LM3445M datasheet(22/39 Pages) TI

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L2 # tOFF x

VLED

'i # tOFF x

VLED

VL(OFF-TIME) = VLED = L x 'i

VL(OFF-TIME) = VLED = L x

(I(MAX) - I(MIN))

= L dt

C12

D10

VLED

VBUCK

VL2

LM3445

SNVS570L – JANUARY 2009 – REVISED MAY 2013

www.ti.com

Figure 27. LM3445 External Components of the Buck Converter

The equation for an ideal inductor is:

(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:

(18)

Re-arranging this gives:

(19)

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.

(20)

Where:

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