SMBus Level 2 Battery Charger
with Remote Sense
The loop-transfer function is given by:
CCS Loop Compensation
The simplified schematic in Figure 11 is sufficient to
describe the operation of the MAX8731A 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
R
OGMI
× C
LTF = GM
× A
×RS2×GMI
CSI
OUT
1+sR
OGMI
CI
This describes a single-pole system. Since:
1
pole is required to compensate this loop. A
is the
CSS
GM
=
internal gain of the current-sense resistor; RS1 = 10mΩ
OUT
A
×RS2
CSI
in the typical application circuits. R
is the equiva-
OGMS
lent output impedance of the GMS amplifier, which is
the loop-transfer function simplifies to:
greater than 10MΩ. GMS is the charge-current amplifier
transconductance = 1µA/mV. GM is the DC-DC con-
IN
R
OGMI
× C
verter’s input-referred transconductance = (1/D) x
LTF = GMI
1+sR
GM
= (1 / D) x 5A/V.
OGMI
CI
OUT
The loop-transfer function is given by:
The crossover frequency is given by:
GMI
R
OGMS
f
=
LTF = GM × A
× RSI× GMS
CSS
CO_CI
IN
2πC
1+ SR
× C
CS
CI
OGMS
For stability, choose a crossover frequency lower than
1/10 the switching frequency:
Since:
1
GM
=
IN
A
×RS2
CSS
C
> 10 × GMI / (2π f
) = 4nF, for a 400kHz switch-
OSC
CI
the loop-transfer function simplifies to:
ing frequency.
R
OGMS
LTF = GMS
Values for C greater than 10 times the minimum value
CI
1+ SR
× C
CS
OGMS
can slow down the current-loop response. Choosing C
CI
= 10nF yields a crossover frequency of 15.9kHz. Figure
10 shows the Bode plot of the current-loop frequency
response using the values calculated above.
ADAPTER
INPUT
100
80
60
40
20
0
0
MAG
PHASE
CSSP
InputCurrent( )
GMS
CSS
RS1
CSSI
-45
-90
CCS
GM
IN
-20
-40
R
OGMS
C
CS
SYSTEM
LOAD
0.1
10
1k
100k
FREQUENCY (Hz)
Figure 10. CCI Loop Response
Figure 11. CCS Loop Diagram
26 ______________________________________________________________________________________
MAXIM [ MAXIM INTEGRATED PRODUCTS ]
