AN827 Datasheet, PDF (7/20 Pages) STMicroelectronics – A 500W HIGH POWER FACTOR WITH THE L4981A

AN827 APPLICATION NOTE
K_r = -₂----^∆â‹---_I-^I-_L-^L--_p---_k- ; I_Lpk =
2
⋅
I_{L rm s}
=
-----²----^â‹---^P-----ⁱ-ⁿ-
V_inrms
The minimum boost inductor value can be calculated as follows:
L_min = ₄-----_â‹---_f--_s---_w-^V----_â‹^o---_∆^u---^t-_I--_L---_m----_a---_x- = ₄-----_â‹---₈----₀---_k--⁴--_H-⁰----^0z----_â‹---₂---_.--₅----₀- = 0.5mH
The Table shown below relates the current ripple to the input voltage.
V_{in (rms)}
V_in(peak)
I_L(rms) I_{in (rms)}
I_L(peak)
Current Ripple
88
124
6.31
8.92
2.13
120
170
4.63
6.55
2.44
141
199
3.94
5.57
2.50
180
255
3.09
4.37
2.31
200
283
2.78
3.93
2.07
220
311
2.53
3.58
1.73
240
339
2.31
3.27
1.29
264
373
2.10
2.97
0.63
K_r
0.119
0.186
0.224
0.264
0.263
0.242
0.197
0.106
The number of turns, N, can be calculated according to the following formula:
N = -_A----_e-^L--_f-_f-^â‹--_â‹-^I--_B^L---^p-_m--^k---_a---_x- = ₂----₁₀---₁-^.-⁵---_â‹-^m--₁---₀-^H---₆---^â‹_m---⁸--₂-^.-⁹--_â‹--²-₀---^m-_.-₃---^A-₆---_T--- = 59 Turns
Where:
L is the calculated inductance value to limit the ripple current, ∆I_L.
I_Lpk is the worst case inductor current occurring at low-line input voltage (88V)
A_eff is the effective cross-sectional area of the core
B_max is the maximum allowable flux density of the core
The air gap is determined by referring to the magnetic core manufacturer’s AL vs. air gap curves. The air gap
needed for the specified inductance, turns and core type is found to be 2.8mm in the center post. To approxi-
mate the minimum core size needed for the conversion, the following equation may be used:
Volume ≥ K ⋅ L[I_Lpk ⋅ (I_Lpk + ∆I_L)]
Where K is the specific energy constant that depends on the ratio of the gap length (l_gap) and the effective length
(l_eff) of the core set and the maximum ∆B swing. Practically, K can be estimated as follows:
K = 11.5I--^I_g--^e-_a--^f-^fp- = 11.5 ⋅ ¹-₂---¹-_.-₈-⁴-- = 468
Thus, we have the following calculation for the minimum core set volume in cm³:
Volume ≥ 468 ⋅ 0.5 ⋅ 10^–3[8.92 ⋅ (8.92 + 2.5)] = 23.8cm³ .
The core chosen for this design is an ETD geometry ferrite core set with the following characteristics:
7/20