LTC4000
30
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applicaTions inForMaTion
APPENDIX—THE LOOP TRANSFER FUNCTIONS
When a series resistor (R
C
) and capacitor (C
C
) is used
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:
V
ITH
V
FB
(s)
=
g
m4-7
R
C
–
1
g
m10
C
C
s
+
1
R
O4-7
• C
C
s
where g
m4-7
is the transconductance of error amplifier A4-
A7, typically 0.5mA/V; g
m10
is the output amplifier (A10)
transconductance, R
O4-7
is the output impedance of the
error amplifier, typically 50mΩ; and R
O10
is the effective
output impedance of the output amplifier, typically 10mΩ
with the ITH pin open circuit.
Note this simplification is valid when g
m10
• R
O10
• R
O4-7
• C
C
= A
V10
• R
O4-7
• C
C
is much larger than any other
poles or zeroes in the system. Typically A
V10
• R
O4-7
= 5 •
10
10
with the ITH pin open circuit. The exact value of g
m10
and R
O10
depends on the pull-up current and impedance
connected to the ITH pin respectively.
In most applications, compensation of the loops involves
picking the right values of R
C
and C
C
. Aside from picking
the values of R
C
and C
C
, the value of g
m10
may also be
adjusted. The value of g
m10
can be adjusted higher by
increasing the pull-up current into the ITH pin and its
value can be approximated as:
g
m10
=
I
ITH
+
5µA
50mV
The higher the value of g
m10
, the smaller the lower limit
of the value of R
C
would be. This lower limit is to prevent
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.
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
IS
).
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
IS
). This loop is shown in detail in Figure 20.
The simplified loop transmission is:
L
IC
(s)
=
g
m4
R
C
–
1
g
m10
C
C
s
+
1
C
C
s
•
20R
IS
R2
CIIMON
s
+
1
(
)
R1
+
R2
(
)
C
IIMON
s
+
1
• Gmi
p
(s)
where Gmi
p
(s) is the transfer function from V
ITH
to the
input current of the external DC/DC converter.
Figure 20. Simplified Linear Model of the Input Current
Regulation Loop
IN
CC
1V
A8
g
m8
= 0.33m
A4
g
m4
= 0.5m
A10
g
m10
= 0.1m
ITH
LTC4000
IN
CLN
R
IS
I
IN
IIMON
IL
C
IIMON
C
IN
+
–
–
+
+
–
–
C
C
4000 F20
R
C
R1
60k
R
O4
R
O10
R
IL
R2
20k
50µA
BIAS
