AN557 datasheet(6/52 Pages) STMICROELECTRONICS

6 / 52 page

AN557 APPLICATION NOTE

6/52

The negative sign may be interpretated with the fact that the current is now decreasing. Assuming that VF

may be neglected against Vo, during the OFF time the following behaviour occurs :

(8)

therefore :

(9)

But, because

∆IL+ = ∆IL– if follows that :

which allows us to calculate Vo:

(10)

where T is the switching period.

Expression (10) links the output voltage Vo to the input voltage Vi and to the duty cycle. The relation-ship

between the currents is the following :

(11)

EFFICIENCY

The system efficiency is expressed by the following formula :

where Po = VoIo (with Io = ILOAD) is the output power to the load and Pi is the input power absorbed by the

system. Pi is given by Po, plus all the other system losses. The expression of the efficiency becomes there-

fore the following :

(12)

DC LOSSES

Psat :saturation losses of the power transistor Q. These losses increase as Vi decreases.

(13)

where

and Vsat is the power transistor saturation at current Io.

PD : losses due to the recirculation diode. These losses increase as Vi increases, as in this case the ON

time of the diode is greater.

(14)

------ t

∆

------ T

OF F

–

()T

-----------------------------------

o TOFF

---------------------

ON TOFF

--------------------------

-----------

iD C

oD C

-----------

⋅

η%

------ 100

⋅

sa t

+++

---------------------------------------------------------------------------------

sat

-----------

sat Io

------

⋅

-----------

------

F Io

–

------------------

FIo 1

------

–







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