LTC3789 LINER [Linear Technology], LTC3789 Datasheet - Page 31

• Manufacturer Part Number: LTC3789
• Description: High Voltage High Current Controller for Battery Charging and Power Management
• Manufacturer: LINER [Linear Technology]

applicaTions inForMaTion
APPENDIX—THE LOOP TRANSFER FUNCTIONS
When a series resistor (R
as the compensation network as shown in Figure 11, the
transfer function from the input of A4-A7 to the ITH pin
is simply as follows:
where g
A7, typically 0.5mA/V; g
transconductance, R
error amplifier, typically 50mΩ; and R
output impedance of the output amplifier, typically 10mΩ
with the ITH pin open circuit.
Note this simplification is valid when g
• C
poles or zeroes in the system. Typically A
10
and R
connected to the ITH pin respectively.
In most applications, compensation of the loops involves
picking the right values of R
the values of R
adjusted. The value of g
increasing the pull-up current into the ITH pin and its
value can be approximated as:
The higher the value of g
of the value of R
the presence of the right half plane zero.
Even though all the loops share this transfer function from
the error amplifier input to the ITH pin, each of the loops
has a slightly different dynamic due to differences in the
feedback signal path.
10
g
C
V
V
m10
ITH
FB
= A
with the ITH pin open circuit. The exact value of g
O10
m4-7
(s) = g
V10
=
depends on the pull-up current and impedance
I
ITH
is the transconductance of error amplifier A4-
• R
50mV
+ 5µA
m4-7
C
O4-7
C
and C
would be. This lower limit is to prevent
⎡
⎢
⎢
⎢
⎢
⎣
O4-7
• C
⎛
⎜
⎝
R
C
C
C
m10
, the value of g
m10
m10
is the output impedance of the
R
–
is much larger than any other
C
O4-7
) and capacitor (C
C
g
is the output amplifier (A10)
, the smaller the lower limit
m10
and C
can be adjusted higher by
1
• C
⎞
⎟ C
⎠
C
C
C
. Aside from picking
s
s + 1
O10
m10
m10
V10
is the effective
⎤
⎥
⎥
⎥
⎥
⎦
• R
may also be
• R
O10
C
) is used
O4-7
• R
= 5 •
O4-7
m10
The Input Current Regulation Loop
The feedback signal for the input current regulation loop
is the sense voltage across the input current sense resis-
tor (R
This voltage is amplified by a factor of 20 and compared
to the voltage on the IL pin by the transconductance er-
ror amplifier (A4). This amplifier then 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
The simplified loop transmission is:
where Gmi
input current of the external DC/DC converter.
C
IIMON
L
⎡
⎢
⎢
⎣
R
IC
20R
IL
Figure 20. Simplified Linear Model of the Input Current
Regulation Loop
(
R1+ R2
IS
(s) = g
IN
).
IS
IIMON
IL
IS
(
p
R2
(s) is the transfer function from V
). This loop is shown in detail in Figure 20.
m4
)
CIIMON
C
C
20k
R2
IN
BIAS
⎡
⎢
⎢
⎢
⎢
⎣
IIMON
⎛
⎜
⎝
IN
R
50µA
C
R
IS
s + 1
s + 1
–
g
A8
g
CLN
m8
m10
R1
60k
C
)
1
⎤
⎥
⎥
⎦
= 0.33m
C
I
IN
s
• Gmi
1V
⎞
⎟ C
⎠
g
m4
C
A4
= 0.5m
+
–
–
R
s + 1
p
O4
(s)
⎤
⎥
⎥
⎥
⎥
⎦
LTC4000
•
g
m10
–
+
R
A10
O10
= 0.1m
LTC4000
ITH
ITH
CC
31
4000 F20
to the
4000f
R
C
C
C