Rainbow Electronics MAX8730 - Manual (Page 23)

MAX8730
Low-Cost Battery Charger
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CCS Loop Compensation
The simplified schematic in Figure 8 is sufficient to
describe the operation of the MAX8730 when the input
current-limit loop (CCS) is in control. Since the output
capacitor’s impedance has little effect on the response
of the input current-limit loop, only a single pole is
required to compensate this loop. A
CSS is the internal
gain of the current-sense amplifier, RS1 = 10m
Ω in the
typical application circuits. R OGMS is the equivalent
output impedance of the GMS amplifier, which is
greater than 10M
Ω. GMS is the charge-current amplifier
transconductance = 1µA/mV. GM IN is the DC-DC con-
verter’s input-referred transconductance = GM OUT /D =
2.22A/V/D.
The loop-transfer function is given by:
the loop-transfer function simplifies to:
The crossover frequency is given by:
For stability, choose a crossover frequency lower than
1/10 of the switching frequency:
Values for CCS greater than 10 times the minimum
value may slow down the current-loop response exces-
sively. Figure 9 shows the Bode plot of the input cur-
rent-limit-loop frequency response using the values
calculated above.
C x
GMS
f
x
V
V
CS
OSC
IN MAX
BATT MIN
_
_
= 5
2 π
f
GMS
C
x
V
V
CO CS
CS
IN MAX
BATT MIN
_
_
_
=
2
π
LTF GMS
R
SR C
x RS RS
OGMS
OGMS CS
/
=
+ × 1
1 2
Since GM
A RS
IN
CSS
=
×
1
2
LTF GM A RSI GMS
R
SR C
IN CSS
OGMS
OGMS CS
= Ч Ч Ч
+ Ч 1
FREQUENCY (Hz)
MAGNITUDE (dB)
100k 1k 10
-20
0
20
40
60
100
80
-40
-45
0
-90
0.1
MAG
PHASE
Figure 7. CCI Loop Response
C
CS
R OGMS
GMS
CSS
CLS
CCS
CSSP
RS1
CSSI
GM IN
SYSTEM
LOAD
ADAPTER
INPUT
Figure 8. CCI Loop Diagram
FREQUENCY (Hz)
MAGNITUDE (dB)
100k 10M 1k 10
-20
0
20
40
60
100
80
-40
-45
0
-90
0.1
MAG
PHASE
PHASE (DEGREES)
Figure 9. CCS Loop Response