INPUT CAPACITOR
Following the calculations from the Input Capacitor section,
Δv
IN(MAX)
will be 48V x 2%
P-P
= 960 mV. The minimum re-
quired capacitance is:
C
IN(MIN)
= (0.5 x 3.3 x 10-6) / 0.96 = 1.7 µF
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:
I
IN-RMS
= 0.5 x Sqrt(0.73 x 0.27) = 222 mA
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 mΩ.
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
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
T
RISE
= 0.047 x 75 = 3.5°C
CB AND C
F
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 C
F
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
Conduction loss, PC, in the internal MOSFET:
PC = (I
F
2
x R
DSON
) x D = (0.52 x 0.8) x 0.73 = 146 mW
Gate charging and VCC loss, PG, in the gate drive and linear
regulator:
PG = (I
IN-OP
+ fSW x QG) x V
IN
PG = (600 x 10-6 + 2.23 x 105 x 6 x 10-9) x 48 = 94 mW
Switching loss, PS, in the internal MOSFET:
PS = 0.5 x VIN x IF x (tR + tF) x f
SW
PS = 0.5 x 48 x 0.5 x 40 x 10-9 x 2.23 x 105 = 107 mW
AC rms current loss, P
CIN
, in the input capacitor:
P
CIN
= I
IN(rms)
2
x ESR = 0.2222 0.003 = 0.1 mW (negligible)
DCR loss, PL, in the inductor
PL = I
F
2
x DCR = 0.52 x 0.56 = 140 mW
Recirculating diode loss, PD = 47 mW
Current Sense Resistor Loss, P
SNS
= 110 mW
Electrical efficiency, η = PO / (PO + Sum of all loss terms) =
17.6 / (17.6 + 0.644) = 96%
Temperature Rise in the LM3404HV IC is calculated as:
T
LM3404
= (PC + PG + PS) x θJA = (0.146 + 0.094 + 0.107) x
155 = 54°C
Layout Considerations
The performance of any switching converter depends as
much upon the layout of the PCB as the component selection.
The following guidelines will help the user design a circuit with
maximum rejection of outside EMI and minimum generation
of unwanted EMI.
COMPACT LAYOUT
Parasitic inductance can be reduced by keeping the power
path components close together and keeping the area of the
loops that high currents travel small. Short, thick traces or
copper pours (shapes) are best. In particular, the switch node
(where L1, D1, and the SW pin connect) should be just large
enough to connect all three components without excessive
heating from the current it carries. The LM3404/04HV operates in two distinct cycles whose high current paths are shown
in Figure 7:
19 www.national.com
LM3404/LM3404HV