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12
2005 Semtech Corp.
www.semtech.com
SC483
POWER MANAGEMENT
(
)
Hz
t
V
V
f
)
MAX
(
VBAT
_
ON
)
MAX
(
BAT
OUT
)
MAX
(
VBAT
_
SW
=
t
ON
is generated by a one-shot comparator that samples
V
via R
, converting this to a current. This current is
used to charge an internal 3.3pF capacitor to V
. The
equations above reflect this along with any internal
components or delays that influence t
ON
. For our example
we select R
tON
= 1M
:
t
ON_VBAT(MIN)
= 563ns and t
ON_VBAT(MAX)
= 255ns
f
SW_VBAT(MIN)
= 266kHz and f
SW_VBAT(MAX)
= 235kHz
Now that we know t
we can calculate suitable values
for the inductor. To do this we select an acceptable
inductor ripple current. The calculations below assume
50% of I
OUT
which will give us a starting place.
(
)
(
5
)
H
I
t
V
V
L
OUT
)
MIN
(
VBAT
_
ON
OUT
)
MIN
(
BAT
)
MIN
(
VBAT
=
and
(
)
(
5
)
H
I
t
V
V
L
OUT
)
MAX
(
VBAT
_
ON
OUT
)
MAX
(
BAT
)
MAX
(
VBAT
=
For our example:
L
VBAT(MIN)
= 1.3μH and L
VBAT(MAX)
= 1.6μH
We will select an inductor value of 2.2μH to reduce the
ripple current, which can be calculated as follows:
(
)
P
P
)
MIN
(
VBAT
L
_
ON
OUT
)
MIN
(
BAT
)
MIN
(
VBAT
_
RIPPLE
I
A
t
V
V
=
and
(
)
P
P
)
MAX
(
VBAT
L
_
ON
OUT
)
MAX
(
BAT
)
MAX
(
VBAT
_
RIPPLE
I
A
t
V
V
=
For our example:
I
RIPPLE_VBAT(MIN)
= 1.74A
P-P
and I
RIPPLE_VBAT(MAX)
= 2.18A
P-P
From this we can calculate the minimum inductor
current rating for normal operation:
)
MIN
(
)
MAX
(
VBAT
2
_
RIPPLE
I
)
MAX
(
OUT
I
)
MIN
(
INDUCTOR
I
A
+
=
For our example:
I
INDUCTOR(MIN)
= 7.1A
(MIN)
Next we will calculate the maximum output capacitor
equivalent series resistance (ESR). This is determined by
calculating the remaining static and transient tolerance
allowances. Then the maximum ESR is the smaller of the
calculated static ESR (R
ESR_ST(MAX)
) and transient ESR
(R
ESR_TR(MAX)
):
(
)
Ohms
I
2
ERR
ERR
R
)
MAX
(
VBAT
_
RIPPLE
DC
ST
)
MAX
(
ST
_
ESR
=
Where ERR
is the static output tolerance and ERR
is
the DC error. The DC error will be 1% plus the tolerance
of the feedback resistors, thus 2% total for 1%
feedback resistors.
For our example:
ERR
ST
= 48mV and ERR
DC
= 24mV, therefore
R
ESR_ST(MAX)
= 22m
(
)
Ohms
2
I
I
ERR
ERR
R
)
MAX
(
VBAT
_
RIPPLE
OUT
DC
TR
)
MAX
(
TR
_
ESR
+
=
Where ERR
is the transient output tolerance. Note that
this calculation assumes that the worst case load
transient is full load. For half of full load, divide the I
OUT
term by 2.
For our example:
ERR
TR
= 96mV and ERR
DC
= 24mV, therefore
R
ESR_TR(MAX)
= 10.2m
for a full 6A load transient