Datasheet

>
IN
V
O
V
SW
1
f
=
1
=
OFF
t+
¸
¸
¹
·
¨
¨
©
§
1MAXL
LI x
-
OIN
VV -
OFFON
tt +
SW
f
= =
1
IN
V
¨
¨
©
§
xK
-
¸
¸
¹
·
O
V
OFF
t
D1-
OFF
t
MINPPL
i
>
'
--
mV24
SNS
R
i
L
(t)
t
0
t
OFF
0
I
L-MAX-H
I
L-MAX-L
I
L-MAX
t
OFF
LM3409, LM3409HV, LM3409-Q1
www.ti.com SNVS602J –MARCH 2009–REVISED MAY 2013
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:
(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:
(12)
At DCM operating points, f
SW
is defined as:
(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:
(14)
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