
REV. 0
ADP3156
–8–
The converter operates at the nominal operating frequency only
at the V
OUT
specified above, and at light load. At higher load
conditions, the operating frequency decreases due to the para-
sitic voltage drops across the power devices. The actual mini-
mum frequency at V
OUT
= 1.8 V is calculated from Equation 1,
and is a function of the finite resistances of various components
in the power converter.
C
OUT
Selection—Determining the ESR
The required ESR and capacitance drive the selection of the
type and quantity of the output capacitors. The ESR must be
small enough that both the resistive voltage deviation due to a
step change in the load current and the output ripple voltage
stay below the values defined in the specification of the supplied
circuitry. The capacitance must be large enough that the output
is held up while the inductor current ramps up or down to the
value corresponding to the new load current.
Taking into account the
±
1% setpoint accuracy of the ADP3156,
and assuming a 1% (or 15mV) peak-to-peak ripple, the allowed
static voltage deviation of the output voltage when the load
changes between the minimum and maximum values is:
(2
×
5%
×
1.5
V
) – (2
×
1%
×
1.5
V
) – (1%
×
1.5
V
) = 105
mV
This sets the maximum ESR at 105 mV/7 A = 15 m
. Four
parallel capacitors of 470
μ
F with a maximum ESR of 60 m
will achieve the 15 m
maximum net ESR. Whether or not the
capacitance is sufficient must be determined after the inductor
is selected.
Inductor Selection
The minimum inductor value can be calculated from ESR, off-
time, dc output voltage and allowed peak-to-peak ripple voltage
using the following equation:
L
V t
R
V
s
m
mV
H
MIN
E MAX
(
RIPPLE p p
1
1 5
.
3 2
15
7
2 24
.
=
=
×
×
=
μ
)
.
μ
The minimum inductance gives a peak-to-peak ripple current of
2.14 A, or 35% of the maximum dc output current I
OMAX
. The
inductor peak current in normal operation is:
I
LPEAK
=
I
OMAX
+
I
RPP
/2 = 8.07
A
The inductor valley current is:
I
LVALLEY
=
I
LPEAK
–
I
RPP
/2 = 5.93
A
The inductor for this application should have an inductance of
not less than 2.24
μ
H at full load current and should not satu-
rate at the worst-case overload or short circuit current at the
maximum specified ambient temperature. For this example, it is
assumed the inductance might drop as much as 33% due to
load current, so its initial value might be as high as 3.36
μ
H.
Tips for Selecting the Inductor Core
Ferrite designs have very low core loss, so the design should
focus on copper loss and on preventing saturation. Molypermalloy,
or MPP, is a low loss core material for toroids, and it yields the
smallest size inductor, but MPP cores are more expensive than
ferrite cores or the Kool M
μ
cores from Magnetics, Inc. The
lowest cost core is made of powdered iron, for example the #52
material from Micrometals, Inc., but yields a larger size inductor.
C
OUT
Selection—Determining the Capacitance
The minimum capacitance of the output capacitor is determined
from the requirement that the output be held up while the in-
ductor current ramps up (or down) to the new value. The mini-
mum capacitance should produce an initial dv/dt which is equal
(but opposite in sign) to the dv/dt obtained by multiplying the
di/dt in the inductor and the ESR of the capacitor.
C
I
I
R
di dt
/
C
A
A
m
V
H
F
MIN
OMAX
OMIN
)
E
MIN
=
=
(
)
=
–
(
.
/3 36
7
0
15
1 8
871
μ
μ
In the above equation the value of di/dt is calculated as the
smaller voltage across the inductor (i.e., the smaller of
V
IN
– V
OUT
and V
OUT
) divided by the maximum inductance
(3.36
μ
H) of the inductor. The four parallel-connected
470
μ
F capacitors have a total capacitance of 1880
μ
F, so the
minimum capacitance requirement is met with ample margin.
R
SENSE
The value of R
SENSE
is based on the required output current.
The current comparator of the ADP3156 has a threshold range
that extends from 0 mV to 125 mV (minimum). Note that the
full 125 mV range cannot be used for the maximum specified
nominal current, as headroom is needed for current ripple and
transients.
The current comparator threshold sets the peak of the inductor
current yielding a maximum output current I
OMAX
, which equals
the peak value less half of the peak-to-peak ripple current. Solv-
ing for R
SENSE
and allowing a 20% margin for overhead, and
using the minimum current sense threshold of 125 mV yields:
R
SENSE
= (125
mV
)/[1.2(
I
OMAX
+
I
RPP
/2)] = 12.9
m
Once
R
SENSE
has been chosen, the peak short-circuit current
I
SC(PK)
can be predicted from the following equation:
I
SC
(
PK
)
= (145
mV
)/
R
SENSE
= (145
mV
)/(12.9
m
)= 11.2
A
The actual short-circuit current is less than the above-calculated
I
SC
(
PK
)
value because the off-time rapidly increases when the
output voltage drops below 1 V. The relationship between the
off-time and the output voltage is:
t
C
V
V
k
A
OFF
T
O
≈
×
+
1
360
2
μ
With a short circuit across the output, the off-time will be about
104
μ
s. During that time the inductor current gradually decays.
The amount of decay depends on the L/R time constant in the
output circuit. With an inductance of 2.24
μ
H and total resis-
tance of 40 m
(the inductor’s series resistance plus the sense
resistor), the time constant will be 56
μ
s. This yields a valley
f
t
V
I
R
I
R
R
R
V
V
I
R
I
R
R
R
R
MIN
OFF
IN
IN
IN
OMAX
(
DS ON HSF
(
SENSE
+
L
O
IN
IN
IN
OMAX
DS ON HSF
(
SENSE
L
DS ON LSF
(
=
×
+
+
+
1
–
–
(
) –
–
–
–
)
)
)
)
(1)