LM3409MY-NOPB Datasheet, PDF (12/43 Pages) Texas Instruments – PFET Buck Controller for High Power LED Drivers

LM3409, LM3409HV, LM3409-Q1
SNVS602J – MARCH 2009 – REVISED MAY 2013
www.ti.com
Using the actual t_OFF equation, the inductor current ripple (Δi_L-PP) of a buck current regulator operating in CCM is:
' i_{L-PP =}
- V_O
x
R _OFF
x(C_OFF
+ 20
L1
pF)
x
ln
¨¨©§^1-
1.24V
V_O
¸¸¹·
(7)
Using the t_OFF approximation, the equation is reduced to:
'i_L
-
PP
|
1.
24
x
R_OFF
L1
x
C_OFF
(8)
Δi_L-PP is independent of both V_IN and V_O when in CCM!
The Δi_L-PP approximation only depends on R_OFF, C_OFF, and L1, therefore the ripple is essentially constant over
the operating range as long as V_O >> 1.24V (when the t_OFF approximation is valid). An exception to the t_OFF
approximation occurs if the IADJ pin is used to analog dim. As the LED/inductor current decreases, the converter
will eventually enter DCM and the ripple will decrease with the peak current threshold. The approximation shows
how the LM3409/09HV achieves constant ripple over a wide operating range, however t_OFF should be calculated
using the actual equation first presented.
AVERAGE LED CURRENT
For a buck converter, the average LED current is simply the average inductor current.
v_SNS (t)
V_CST
t_ON
0
t_OFF
t
Figure 25. Sense Voltage v_SNS(t)
Using the COFT architecture, the peak transistor current (I_T-MAX) is sensed as shown in Figure 25, which is equal
to the peak inductor current (I_L-MAX) given by the following equation:
I_{L- MAX =} I_{T-MAX =}
V_CST
R_SNS
=
V_ADJ
5 x R_SNS
(9)
Because I_L-MAX is set using peak current control and Δi_L-PP is set using the controlled off-timer, I_L and
correspondingly I_LED can be calculated as follows:
I_{LED =} I_{L =} I_{L - MAX} -
'i_{L- PP}
2
=
V_ADJ
5 x R_SNS
-
V_O x t_OFF
2 x L1
(10)
The threshold voltage V_CST seen by the high-side sense comparator is affected by the comparator’s input offset
voltage, which causes an error in the calculation of I_L-MAX and ultimately I_LED. To mitigate this problem, the
polarity of the comparator inputs is swapped every cycle, which causes the actual I_L-MAX to alternate between two
peak values (I_L-MAXH and I_L-MAXL), equidistant from the theoretical I_L-MAX as shown in Figure 26. I_LED remains
accurate through this averaging.
12
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