AN557 datasheet(8/52 Pages) STMICROELECTRONICS

8 / 52 page

AN557 APPLICATION NOTE

8/52

Figure 5. Equivalent Circuit Showing Recirculation when Q1 is Turned Off.

From the behaviour shown in Fig. 4 it may be calculated that the charge current of the output capacitor,

within a period, is

∆IL/4, which is supplied for a time T/2. It follows therefore that :

(19)

but, remembering expression (4) :

and

therefore equation (19) becomes :

Finally, calculating C it follows that :

(20)

where :

L is in Henrys

C is in Farads

f is in Hz

Finally, the following expression should be true :

(21)

It may happen that to satisfy relation (21) a capacitance value much greater than the value calculated

through (20) must be used.

TRANSIENT RESPONSE

Sudden variations of the load current give rise to overvoltages and undervoltages on the output voltage.

Since ic = C (dvc/dt) (22), where dvc = ∆Vo, the instantaneous variation of the load current ∆Io is supplied

during the transient by the output capacitor. During the transient, also current through the coil tends to

change its value. Moreover, the following is true :

(23)

where diL = ∆Io

vL = Vi – Vo for a load increase

vL = Vo

for a load decrease

∆

--------

---

L T

∆

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

∆

8fc

--------

∆

–

()T

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

------ T

∆

–

()V

8 V

i f

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

–

()V

8 V

C f

∆

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

ESR

ma x

Cm a x

∆

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

--------

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