AN2459 datasheet(31/35 Pages) STMICROELECTRONICS

31 / 35 page

AN2459 - Application note

Components calculation

31/35

An air gap needs to be introduced to prevent the core from saturating because of its high

permeability and to allow an adequate

∆H.

Despite the fact that gap length lgap is only a small per cent of le, the permeability of ferrite is

so high (for power ferrites the typical value of µr is 2500) that it is possible to assume, with

good approximation (

∆H » ∆Hgap), that the whole magnetic field is concentrated in the air

gap. For instance, with an lgap/le value of 1% (which is the minimum suggested value) the

error caused by the above assumption is approximately 4%. The error is smaller if the lgap/le

ratio is larger. As a result, the fringing flux in the air gap region may be neglected and the

energy balance can be re-written as:

The flux density

∆B, is the same throughout the core and the air gap, and is related to the

field strength inside the air gap by the well-known relationship:

Then, taking Ampere's law into account (but applying it only to the air gap region):

it is possible to obtain the following equation from the energy balance equation :

where N is the turn number of the winding.

Because N is defined, it is recommended to check the core saturation. If the core saturation

result is too close to the rated limit, it will be necessary to increase the value of lgap and

make a new calculation.

The wire gauge selection is based on limiting the copper losses to an acceptable value:

Due to the high ripple frequency, the effective wire resistance RCU, increases by skin and

proximity effects. For this reason litz wire or multi-wire solutions are recommended. Finally,

the space occupied by the winding needs to be evaluated. If it does not fit the winding area

of the bobbin, a bigger core set needs to be considered and the winding calculation

repeated. It is also necessary to add an auxiliary winding to the inductor, in order for the

ZCD pin to recognize at what point the current flowing through the inductor has fallen to

zero. The winding is a low cost thin wire and the turn number is the only parameter to be

defined.

L • ILpk ≈ ∆Hgap • ∆B • Ae• Igap

∆Β = µ

0 • ∆Hgap

Igap • ∆Hgap ≈ N • ILpk

PCU =

• Irms • RCU

AN2459 датащи(PDF) 31 Page - STMicroelectronics