AN557 datasheet(7/52 Pages) STMICROELECTRONICS

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AN557 APPLICATION NOTE

where VF is the forward voltage of the recirculation diode at current Io.

PL : losses due to the series resistance RS of the coil

PL = RS Io

2 (15)

Pq: losses due to the stand-by current and to the power driving current:

Pq = Vi Iq, (16)

in which Iq is the operating supply current at the operating switching frequency. Iq includes the oscillator

current.

SWITCHING LOSSES

Psw: switching losses of the power transistor :

The switching losses of the recirculation diode are neglected (which are anyway negligible) as it is as-

sumed that diode is used with recovery time much smaller than the rise time of the power transistor.

We can neglect losses in the coil (it is assumed that

∆IL is very small compared to Io) and in the output

capacitor, which is assumed to show a low ESR.

Calculation of the inductance value, L

Calculation TON and TOFF through (4) and (9) respectively it follows that :

But because :

TON + TOFF = T and ∆IL

+ =

∆IL– = ∆IL, it follows that :

(17)

Calculating L, the previous relation becomes :

(18)

Fixing the current ripple in the coil required by the design (for instance 30% of Io), and introducing the fre-

quency instead of the period, it follows that :

where L is in Henry and f in Hz Vi × 0.3 × Io × f

Calculation of the output capacitor C

From the output node in fig. 3 it may be seen that the current through the output capacitor is given by:

ic (t) = iL (t) – Io

i Io

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

∆

⋅

–

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

OFF

∆

⋅

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

∆

⋅

–

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

∆

⋅

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

–

()V

i IL

∆

------------------------------ T

–

()V

0.3 I

⋅⋅

⋅

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

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