LTC4000-1 Datasheet, PDF (34/40 Pages) Linear Technology – High Voltage High Current Controller for Battery Charging with Maximum Power Point Control

LTC4000-1
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 19, the
transfer function from the input of A4-A7 to the ITH pin
is simply as follows:
V_ITH
V_FB
(s)
=
g_m
4-7







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 Voltage Regulation Loop
The feedback signal for the input voltage regulation loop
is the voltage on the IFB pin, which is connected to the
center node of the resistor divider between the input
voltage (connected to the IN pin) and GND. This voltage
is compared to an internal reference (1.000V typical) by
the transconductance error 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 output volt-
age observed by the IFB pin. This loop is shown in detail
in Figure 28.
Assuming R_IS << R_IN << (R_IFB1 + R_IFB2), the simplified
loop transmission is as follows:
L_IV (s)
=
g_m4







R_C
–
1
g_m10 
C_Cs
C_Cs
+
1^



•
Gmi_p(s)
•


( ) ^


R_IN
R_IN
C_IN + C_CLN
s
+

1_
•
 RR_IIFFBB2



where Gmi_p(s) is the transfer function from V_ITH to the
input current of the external DC/DC converter, R_IN is the
equivalent output impedance of the input source, and
R_IFB = R_IFB1 + R_IFB2.
R_IS
IN
DC/DC INPUT
C_IN
C_CLN
(OPTIONAL)
IN
CLN
R_IFB1
IFB
R_IFB2
A4
g_m4 = 0.5m
–
1V +
R_O4
LTC4000-1
CC
A10
g_m10 = 0.1m
–
ITH
+
R_O10
C_C
R_C
TO DC/DC
40001 F28
Figure 28. Simplified Linear Model of the Input Voltage
Regulation Loop
40001f
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