Rainbow Electronics MAX8724 - Manual (Page 20)

MAX1908/MAX8724
CCV Loop Definitions
Compensation of the CCV loop depends on the para-
meters and components shown in Figure 5. C
CV and
R CV are the CCV loop compensation capacitor and
series resistor. R
ESR
is the equivalent series resistance
(ESR) of the charger output capacitor (C OUT ). R L is the
equivalent charger output load, where R L = V BATT /
I
CHG
. The equivalent output impedance of the GMV
amplifier, R OGMV ≥ 10MΩ. The voltage amplifier
transconductance, GMV = 0.125µA/mV. The DC-DC
converter transconductance, GM
OUT = 3.33A/V:
where A CSI = 20, and RS2 is the charging current-
sense resistor in the Typical Application Circuits.
The compensation pole is given by:
The compensation zero is given by:
The output pole is given by:
where R L varies with load according to R L = V BATT / I CHG.
Output zero due to output capacitor ESR:
The loop transfer function is given by:
Assuming the compensation pole is a very low
frequency, and the output zero is a much higher fre-
quency, the crossover frequency is given by:
To calculate R CV and C CV values of the circuit of Figure 2:
Cells = 4
C
OUT
= 22µF
V BATT = 16.8V
I CHG = 2.5A
GMV = 0.125µA/mV
GM
OUT = 3.33A/V
R OGMV = 10MΩ
f = 400kHz
Choose crossover frequency to be 1/5th the
MAX1908’s 400kHz switching frequency:
Solving yields R CV = 26kΩ.
Conservatively set R CV = 1kΩ, which sets the crossover
frequency at:
f CO_CV = 3kHz
Choose the output-capacitor ESR such that the output-
capacitor zero is 10 times the crossover frequency:
f
R C
MHz
Z ESR
ESR OUT
_
. =
×
=
1
2
2 412
π
R
f C
ESR
CO CV OUT
=
Ч Ч Ч
=
1
2 10
0 24
π
_
. Ω
f
GMV R GM
C
kHz
CO CV
CV OUT
OUT
_
=
Ч Ч
=
2
80
π
f
GMV R GM
C
CO CV
CV OUT
OUT
_
=
Ч Ч
2π
LTF GM R GMV R
sC R sC R
sC R sC R
OUT L OGMV
OUT ESR CV CV
CV OGMV OUT L
= Ч Ч Ч Ч
+ Ч
( )
+ Ч
( )
+ Ч ( ) + Ч ( )
1 1
1 1
f
R C
Z ESR
ESR OUT
_
=
×
1
2π
f
R C
P OUT
L OUT
_
=
×
1
2π
f
R C
Z CV
CV CV
_
=
×
1
2π
f
R C
P CV
OGMV CV
_
=
×
1
2π
GM
A RS
OUT
CSI
=
×
1
2
Low-Cost Multichemistry Battery Chargers
20 ______________________________________________________________________________________
GM OUT
BATT
CCV
GMV
REF
R
CV
C
CV
R
OGMV
R ESR R L
C OUT
Figure 5. CCV Loop Diagram