STEVAL-ILL013V1 Datasheet, PDF (41/43 Pages) STMicroelectronics – 80 W offline LED driver with PFC

Design calculation
The number of turns for the inductor is:
Equation 21
N= --^L----= ----¹---^.--⁶-----^×-----¹----⁰---^–---³---- = 172
A_{L 54.22 × 10}^–9
where the inductance factor Al for the E25 core and 2 mm gap is calculated:
Equation 22
UM0670
A_L=
K₁ ×
--¹----
K₂
s=
90 ×
–----0^--1-.^--7^---3^--
2=
54.22nH
K₁ = 70 (see datasheet Section 11: References and related materials: 5.)
K₂ = – 0,73 (see datasheet Section 11: References and related materials: 5.)
s = E25 core air gap [mm].
The last step to complete the inductor design is to calculate the wire diameter.
Maximum inductor power dissipation is:
Equation 23
P_MAX
LOSS⁼
T_{----M-----A---X-----–----}T_----A--
R_T
=
7_----0_{-----–----}3_----0_-
40
=
1W
The wire resistance on the inductor is (copper wire with diameter of 0.28 mm is chosen):
Equation 24
R= ρ ×
s^{-l- =}
ρ×
-^l-^N-----^×------^N--
π× d
=
1.76 ×
10^–6 ×
-------⁵-----^×------¹---⁷----²--------
3.14 × 0.028
=
17.2 m Ω
where average turn length I_N is written in the core datasheet (see datasheet Section 11:
References and related materials 5.).
The power dissipation on the wire is:
Equation 25
P_WIRE= R × l_{A2 VR}= 17.2 × 10^–3 × 1²= 17.2mW
The power loss in the wire is much lower than the maximum power loss in the inductor, and
so a wire with a diameter of 0.28 mm is suitable for this inductor.
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Doc ID 15327 Rev 2