LM3406_09 Datasheet, PDF (18/26 Pages) National Semiconductor (TI) – 1.5A Constant Current Buck Regulator for Driving High Power LEDs

I_L(PEAK) = I_L + 0.5 x Δi_L(MAX)
I_L(PEAK) = 1.5 + 0.5 x 0.516 = 1.76A
In order to prevent inductor saturation the inductor’s peak
current rating must be above 1.8A. A 15 µH off-the shelf in-
ductor rated to 2.4A (peak) and 2.2A (average) with a DCR of
47 mΩ will be used.
USING AN OUTPUT CAPACITOR
This application does not require high frequency PWM dim-
ming, allowing the use of an output capacitor to reduce the
size and cost of the output inductor while still meeting the 20%
P-P ^{(300 mA) target for LED ripple current. To select the proper}
output capacitor the equation from Buck Regulators with Out-
put Capacitors is re-arranged to yield the following:
The dynamic resistance, r_D,of one LED can be calculated by
taking the tangent line to the V_F vs. I_F curve in the LED
datasheet. Figure 8 shows an example r_D calculation.
30020324
FIGURE 10. Calculating r_D from the V_F vs. I_F Curve
Extending the tangent line to the ends of the plot yields values
for ΔV_F and ΔI_F of 0.7V and 2000 mA, respectively. Dynamic
resistance is then:
r_D = ΔV_F / ΔI_F = 0.5V / 2A = 0.25Ω
The most filtering (and therefore the highest output capaci-
tance) is needed when ΔI_L is highest, which occurs at V_IN-
MAX^{. Inductor ripple current with one LED is 516 mA}P-P^{. The}
required impedance of C_O is calculated:
Z_C = [0.3 / (0.516 - 0.3] x 0.35 = 0.35Ω
A ceramic capacitor will be used and the required capacitance
is selected based on the impedance at 440 kHz:
C_O = 1/(2 x π x 0.49 x 4.4 x 10⁵) = 1.03 µF
This calculation assumes that C_O will be a ceramic capacitor,
and therefore impedance due to the equivalent series resis-
tance (ESR) and equivalent series inductance (ESL) of of the
device is negligible. The closest 10% tolerance capacitor val-
ue is 1.5 µF. The capacitor used should have an X7R dielec-
tric 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 pro-
duce ceramic capacitors with these specifications in the 1206
case size. With only 4V of DC bias a 50V rated ceramic ca-
pacitor 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
R_SNS = 0.2 / 1.5 = 0.133Ω
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% toler-
ance requirement. From the expression for average LED
current:
I_F = 0.2 / 0.13 = 1.54A, 3% above the target current
INPUT CAPACITOR
Controlling input ripple current and voltage is critical in auto-
motive applications where stringent conducted electromag-
netic 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
As with the output capacitor, this required value is low enough
to use a ceramic capacitor, and again the effective capaci-
tance will be lower than the rated value with 16V across C_IN.
Reviewing plots of %C vs. DC Bias for several capacitors re-
veals 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
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.
www.national.com
18