LM3409MY-NOPB Datasheet, PDF (28/43 Pages) Texas Instruments – PFET Buck Controller for High Power LED Drivers

LM3409, LM3409HV, LM3409-Q1
SNVS602J – MARCH 2009 – REVISED MAY 2013
η = 0.90
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1. NOMINAL SWITCHING FREQUENCY
Assume C_OFF = 470pF and η = 0.90. Solve for R_OFF:
R_OFF
=
C_OFF
+
20
-
¨¨©§^1-
K
V_O
x V_IN
¸¸¹·
pFx f_SW x ln
¨¨©§^1-
1.2V4_OV_{¸¸¹·}
- ¨§1- ^14V ¸·
R_OFF
=
490
pF
x
© ^{0.90 x 24V}¹
500 kHz x ln _¨§1-
1.24V_¸·
=
15.5
k:
© ^14V ¹
(75)
The closest 1% tolerance resistor is 15.4 kΩ therefore the actual t_OFF and target f_SW are:
t_{OFF =} - (C_OFF + 20 pF) x R_OFF x ln _{¨¨©§}1- ^1.2V_O^4V_{¸¸¹·}
t_OFF
=
-
490
pF
x
15.4
k:
x
ln
¨¨©§^1-
1.24V
14V
¸¸¹·
=
700
ns
(76)
f_SW
1-
=
¨¨©§K
V_O
x V_IN
t _OFF
¸¸¹·
1-
=
¨§ ^14V ¸·
©^{0.90 x 24V}¹
700 ns
=
503
kHz
(77)
The chosen components from step 1 are:
C_OFF = 470 pF
R_OFF = 15.4 k:
(78)
2. INDUCTOR RIPPLE CURRENT
Solve for L1:
L1 = ^{VO x tOFF} = ^{14V x 700 ns} = 21.8 PH
'i_L-PP
450 mA
(79)
The closest standard inductor value is 22 µH therefore the actual Δi_L-PP is:
'i_{L - PP}
=
V_O
x t_OFF
L1
=
14V x 700 ns
22 PH
=
445
mA
(80)
The chosen component from step 2 is:
L1= 22 PH
(81)
3. AVERAGE LED CURRENT
Determine I_L-MAX:
I_{L- MAX}
=
I_LED
+
'i_{L - PP}
2
= 1A +
445 mA
2
= 1.22A
(82)
Assume V_ADJ = 1.24V and solve for R_SNS:
28
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