LM3406 Datasheet, PDF (26/37 Pages) National Semiconductor (TI) – 1.5A Constant Current Buck Regulator for Driving High Power LEDs

LM3406, LM3406HV
SNVS512C – SEPTEMBER 2008 – REVISED FEBRUARY 2010
www.ti.com
This calculation assumes that C_O will be a ceramic capacitor, and therefore impedance due to the equivalent
series resistance (ESR) and equivalent series inductance (ESL) of of the device is negligible. The closest 10%
tolerance capacitor value is 1.5 µF. The capacitor used should have an X7R dielectric and should be rated to
50V. The high voltage rating ensures that C_O will not be damaged if the LED fails open circuit and a load dump
occurs. Several manufacturers produce ceramic capacitors with these specifications in the 1206 case size. With
only 4V of DC bias a 50V rated ceramic capacitor will have better than 90% of it's rated capacitance, which is
more than enough for this design.
R_SNS
Using the expression for R_SNS:
R_SNS = 0.2 / I_F
(76)
R_SNS = 0.2 / 1.5 = 0.133Ω
(77)
Sub-1Ω resistors are available in both 1% and 5% tolerance. A 1%, 0.13Ω device is the closest value, and a
0.33W, 1210 size device will handle the power dissipation of 290 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:
I_F = 0.2 / 0.13 = 1.54A, 3% above the target current
(78)
INPUT CAPACITOR
Controlling input ripple current and voltage is critical in automotive applications where stringent conducted
electromagnetic interference tests are required. Δv_IN(MAX) will be limited to 300 mV_P-P or less. The minimum
required capacitance is calculated for the largest t_ON, 1090 ns, which occurs at the minimum input voltage. Using
the equations from the Input Capacitors section:
C_IN(MIN) = (1.5 x 1.09 x 10^-6) / 0.3 = 5.5 µF
(79)
As with the output capacitor, this required value is low enough to use a ceramic capacitor, and again the effective
capacitance will be lower than the rated value with 16V across C_IN. Reviewing plots of %C vs. DC Bias for
several capacitors reveals that a 3.3 µF, 1210-size capacitor in X7R rated to 50V loses about 22% of its rated
capacitance at 16V, hence two such caps are needed.
Input rms current is high in buck regulators, and the worst-case is when the duty cycle is 50%. Duty cycle in a
buck regulator can be estimated as D = V_O / V_IN, and when V_IN drops to 9V the duty cycle will be nearly 50%.
I_IN-RMS = 1.5 x Sqrt(0.5 x 0.5) = 750 mA
(80)
Ripple current ratings for 1210 size ceramic capacitors are typically higher than 2A, so two of them in parallel can
tolerate more than enough for this design.
RECIRCULATING DIODE
To survive an input voltage transient of 40V the Schottky diode must be rated to a higher voltage. 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. The lower the duty cycle the
more thermal stress is placed on the recirculating diode. When driving one LED the duty cycle can be estimated
as:
D = 4.1 / 13.8 = 0.3
(81)
The estimated average diode current is then:
I_D = (1 - 0.3) x 1.54 = 1.1A
(82)
A 2A-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. V_D for a case size such as SMB in a 60V, 2A
Schottky diode at 1.5A is approximately 0.4V and the θ_JA is 75°C/W. Power dissipation and temperature rise can
be calculated as:
P_D = 1.1 x 0.4 = 440 mW T_RISE = 0.44 x 75 = 33°C
(83)
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