AN2928 Datasheet, PDF (16/21 Pages) STMicroelectronics – Modified buck converter for LED applications

Design equations for the modified buck converter
AN2928
First, the inductor core size must be selected, for which it may be helpful to calculate the
minimum area product using application parameters. The minimum required core area
product (AP), where the flux swing is limited by core saturation is:
Equation 35
AP_MIN
=
⎛
⎝
-^L----^â‹----_B--^I--^P-_M---^E-_A--^A-_X--^K---_â‹--^â‹----_C--^I--^R_l---^M-----^S- _⎠⎞
4_--
3
AP_MIN = minimum area product (cm⁴)
I_PEAK = inductor peak current (A)
I_RMS = inductor RMS current (A)
B_MAX = saturation limited flux density (T) (power ferrites like N27 or N67 have typically 0.3 T)
Equation 36
Cl = J_MAX ⋅ C_R ⋅ 10^–4
J_MAX = maximum current density (A/cm²) (That commonly used for natural convection
cooling is 420 A/cm²)
C_R = ratio of the total copper area to the window area (-)
The constant C_R gives an estimation of how effectively the wires are placed on the core. For
example, if the input voltage of the modified buck converter is 400 V (such as when a power
factor preregulator is used), then the wires must be well-isolated and the ratio between the
copper and window area is about 0.5, which in the end means that there is 50% of the wire
on the inductor core. The exact calculation using the equation listed here can be found in the
user manual UM0670 (see Section 3: Reference and related materials).
Once the minimum area product is calculated, the designer should then select the right
inductor core and ferrite material according to the higher AP value. The AP value is
calculated from the winding cross section and core cross section. For example, the ETD29
core with ferrite material N27 from EPCOS has a winding cross section of 97 mm² and
a core cross section of 71 mm². Maximum flux density for the N27 is 0.3 T.
Equation 37
AP = A_N ⋅ A_MIN
A_N = winding cross section (mm²)
A_MIN = minimum core cross section (mm²)
For a proper inductor core, the calculated area product must be higher than the AP_MIN
calculated in Equation 35. If the condition derived from Equation 38 is not fulfilled, the
designer must select a bigger inductor core.
Equation 38
AP_MIN < AP
A simple way how to calculate the number of inductor turns is shown in Equation 39, since
manufacturers also include the inductance factor A_L, which depends on air gap, in the
product datasheets. For example, the ETD29 core with 1 mm gap and N27 ferrite material
has an inductance factor of 124 nH.
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