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f
SW
=
V
OUT
V
IN
x K x t
ON
Or:
f
SW
=
1
t
ON
+ t
OFF
'i
R
ON
L =
x k
t
ON
k
R
ON
=
(V
IN
- V
OUT
)
V
OUT
V
IN
x K
t
ON
=
1
f
SW
Modified Application Circuit Design Example 4 www.ti.com
• V
OUT
= 4 x 3.4V + 200 mV = 13.8V
• V
OUT
= 5 x 3.4V + 200 mV = 17.2V
Reduce switching frequency for the typical application to about 500 kHz to increase efficiency.
Calculate t
ON
, t
OFF
and R
ON
(38)
• V
OUT
= 13.8V
• V
IN
= 48V
• I
F
= 500 mA
• t
D
= 220 ns
• η = 0.85
• f
SW
= 500 kHz
t
ON
≊ 705 ns
(39)
R
ON
≊ 179 kΩ (use standard value of 182 kΩ)
Calculate Inductor Value
(40)
• I
F
= 500 mA
• Δi
L
= 250 mA (target)
• R
ON
= 182 kΩ
• L = 100 µH
Calculate Δi
L
with L = 100 µH (V
IN
= 48V, V
OUT
= 13.8V)
Δi
L
= 241 mA (all combinations)
Calculate Switching Frequency
(41)
Table 10. Example 4 Switching Frequency
V
IN
(V) V
OUT
(V) f
SW
(kHz)
Three Series LEDs
36 10.4 374
48 10.4 412
60 10.4 435
Four Series LEDs
36 13.8 430
48 13.8 497
60 13.8 537
Five Series LEDs
36 17.2 454
48 17.2 558
60 17.2 620
16
AN-1839 LM3402/LM3404 Fast Dimming and True Constant LED Current SNVA342E–July 2008–Revised April 2013
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