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RC5052
20
P
Appendix
Worst-Case Formulae for the Calculation of
C
out
, R5, and C
in
(Circuit of Figure 1 Only)
The following formulae design the RC5052 for worst-case
operation, including initial tolerance and temperature depen-
dence of all of the IC parameters (initial setpoint, reference
tolerance and tempco, active droop tolerance, current sensor
gain), the initial tolerance and temperature dependence of
the MOSFET, and the ESR of the capacitors. The following
information must be provided:
V
T+
, the value of the positive transient voltage limit;
|V
T-
|, the absolute value of the negative transient voltage limit;
I
O
, the maximum output current;
V
nom
, the nominal output voltage;
V
in
, the input voltage (typically 5V);
ESR, the ESR of the output caps, per cap (44m
for the
Sanyo parts shown in this datasheet);
R
D
, the on-resistance of the MOSFET (20m
for the
FDB6030);
R
D
, the tolerance of the current sensor (usually about 67%
for MOSFET sensing, including temperature).
I
rms
, the rms current rating of the input caps (2A for the
Sanyo parts shown in this datasheet).
Number of capacitors needed for C
out
= the greater of:
Example:
Suppose that the transient limits are ±134mV,
current I is 14.2A, and the nominal voltage is 2.000V, using
MOSFET current sensing and the usual caps. We have V
T+
=
|V
T-
| = 0.134, I
O
= 14.2, V
nom
= 2.000, and
R
D
= 0.67.
We calculate:
Since X > Y, we choose X, and round up to find we need 5
capacitors for C
OUT
.
A detailed explanation of this calculation, and the calculations
used for Figure 2, may be found Applications Bulletin AB-XX.
2
I
rms
V
in
V
nom
V
in
V
nom
*
IO
C
in
–
=
50 * 10
-6
I
O
* R
D
* (1 +
R
D
) * 1.10
R5 =
V
T-
ESR * I
O
ESR * I
O
X =
18 * R5 * 1.1
14400 * I
O
* R
D
Y
or
V
T+
–0.004 * V
nom
+
=
2
5
2.000
5
2.000
*
14.2
C
in
2
3.47
4 caps
=
–
=
=
=
10.4K
50 * 10
-6
14.2 * 0.020 * (1 + 0.67) * 1.10
R5
4.66
0.134
0.044 * 14.2
X
=
=
4.28
18 * 10400 * 1.1
14400 * 14.2 * 0.020
0.134 – 0.004 * 2.000
0.044 * 14.2
Y
=
+
=