LM3409MY-NOPB Datasheet, PDF (13/43 Pages) Texas Instruments – PFET Buck Controller for High Power LED Drivers

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i_L(t)
I_L-MAX
LM3409, LM3409HV, LM3409-Q1
SNVS602J – MARCH 2009 – REVISED MAY 2013
I_L-MAX-H
I_L-MAX-L
0
t
0
t_OFF
t_OFF
Figure 26. Inductor Current i_L(t) Showing I_L-MAX Offset
INDUCTOR CURRENT RIPPLE
Because the LM3409/09HV swaps the polarity of the differential current sense comparator every cycle, a
minimum inductor current ripple (Δi_L-PP) is necessary to maintain accurate I_LED regulation. Referring to Figure 26,
the first t_ON is terminated at the higher of the two polarity-swapped thresholds (corresponding to I_L-MAXH). During
the following t_OFF, i_L decreases until the second t_ON begins. If t_OFF is too short, then as the second t_ON begins, i_L
will still be above the lower peak current threshold (corresponding to I_L-MAXL) and a minimum t_ON pulse will follow.
This will result in degraded I_LED regulation. The minimum inductor current ripple (Δi_L-PP-MIN) should adhere to the
following equation in order to ensure accurate I_LED regulation:
'i_{L- PP- MIN}
>
24 mV
R_SNS
(11)
SWITCHING FREQUENCY
The switching frequency is dependent upon the actual operating point (V_IN and V_O). V_O will remain relatively
constant for a given application, therefore the switching frequency will vary with V_IN (frequency increases as V_IN
increases). The target switching frequency (f_SW) at the nominal operating point is selected based on the tradeoffs
between efficiency (better at low frequency) and solution size/cost (smaller at high frequency). The off-time of the
LM3409/09HV can be programmed for switching frequencies up to 5 MHz (theoretical limit imposed by minimum
t_ON). In practice, switching frequencies higher than 1MHz may be difficult to obtain due to gate drive limitations,
high input voltage, and thermal considerations.
At CCM operating points, f_SW is defined as:
f_SW
=
1- D
t _OFF
=
1-
¨¨©§K
V_O
x V_IN
¸¸¹·
t _OFF
(12)
At DCM operating points, f_SW is defined as:
f_{SW =}
t_ON
1
+ t_OFF
=
1
¨§^{IL- MAX}
© ^VIN ^-
xV_OL_{1¸¸¹·}
+
t _OFF
(13)
In the CCM equation, it is apparent that the efficiency (η) factors into the switching frequency calculation.
Efficiency is hard to estimate and, since switching frequency varies with input voltage, accuracy in setting the
nominal switching frequency is not critical. Therefore, a general rule of thumb for the LM3409/09HV is to assume
an efficiency between 85% and 100%. When approximating efficiency to target a nominal switching frequency,
the following condition must be met:
>
V_O
V_IN
(14)
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