UCC28019 boost coil equation

[MacIntoshCZ]

Hi,
i dont know why there is D(1-D) in equation. Duty/Frequency stays for time... But why 0,5*(1-0,5)...
L= V*t/Iripple

https://www.ti.com/lit/ds/symlink/ucc28019.pdf?ts=1634493140457

page 28
thanks

 

[Pommie]

If you plot a chart from d=0.1 to d=0.9 compared to d(1-d) you will see that 0.5 is where it peaks. They are simply using the worst case.

Mike.

 

[MacIntoshCZ]

If you plot a chart from d=0.1 to d=0.9 compared to d(1-d) you will see that 0.5 is where it peaks. They are simply using the worst case.

Mike.

Thanks pommie for reply, now i get that d*(1-d) is biggest when duty is 0,5. But i still dont know why is there d*(1-d) in eq. instead of just d or (1-d).

 

[rjenkinsgb]

It symmetrically "shapes" the result to peak at 50% duty; eg. that give 0.25 while eg. 10% and 90% both give 0.09

 

[ronsimpson]

biggest when duty is 0,5. But i still dont know why is there d*(1-d) in eq. instead of just d or (1-d).

For that "biggest" equation it would be "0.5d". But for all duty cycles it is d*(1-d).
Worse case duty cycle = d/2=0.5d,,,, For any duty cycles d*(d-1)