LTC4245
27
4245fa
The inputs to the above equations are pre-calculated in
Table 3.
Table 3. t
3
Calculation Inputs
SUPPLY    V
OUT
V
FB
(dI/dt)
(MIN)
I
FBL(MIN)
I
FBH(MIN)
12V
12V
6V
60mA/ms
198mA
792mA
5V
5V
3V
430mA/ms
1.13A
6.22A
3.3V
3.3V
2V
602mA/ms
1.58A
8.71A
12V
12V
6V
30mA/ms
109mA
396mA
Equations 8 to 11, when applied to the four supplies
yields:
Table 4. t
3
Calculation Results
SUPPLY
t
31
t
32
t
33
t
34
TOTAL(t
3
)
12V
3.3ms
1.4ms
2.3ms
0
7ms
5V
2.6ms
4.5ms
2.6ms
0
9.7ms
3.3V
2.6ms
1.5ms
1.4ms
0
5.5ms
12V
3.6ms
3.7ms
3.7ms
0
11ms
Therefore the TIMER capacitance value is constrained by
the 12V supply inrush current. The total time (t
1
+ t
2
+
t
3
) is approximately 30ms. Equation 4 gives the capacitor
value to be:
  C
T(MIN)
e 30ms / K
TMCAP(MIN)
= 1.5糉
(12)
So a value of 2.2糉 (?0%) should suf ce.
4. The next step is to select MOSFETs for the four sup-
plies. The IRF7413 is selected for 12V, Si7880DP for 5V
and 3.3V, and Si4872 for 12V Supply. The Si7880DPs
on resistance is less than 4.25m?for V
GS
= 4.5V and a
junction temperature of 25癈.
Since the maximum load current requirement for the
3.3V supply is 7A, the steady-state power the MOSFET
may be required to dissipate is 208mW. The Si7880DP
has a maximum junction-to-ambient thermal resistance
of 65癈/W. If a maximum ambient temperature of 50癈
is assumed, this yields a junction temperature of 63.5癈.
According to the Si7880DPs Normalized On-Resistance
vs Junction Temperature curve, the devices on-resistance
can be expected to increase by about 15% over its room
temperature value. Recalculation of the steady-state values
of R
ON
and junction temperature yields approximately
4.9m?and 67癈, respectively. The I " R drop across the
3.3V sense resistor and series MOSFET at maximum load
current under these conditions will be less than 52mV.
The energy dissipated in the MOSFET during power-up
is the same as that stored into the load capacitor. The
average power dissipated in the MOSFET is:
P
C    V
t
ON
L    OUT
=
"
"
2
3
2
(13)
The 12V MOSFETs single-pulse ?/DIV>
JA(MAX)
, as read from
its Transient Thermal Impedance Graph, is 3癈/W for a
time, t
3
, of 7ms. P
ON
is calculated to be 1W and therefore
the 12V MOSFET temperature rise during power-up is
3癈. The other supplies show a smaller rise in MOSFET
temperature than this value.
When a supply powers-up into a short-circuit at the output,
the supply current rises linearly to the lower foldback level
and stays there till the timer expires and the MOSFETs are
shut-off. To simplify calculations it will be assumed that
the MOSFET conducts the lower foldback current from
the moment it turns on. This time (t
SC
) is the actual time
the MOSFET is conducting current minus a correction
for the assumption, which is half of the time required for
the current to rise from zero to the lower foldback level.
Therefore:
t
C
K
V
SC MAX
T MAX
TMCAP MAX
SNS FBL
(    )
(    )
(    )
(
"
( .  "
=
1 5  
))(    )
(    )
(    )
)"
"
MAX
SS MIN
SS   SS MAX
C
G    I
(14)
The 1.5 " 擵
SNS(FBL)(MAX)
term is due to the correction
factor and the time spent in ramping the starting negative
current limit to zero. t
SC(MAX)
turns out to be about 58ms
for all four supplies. The maximum power dissipated in
the MOSFET is given by:
P
I
V
SC MAX    FBL MAX
OUT
(    )
(    )
"
=
(15)
P
SC(MAX)
for the 5V supply is 3.2A " 5V, or 16W. ?/DIV>
JA(MAX)
for the 5V MOSFET is 3.25癈/W. Therefore the MOSFET
temperature rise during power-up into a 5V
OUT
short-
circuit is 52癈. Similar calculations show that the other
supplies experience a smaller MOSFET temperature rise.
The ?/DIV>
JA(MAX)
value is read from the MOSFET datasheets
Transient Thermal Impedance Graph for a duty cycle of
0.02, which is the case when the LTC4245 is con gured
for auto-retry on overcurrent faults.
APPLICATIO  S I FOR  ATIO
U
U
U
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