12
LTC4210-1/LTC4210-2
 421012f
The current through R
SENSE
  can be divided into two
components; I
CLOAD
  due to the total load capacitance
(C
LOAD
) and I
LOAD
 due to the noncapacitive load elements.
The capacitive load typically dominates.
For a successful start-up without current limit, I
RSENSE
 <
I
LIMIT
:
I
RSENSE
 = I
CLOAD
 + I
LOAD
 < I
LIMIT
I
C
V
T
I
I
RSENSE
LOAD
OUT
LOAD    LIMIT
=


?/DIV>
?/DIV>
?/DIV>
?/DIV>
?/DIV>
?/DIV>
+
<
"
(7)
Due to the voltage follower configuration, the V
OUT
 ramp
rate approximately tracks V
GATE
:


=
H


=
V
T
I
C
V
T
I
C
OUT    CLOAD
LOAD
GATE
GATE
GATE
(8)
At time point 6, V
OUT
 is approximately V
IN
 but GATE ramp-
up continues until it reaches a maximum voltage. This
maximum voltage is determined either by the charge
pump or the internal clamp.
Start-Up Cycle With Current Limit
If the duration of the current limit is brief during start-up
(Figure 4) and it did not last beyond the circuit breaker
function time out, the GATE behaves the same as in start-
up without current limit except for the time interval be-
tween time point 5A and time point 5B. The servo amplifier
limits I
RSENSE
 by decreasing the I
GATE
 current (<10礎).
I
I
mV
R
RSENSE    LIMIT
SENSE
=
=
50
(9)
Equations 8 and 9 are applicable but with a lower GATE and
V
OUT
 ramp rate.
Gate Start-Up Time
The start-up time without current limit is given by:
t
C
V
V
I
t
C
V
I
C
V
I
STARTUP
GATE
TH    IN
GATE
STARTUP
GATE
TH
GATE
GATE
IN
GATE
=
+
=
+
"
"
"
(10)
During current limiting, the second term in Equation 10 is
partly modified from C
GATE
  " V
IN
/I
GATE
  to C
LOAD
  "
V
IN
/I
CLOAD
. The start-up time is now given by:
C
V
I
C
V
I
C
V
I
C
V
I
I
STARTUP
GATE
TH
GATE
LOAD
IN
CLOAD
GATE
TH
LOAD
IN
=
+
=
+
"
"
"
"

For successful completion of current limit start-up cycle
there must be a net current to charge C
LOAD
 and the
current limit duration must be less than t
CBDELAY
. The
second term in equation 11 has to fulfill equation 12.
C
V
I
I
t
LOAD
IN
RSENSE   LOAD
CBDELAY
"

<
 (12)
APPLICATIO S I FOR ATIO
U
U
U
V
TIMER
V
GATE
V
OUT
I
RSENSE
V
ON
V
IN
>2.5V
1   2
3  4  5
5A   5B 6
7
RESET
MODE
INITIAL
CYCLE
START-UP
CYCLE
NORMAL
CYCLE
5礎
100礎
COMP1
10礎
10礎
60礎
100礎
DISCHARGE
BY LOAD
REGULATED AT 50mV/R
SENSE
V
TH
COMP2
2礎
<10礎
4210 F04
>1.3V
Figure 4. Operating Sequence with
Current Limiting at Start-Up Cycle
(11)
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