LM3406_09 Datasheet, PDF (14/26 Pages) National Semiconductor (TI) – 1.5A Constant Current Buck Regulator for Driving High Power LEDs

FIGURE 7. Schematic for Design Example 1
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R_ON and t_ON
A moderate switching frequency of 500 kHz will balance the
requirements of inductor size and overall power efficiency.
The LM3406 will allow some shift in switching frequency when
V_O changes due to the number of LEDs in series, so the cal-
culation for R_ON is done at the mid-point of three LEDs in
series, where V_O = 11.8V. Note that the actual R_ON calculation
is done with the high accuracy expression listed in the Ap-
pendix.
R_ON = 144 kΩ
The closest 1% tolerance resistor is 143 kΩ. The switching
frequency and on-time of the circuit should be checked for
one, three and five LEDs using the equations relating R_ON and
t_ON to f_SW. As with the R_ON calculation, the actual f_SW and
t_ON values have been calculated using the high accuracy ex-
pressions listed in the Appendix.
t_{ON(3 LEDs)} = 1014 ns
t_{ON(5 LEDs)} = 1512 ns
OUTPUT INDUCTOR
Since an output capacitor will be used to filter some of the AC
ripple current, the inductor ripple current can be set higher
than the LED ripple current. A value of 40%_P-P is typical in
many buck converters:
Δi_L = 0.4 x 1.5 = 0.6A_P-P
With the target ripple current determined the inductance can
be chosen:
L_MIN = [(24 – 11.8) x 1.01 x 10^-6] / (0.6) = 20.5 µH
The closest standard inductor value is 22 µH. The average
current rating should be greater than 1.5A to prevent over-
heating in the inductor. Inductor current ripple should be
calculated for one, three and five LEDs:
f_{SW(1 LED)} = 362 kHz
f_{SW(3 LEDs)} = 504 kHz
f_{SW(5 LEDs)} = 555 kHz
Δi_{L(1 LED)} = [(24 - 4.1) x 5.28 x 10^-7] / 22 x 10^-6
= 478 mA_P-P
Δi_{L(3 LEDs)} = [(24 - 11.8) x 1.01 x 10^-6] / 22 x 10^-6
= 560 mA_P-P
t_{ON(1 LED)} = 528 ns
Δi_{L(5 LEDs)} = [(24 - 19.7) x 1.51 x 10^-6] / 22 x 10^-6
= 295 mA_P-P
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