LTC4000_15 Datasheet, PDF (30/40 Pages) Linear Technology – High Voltage High Current Controller for Battery Charging and Power Management

LTC4000
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
R_O4-7 •


C_Cs
C_Cs
+
1^





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 •
10¹⁰ 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






 ^RC
–
1^
g_m10 
C_Cs
C_Cs
+

1_



•


( ) ^


20R_IS
(R1+
R2_CIIMONs + 1
R2)C_IIMONs + 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.
R_IS
IN
I_IN
C_IN
C_IIMON
R_IL
IN
CLN
LTC4000
A8
R2
IIMON ^20k
g_m8 = 0.33m
A4
CC
BIAS
50µA
g_m4 = 0.5m
R1
60k
+
–
A10
g_m10 = 0.1m
–
ITH
C_C
R_C
1V –
+
IL
R_O4
R_O10
4000 F20
Figure 20. Simplified Linear Model of the Input Current
Regulation Loop
30
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