LM3404MASLASHNOPB datasheet(29/39 Pages) TI1

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RSNS =

VIN - VO

0.2 x L

IF x L + VO x tSNS -

x tON

LM3404, LM3404HV

www.ti.com

SNVS465F – OCTOBER 2006 – REVISED MAY 2013

RSNS

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

calculations for

ΔiF:

(67)

tSNS = 220 ns, RSNS = 0.43Ω

(68)

Sub-1

Ω resistors are available in both 1% and 5% tolerance. A 1%, 0.43Ω device is the closest value, and a

0.25W, 0805 size device will handle the power dissipation of 110 mW. With the resistance selected, the average

value of LED current is re-calculated to ensure that current is within the ±10% 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 = 505 mA

(69)

INPUT CAPACITOR

Following the calculations from the Input Capacitor section,

ΔvIN(MAX) will be 48V x 2%P-P = 960 mV. The

minimum required capacitance is:

CIN(MIN) = (0.5 x 3.3 x 10

-6) / 0.96 = 1.7 µF

(70)

To provide additional safety margin a 2.2 µF ceramic capacitor rated to 100V with X7R dielectric in an 1812 case

size will be used. From the Design Considerations section, input rms current is:

IIN-RMS = 0.5 x Sqrt(0.73 x 0.27) = 222 mA

(71)

Ripple current ratings for 1812 size ceramic capacitors are typically higher than 2A, more than enough for this

design, and the ESR is approximately 3 m

Ω.

RECIRCULATING DIODE

The input voltage of 48V requires Schottky diodes with a reverse voltage rating greater than 50V. The next

highest standard voltage rating is 60V. Selecting a 60V rated diode provides a large safety margin for the ringing

of the switch node and also makes cross-referencing of diodes from different vendors easier.

The next parameters to be determined are the forward current rating and case size. In this example the high duty

cycle (D = 35.2 / 48 = 73%) places a greater thermal stress on the internal power MOSFET than on D1. The

estimated average diode current is:

ID = 0.5 x 0.27 = 135 mA

(72)

A Schottky with a forward current rating of 0.5A would be adequate, however reducing the power dissipation is

critical in this example. Higher current diodes have lower forward voltages, hence a 1A-rated diode will be used.

To determine the proper case size, the dissipation and temperature rise in D1 can be calculated as shown in the

Design Considerations section. VD for a case size such as SMA in a 60V, 1A Schottky diode at 0.5A is

approximately 0.35V and the

θJA is 75°C/W. Power dissipation and temperature rise can be calculated as:

PD = 0.135 x 0.35 = 47 mW TRISE = 0.047 x 75 = 3.5°C

(73)

CB AND CF

The bootstrap capacitor CB should always be a 10 nF ceramic capacitor with X7R dielectric. A 25V rating is

appropriate for all application circuits. The linear regulator filter capacitor CF should always be a 100 nF ceramic

capacitor, also with X7R dielectric and a 25V rating.

EFFICIENCY

To estimate the electrical efficiency of this example the power dissipation in each current carrying element can

be calculated and summed. Electrical efficiency,

η, should not be confused with the optical efficacy of the circuit,

which depends upon the LEDs themselves.

Total output power, PO, is calculated as:

PO = IF x VO = 0.5 x 35.2 = 17.6W

(74)

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