LM3404MASLASHNOPB datasheet(25/39 Pages) TI1

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RSNS =

VIN - VO

0.2 x L

IF x L + VO x tSNS -

x tON

'iF

x rD

'iL - 'iF

ZC =

LM3404, LM3404HV

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SNVS465F – OCTOBER 2006 – REVISED MAY 2013

The peak LED/inductor current is then estimated:

IL(PEAK) = IL + 0.5 x ΔiL(MAX)

(27)

IL(PEAK) = 0.7 + 0.5 x 0.330 = 866 mA

(28)

In the case of a short circuit across the LED array, the LM3404 will continue to deliver rated current through the

short but will reduce the output voltage to equal the CS pin voltage of 200 mV. The inductor ripple current and

peak current in this condition would be equal to:

ΔiL(LED-SHORT) = [(24 – 0.2) x 7.43 x 10

-7] / 38 x 10-6 = 465 mA

P-P

(29)

IL(PEAK) = 0.7 + 0.5 x 0.465 = 933 mA

(30)

In the case of a short at the switch node, the output, or from the CS pin to ground the short circuit current limit

will engage at a typical peak current of 1.5A. In order to prevent inductor saturation during these fault conditions

the inductor’s peak current rating must be above 1.5A. A 47 µH off-the shelf inductor rated to 1.4A (peak) and

1.5A (average) with a DCR of 0.1

Ω will be used.

USING AN OUTPUT CAPACITOR

This application does not require high frequency PWM dimming, allowing the use of an output capacitor to

reduce the size and cost of the output inductor. To select the proper output capacitor the equation from Buck

Regulators with Output Capacitors is re-arranged to yield the following:

(31)

The target tolerance for LED ripple current is 100 mAP-P, and a typical value for rD of 1.8Ω at 700 mA can be read

from the LED datasheet. The required capacitor impedance to reduce the worst-case inductor ripple current of

333 mAP-P is therefore:

ZC = [0.1 / (0.333 - 0.1] x 1.8 = 0.77Ω

(32)

A ceramic capacitor will be used and the required capacitance is selected based on the impedance at 400 kHz:

CO = 1/(2 x π x 0.77 x 4 x 10

5) = 0.51 µF

(33)

This calculation assumes that impedance due to the equivalent series resistance (ESR) and equivalent series

inductance (ESL) of CO is negligible. The closest 10% tolerance capacitor value is 1.0 µF. The capacitor used

should be rated to 25V or more and have an X7R dielectric. Several manufacturers produce ceramic capacitors

with these specifications in the 0805 case size. A typical value for ESR of 3 m

Ω can be read from the curve of

impedance vs. frequency in the product datasheet.

RSNS

A preliminary value for RSNS was determined in selecting ΔiL. This value should be re-evaluated based on the

calculations for

ΔiF:

(34)

tSNS = 220 ns, RSNS = 0.33Ω

(35)

Sub-1

Ω resistors are available in both 1% and 5% tolerance. A 1%, 0.33Ω device is the closest value, and a

0.33W, 1206 size device will handle the power dissipation of 162 mW. With the resistance selected, the average

value of LED current is re-calculated to ensure that current is within the ±5% tolerance requirement. From the

expression for average LED current:

IF = 0.2 / 0.33 - (7.1 x 2.2 x 10

-7) / 47 x 10-6 + 0.266 / 2

(36)

= 706 mA, 1% above 700 mA

(37)

INPUT CAPACITOR

Following the calculations from the Input Capacitor section,

ΔvIN(MAX) will be 24V x 2%P-P = 480 mV. The

minimum required capacitance is:

CIN(MIN) = (0.7 x 7.4 x 10

-7) / 0.48 = 1.1 µF

(38)

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