LTC4000
32
4000fb
For more information
In Figure 22 the battery is approximated to be a signal
ground in series with the internal battery resistance R
BAT
.
Therefore, the simplified loop transmission is as follows:
L
BV
(s)
=
g
m6
R
C
–
1
g
m10
C
C
s
+
1
C
C
s
•
R
BFB2
R
BFB
•
R
LB
R
LB
• C
L
s
+
1
• Gmo
p
(s)
where Gmo
p
(s) is the transfer function from V
ITH
to
the output current of the external DC/DC converter,
R
BFB
= R
BFB1
+ R
BFB2
, and R
LB
= R
L
//(R
DS(ON)
+ R
CS
+
R
BAT
) represents the effective output resistance from the
LOAD node to GND.
The Battery Charge Current Regulation Loop
This final regulation loop combines certain dynamic char-
acteristics that are found in all the other three loops. The
feedback signal for this charge current regulation loop is
the sense voltage across the charge current sense resis-
tor (R
CS
). This voltage is amplified by a factor of 20 and
compared to the voltage on the CL pin by the transcon-
ductance error amplifier (A5). In a familiar fashion, this
amplifier drives the output transconductance amplifier
(A10) to appropriately adjust the voltage on the ITH pin
driving the external DC/DC converter to regulate the input
current across the sense resistor (R
CS
).
Due to the presence of the instant-on feature, description
of the charge current regulation loop has to be divided into
two separate operating regions. These regions of operation
depend on whether the voltage on the OFB pin is higher
or lower than the instant-on threshold (V
OUT(INST_ON)
).
The Battery Charge Current Regulation Loop when
V
OFB
> V
OUT(INST_ON)
In this operating region, the external charging PFET’s gate
is driven low and clamped at V
BGATE(ON)
. The detail of this
loop is shown in Figure 23.
The simplified loop transmission is:
L
CC
(s)
=
g
m5
R
C
–
1
g
m10
C
C
s
+
1
C
C
s
•
20R
CS
•
R2 • C
IBMON
s
+
1
(
)
R1
+
R2
(
)
C
IBMON
s
+
1
•
R
L
R
f
+
R
L
•
1
R
L
P R
f
(
)
C
L
s
+
1
• Gmo
p
(s)
where Gmo
p
(s) is the transfer function from V
ITH
to the
output current of the external DC/DC converter, R
f
=
R
CS
+ R
DS(ON)
+ R
BAT
, and R
L
//R
f
represents the effective
resistance value resulting from the parallel combination
of R
L
and R
f
.
applicaTions inForMaTion
Figure 23. Simplified Linear Model of the Charge Current
Regulation Loop with the External Charging PFET Driven On
CC
A8
g
m8
= 0.33m
A10
g
m10
= 0.1m
ITH
INPUT
CSP
CSN
LTC4000
BAT
C
C
4000 F23
R
C
Gmo
p
(s)
R2
20k
R1
60k
R
O10
R
O5
–
+
C
L
R
L
C
IBMON
IBMON
CL
+
–
R
BAT
R
DS(ON)
R
CS
1V
A5
g
m5
= 0.5m
R
CL
+
–
+
–
–
50µA/
5µA
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