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Buck Equation Derivation

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adnan012

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Hi,

How last equation is derived?

I
BuckEquation.PNG
 

Hi,

V_o / V_in is the expectable duty cycle
(V-in -V_o) is the voltage across the inductor dring ON time
L is the inductance.
T is the cycle time

t_on = cycle_time * duty_cycle = T * (Vo / V_in)

at an inductor: dI = V * t_on / L

So the formula tells how much the current rises during ON time.
And since Vin does not change and V_o does not change ... this also is the current that drops during OFF time.
(true for CCM)

Klaus
 

    adnan012

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