Low-Cost Multichemistry Battery Chargers
where R varies with load according to R = V / I
BATT CHG.
L
L
Output zero due to output capacitor ESR:
BATT
1
f
=
GM
OUT
Z _ESR
2πR
× C
OUT
ESR
The loop transfer function is given by:
LTF = GM ×R ×GMV ×R ×
OGMV
R
R
L
ESR
CCV
OUT
L
GMV
C
OUT
1+sC
× R
1+sC × R
(
)(
)
)
OUT
ESR CV CV
1+sC × R
1+sC
)(
× R
L
(
CV
OGMV
OUT
R
CV
R
OGMV
REF
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:
C
CV
GMV × R
× GM
OUT
CV
f
=
CO_CV
Figure 5. CCV Loop Diagram
2πC
OUT
CCV Loop Definitions
Compensation of the CCV loop depends on the para-
meters and components shown in Figure 5. C and
To calculate R and C values of the circuit of Figure 2:
Cells = 4
CV
CV
CV
C
OUT
= 22µF
R
are the CCV loop compensation capacitor and
CV
V
I
= 16.8V
= 2.5A
BATT
CHG
series resistor. R
(ESR) of the charger output capacitor (C
equivalent charger output load, where R = V
CHG
is the equivalent series resistance
ESR
). R is the
L
OUT
/
BATT
GMV = 0.125µA/mV
L
I
. The equivalent output impedance of the GMV
GM
= 3.33A/V
OUT
amplifier, R
≥ 10MΩ. The voltage amplifier
OGMV
R
OGMV
= 10MΩ
transconductance, GMV = 0.125µA/mV. The DC-DC
converter transconductance, GM = 3.33A/V:
f = 400kHz
OUT
Choose crossover frequency to be 1/5th the
MAX1908’s 400kHz switching frequency:
1
GM
=
OUT
A
× RS2
CSI
GMV × R
× GM
OUT
CV
f
=
= 80kHz
CO_CV
2πC
OUT
where A
= 20, and RS2 is the charging current-
CSI
sense resistor in the Typical Application Circuits.
Solving yields R = 26kΩ.
CV
The compensation pole is given by:
Conservatively set R = 1kΩ, which sets the crossover
CV
frequency at:
1
f
=
P _CV
f
= 3kHz
2πR
× C
CV
CO_CV
OGMV
Choose the output-capacitor ESR such that the output-
capacitor zero is 10 times the crossover frequency:
The compensation zero is given by:
1
1
f
=
R
=
= 0.24Ω
Z _CV
ESR
2πR
× C
CV
2π ×10× f
×C
OUT
CV
CO_CV
The output pole is given by:
1
f
=
= 2.412MHz
Z_ESR
2πR
×C
1
ESR
OUT
f
=
P _OUT
2πR × C
L
OUT
20 ______________________________________________________________________________________
MAXIM [ MAXIM INTEGRATED PRODUCTS ]
