
22
2005 Semtech Corp.
www.semtech.com
POWER MANAGEMENT
Applications Information (Cont.)
SC2441
form of foldback current limiting. The following
calculations estimate the average inductor current when
the converter output is shorted to the ground.
a) The time taken to discharge the capacitor from 3.25V
to 0.47V is
.
A
4
V
)
47
.
μ
25
.
C
t
32
ssf
=
If
C
= 0.1
μ
F,
t
will then be 200ms.
b) The soft-start time from 0.47V to 3.25V is
.
A
3
V
)
47
.
μ
25
.
(
C
t
32
ssr
=
If
C
32
= 0.1
μ
F,
t
ssr
will then be 121ms. Note that during
soft-start, the converter only starts switching when the
voltage at SS/EN exceeds 1.3V.
c) The effective start-up time is
.
A
3
V
)
3
μ
25
.
(
C
t
32
sso
=
The average inductor current is then
.
t
t
t
I
I
ssr
ssf
sso
+
LMcp
Leff
=
I
=
0.27I
and is independent of the soft start
capacitance. The converter will not overheat in hiccup.
Setting the Output Voltage
The non-inverting inputs of the error amplifiers are
internally biased to 0.5V voltage reference. A simple
voltage divider (R
at top and R
at bottom) sets the
converter output voltage. R
can be expressed as a
function of the voltage feedback gain h=0.5/V
o
and R
o1
.
o
2
o
R
h
1
h
R
=
Once either R
or R
is chosen, the other can be calculated
for the desired output voltage V
. Since the number of
standard resistance values is limited, the calculated
resistance may not be available as a standard value
resistor. As a result, there will be a set error in the
converter output voltage. This non-random error is
caused by the feedback voltage divider ratio. It cannot
be corrected by the feedback loop.
The following table lists a few standard resistor
combinations for realizing some commonly used output
voltages.
)
V
(
o
V
6
9
2
5
8
5
3
h
2
8
4
2
6
4
6
)
m
h
O
(
1
o
R
0
0
2
6
0
8
K
4
K
2
K
1
6
K
2
0
K
2
6
)
m
h
O
(
2
o
R
K
1
K
1
K
1
K
1
K
1
K
1
K
1
Only the voltages in boldface can be precisely set with
standard 1% resistors.
The input bias current of the error amplifier also causes
an error in the output voltage. The inverting input bias
currents of error amplifiers 1 and 2 are –160nA and –
260nA respectively. Since the non-inverting input is biased
to 0.5V, the percentage error in the second output voltage
will be –100% · (0.26
μ
A) · Ro1Ro2 /[0.5 · (Ro1+Ro2)]. To
keep this error below 0.2%, Ro2 < 4k
.
Loop Compensation
The SC2441 uses current-mode control for both step-down
channels. Current-mode control is a dual-loop control
system in which the inductor peak current is loosely
controlled by the inner current-loop. The higher gain outer
loop regulates the output voltage. Since the current loop
makes the inductor appear as a current source, the complex
high-Q poles of the output LC networks is split into a
dominant pole determined by the output capacitor and
the load resistance and a high frequency pole. This pole-
splitting property of current-mode control greatly simplifies
loop compensation.
The inner current-loop is unstable (sub-harmonic oscillation)
unless the inductor current up-slope is steeper than the
inductor current down-slope. For stable operation above
50% duty-cycle, a compensation ramp is added to the