AN2459 datasheet(30/35 Pages) STMICROELECTRONICS

30 / 35 page

Components calculation

AN2459 - Application note

30/35

Substituting this relationship in the expressions of Ton and Toff, after some algebra it is

possible to find the instantaneous switching frequency along a line cycle:

The switching frequency will be minimum at the top of the sinusoid (

θ =

π/2 ⇒sin(θ) =1 ),

maximum at the zero crossings of the line voltage (

θ = 0 or

π ⇒sin (θ) = 0) where T

off = 0.

The absolute minimum frequency fsw(min) can occur at either the maximum or the minimum

mains voltage, thus the inductor value is defined by:

where Virms can be either Virms(min) or Virms(max), whichever gives the lower value for L.

Once the value of L is defined, the real design of the inductor can start. Standard high

frequency ferrite (gapped core-set with bobbin) is the usual choice in PFC applications.

Selection of the most suitable one, among the various types offered by manufacturers, will

depend on technical and economic considerations.

The next step is to estimate the core size. To calculate an approximate value of the minimum

core size, the following practical equation may be used:

where Volume is expressed in cm3, L in mH and the specific energy constant K depends on

the ratio of the gap length (lgap) and the effective magnetic length (le) of the ferrite core:

The ratio le/lgap is fixed by the designer.

Next, the winding has to be specified. Quantities to be defined include the turn number and

the wire cross-section.

The (maximum) instantaneous energy inside the boost inductor (1/2 × L × ILpk^2) can be

expressed in terms of energy stored in the magnetic field, given by the maximum energy

density times and the effective core volume Ve:

where: Ae is the effective area of the core cross-section, ∆H is the swing of the magnetic

field strength and

∆B is the swing of the magnetic flux density.

Volume

≥ 4K • L • Irms

≅ 14 • 10–3 •

Igap

• L • ILpk =

•

∆H • ∆B • V

e ≈

•

∆H • ∆B • A

e• Ie

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