AN4501 Datasheet, PDF (20/48 Pages) STMicroelectronics – Design of a boost LED driver using L99LD01

Selection of the inductor
AN4501
Equation 7:
-^d---^l-_d-^L---^,_D--^P----^P-- = -^V----^O--_L--^U--_×--^T---_F--^×--_S---⁽-_W-¹-----–_×----²-_η---^D-----⁾
This shows that the maximum value of the inductor peak-to-peak current is reached for a
duty cycle of D₅₀ = 50%.
4.4
Inductor current ripple ratio
The inductor current ripple ratio r is defined as the ratio between the peak-to-peak current
ripple and the average current.
Equation 8:
r = -^I-^L---^,_I--_L-^P---^P--
Increasing the value of the inductance, we reduce the inductor current ripple and the output
voltage ripple, as we will see in the section Section 6.1.2. In general, the max allowed
inductor current ripple ratio is optimal for a value in the range of 0.3 to 0.5, from the
standpoint of the cost / current ripple.
Indeed, reducing r to a value much lower than 0.3 leads a very large inductor size.
Increasing r to a value which is much higher than 0.5, does not lead to a significant size
reduction (see Appendix C: Document management). Therefore setting r to 0.4 or 0.5 is a
good starting point.
I_L,PP,MAX = r × I_{L, MAX} = r × ₁-----–--^I--^O-_D---^U-_M---^T--_A----_X--
Once the maximal inductor peak-to-peak current is fixed, we can estimate the minimum
required inductance value, using Equation 6 applied at V_IN,MIN which corresponds to a duty
cycle D_MAX.
Equation 9:
L_MIN = -^V----^O----^U--_I--_LT---_,-_P-^×---_P--^D-_,--_M-^M---_A--^A-_X---^X--_×--^×---_F--⁽--_S-¹---_W--–----_×^D-----^M_η----^A----^X----⁾
4.5
Inductor peak current
The inductor peak current must be calculated to make sure that in all cases, the inductor
saturation current is not reached.
The inductor peak current, I_LPEAK is given by:
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