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SNVS570L – JANUARY 2009 – REVISED MAY 2013
C12
D10
V BUCK
V LED
-
L2
V L2
-
Q2
R3
Figure 27. LM3445 External Components of the Buck Converter
The equation for an ideal inductor is:
Q = L di
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,
V L(ON-TIME) = V BUCK - (V LED + V DS(Q2) + I L2 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,
V L(ON-TIME) = V BUCK - V LED
During the off-time, the voltage seen by the inductor is approximately:
V L(OFF-TIME) = V LED
(16)
(17)
The value of V L(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:
V L(OFF-TIME) = V LED = L x ' ' t i
' i # t OFF x V L2
V L(OFF-TIME) = V LED = L x
Re-arranging this gives:
LED
(I (MAX) - I (MIN) )
' t
(18)
(19)
From this we can see that the ripple current ( Δ i) is proportional to off-time (t OFF ) multiplied by a voltage which is
dominated by V LED divided by a constant (L2).
These equations can be rearranged to calculate the desired value for inductor L2.
L2 # t OFF x ' LED
Where:
V
i
(20)
22
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