on a flyback converter when the switch opens:
Please note that these are idealized waveforms and switching losses are extremely difficult to theoretically evaluate. This is because many parasitics (components, layout and so on) are involved which can significantly affect final waveforms. Same with simulation which usually leads to wrong results for switching losses.
Here is the "starting" idea ...
Formulas being proportional to FS is obvious.
Integration done for ONE cycle. So, multiply by frequency.
Next case :