LM3444
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SNVS682C –NOVEMBER 2010–REVISED MAY 2013
V
BUCK
V
LED
C12
-
D10
L2
V
L2
-
Q2
R3
Figure 18. LM3444 External Components of the Buck Converter
The equation for an ideal inductor is:
di
n = L
dt
(14)
Given a fixed inductor value, L, this equation states that the change in the inductor current over time is
proportional to the voltage applied across the inductor.
During the on-time, the voltage applied across the inductor is,
VL(ON-TIME) = VBUCK - (VLED + VDS(Q2) + IL2 x R3)
(15)
Since the voltage across the MOSFET switch (Q2) is relatively small, as is the voltage across sense resistor R3,
we can simplify this to approximately,
VL(ON-TIME) = VBUCK - VLED
(16)
During the off-time, the voltage seen by the inductor is approximately:
VL(OFF-TIME) = VLED
(17)
The value of VL(OFF-TIME) will be relatively constant, because the LED stack voltage will remain constant. If we
rewrite the equation for an inductor inserting what we know about the circuit during the off-time, we get:
Di
VL(OFF-TIME) = VLED = L x
Dt
(I(MAX) - I(MIN)
)
VL(OFF-TIME) = VLED = L x
Dt
(18)
(19)
Re-arranging this gives:
VLED
t
OFF x
Di @
L2
From this we can see that the ripple current (Δi) is proportional to off-time (tOFF) multiplied by a voltage which is
dominated by VLED divided by a constant (L2).
These equations can be rearranged to calculate the desired value for inductor L2.
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