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15
2007 Semtech Corp.
www.semtech.com
SC411
POWER MANAGEMENT
Application Information (Cont.)
Where TOL
TR
is the transient tolerance. For our example:
POSLIM
TR
= 1.296V
The minimum output capacitance is calculated as
follows:
This calculation assumes the absolute worst case condi-
tion of a full-load to no load step transient occurring when
the inductor current is at its highest. The capacitance
required for smaller transient steps may be calculated by
substituting the desired current for the I
OUT
term.
For our example:
C
OUT(MIN)
= 626
μ
F.
We will select 440
μ
F, using two 220
μ
F, 25m
Ω
capacitors
in parallel. For smaller load release overshoot, 660
μ
F
may be used. Alternatively, one 15m
Ω
or 12m
Ω
, 220
μ
F,
330
μ
F or 470
μ
F capacitor may be used (with the appro-
priate change to the calculation for C
TOP
), depending upon
the load transient requirements.
Next we calculate the RMS input ripple current, which is
largest at the minimum battery voltage:
(
)
RMS
MIN
_
BAT
OUT
I
OUT
)
MIN
(
BAT
OUT
)
RMS
(
IN
I
A
V
V
V
V
=
For our example:
I
IN(RMS)
= 2.14A
RMS
Input capacitors should be selected with suf
fi
cient ripple
current rating for this RMS current, for example a 10
μ
F,
1210 size, 25V ceramic capacitor can handle approxi-
mately 3A
. Refer to manufacturer’s data sheets and
derate appropriately.
Finally, we calculate the current limit resistor value. As
described in the current limit section, the current limit
looks at the “valley current”, which is the average output
current minus half the ripple current. We use the maxi-
mum room temperature speci
fi
cation for MOSFET R
DS(ON)
at V
GS
= 4.5V for purposes of this calculation:
The ripple at low battery voltage is used because we want
to make sure that current limit does not occur under nor-
mal operating conditions.
For our example:
I
VALLEY
= 5.13A, R
DS(ON)
= 9m
Ω
and R
ILIM
= 7.76k
Ω
We select the next lowest 1% resistor value: 7.68k
Ω
Thermal Considerations
The junction temperature of the device may be calculated
as follows:
Where:
T
A
= ambient temperature (°C)
P
D
= power dissipation in (W)
θ
= thermal impedance junction to ambient
from absolute maximum ratings (°C/W)
The power dissipation may be calculated as follows:
Where:
VCCA = chip supply voltage (V)
I
= operating current (A)
VDDP = gate drive supply voltage (V)
C
COUT(MIN)
= L
F
I
RIPPLE_VBAT(MAX)
2
I
OUT
+
2
POSLIM
TR2
V
OUT_ST_POS2
A
2
I
I
I
)
MIN
(
VBAT
_
RIPPLE
OUT
VALLEY
=
(
I
)
Ohms
10
10
4
R
2
R
6
)
ON
(
DS
VALLEY
ILIM
=
C
P
T
T
JA
D
A
J
°
θ
+
=
W
D
mA
1
VBST
f
Q
V
I
VDDP
I
VCCA
P
+
g
g
VDDP
VCCA
D
+
+
=