27
LTC3733/LTC3733-1
3733f
APPLICATIO S I FOR ATIO
WUUU
The worst-case input RMS ripple current for a single stage
design peaks at twice the value of the output voltage. The
worst-case input RMS ripple current for a two stage
design results in peaks at 1/4 and 3/4 of the input voltage,
and the worst-case input RMS ripple current for a three
stage design results in peaks at 1/6, 1/2, and 5/6 of the
input voltage. The peaks, however, are at ever decreasing
levels with the addition of more phases. A higher effective
duty factor results because the duty factors “add” as long
as the currents in each stage are balanced. Refer to AN19
for a detailed description of how to calculate RMS current
for the single stage switching regulator.
Figure 6 illustrates the RMS input current drawn from the
input capacitance versus the duty cycle as determined by
the ration of input and output voltage. The peak input RMS
current level of the single phase system is reduced by 2/3
in a 3-phase solution due to the current splitting between
the three stages.
The output ripple current is reduced significantly when
compared to the single phase solution using the same
inductance value because the V
OUT
/L discharge currents
term from the stages that has their bottom MOSFETs on
subtract current from the (V
CC
– V
OUT
)/L charging current
resulting from the stage which has its top MOSFET on. The
output ripple current for a 3-phase design is:
I
P-P
=
()()
()
>
V
fL
DC V V
OUT
IN OUT
13 3–
The ripple frequency is also increased by three, further
reducing the required output capacitance when V
CC
< 3V
OUT
as illustrated in Figure 4.
Efficiency Calculation
To estimate efficiency, the DC loss terms include the input
and output capacitor ESR, each MOSFET R
DS(ON)
, induc-
tor resistance R
L
, the sense resistance R
SENSE
and the
forward drop of the Schottky rectifier at the operating
output current and temperature. Typical values for the
design example given previously in this data sheet are:
Main MOSFET R
DS(ON)
= 7mΩ (9mΩ at 90°C)
Sync MOSFET R
DS(ON)
= 7mΩ (9mΩ at 90°C)
C
INESR
= 20mΩ
C
OUTESR
= 3mΩ
R
L
= 2.5mΩ
R
SENSE
= 3mΩ
V
SCHOTTKY
= 0.8V at 15A (0.7V at 90°C)
V
OUT
= 1.3V
V
IN
= 12V
I
MAX
= 0.8V at 15A (0.7V at 90°C)
δ = 0.01%°C
N = 3
f = 400kHz
The main MOSFET is on for the duty factor V
OUT
/V
IN
and
the synchronous MOSFET is on for the rest of the period
or simply (1 – V
OUT
/V
IN
). Assuming the ripple current is
small, the AC loss in the inductor can be made small if a
good quality inductor is chosen. The average current,
I
OUT
is used to simplify the calaculations. The equation
below is not exact but should provide a good technique
for the comparison of selected components and give a
result that is within 10% to 20% of the final application.
