LM3445 datasheet(21/46 Pages) TI2

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VLED

= K u D

VBUCK

tON

fSW =

, and

1 - D

tOFF

fSW =

tOFF + tON

fSW =

D =

tON

tON + tOFF

VLED

VBUCK

'¶ =

tOFF

tON + tOFF

tOFF = C11 x 1.276V x

VLED

i = C dt

= D

VLED

VBUCK

= D =

tON

tON + tOFF

= tON x fSW

VLED

VBUCK

LM3445

www.ti.com

SNVS570M – JANUARY 2009 – REVISED NOVEMBER 2015

8 Application and Implementation

NOTE

Information in the following applications sections is not part of the TI component

specification, and TI does not warrant its accuracy or completeness. TI’s customers are

responsible for determining suitability of components for their purposes. Customers should

validate and test their design implementation to confirm system functionality.

8.1 Application Information

8.1.1 Determining Duty-Cycle (D)

As shown in Equation 4, duty cycle (D) approximately equals:

(4)

With efficiency considered:

(5)

For simplicity, choose efficiency between 75% and 85%.

8.1.2 Calculating Off-Time

The Off-Time of the LM3445 is set by the user and remains fairly constant as long as the voltage of the LED

stack remains constant. Calculating the off-time is the first step in determining the switching frequency of the

converter, which is integral in determining some external component values.

PNP transistor Q3, resistor R4, and the LED string voltage define a charging current into capacitor C11. A

constant current into a capacitor creates a linear charging characteristic, as shown in Equation 6.

(6)

Resistor R4, capacitor C11 and the current through resistor R4 (iCOLL), which is approximately equal to VLED/R4,

are all fixed. Therefore, dv is fixed and linear, and dt (tOFF) can now be calculated.

(7)

Equation 8 shows common equations for determining duty cycle and switching frequency in any buck converter.

(8)

Therefore:

(9)

With efficiency of the buck converter in mind, as shown in Equation 10.

(10)

Substitute equations and rearrange:

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